No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Numerical investigation of thermo-bioconvection in a suspension of gravitactic microorganisms
Abstract
This paper investigates the effect of heating or cooling from below on the development of gravitactic bioconvection in a square enclosure with stress free sidewalls. The governing equations are the Navier–Stokes equations with the Boussinesq approximation, the diffusion equation for the motile microorganism and the energy equation for the temperature. The control volume method is used to solve numerically the complete set of governing equations. It was found that the suspension is destabilized by heating from below and stabilized by cooling from below. A transition from a subcritical bifurcation to a supercritical bifurcation was observed in the case of heating from below when the thermal Rayleigh number was increased.
... In addition, the relationship between the Rayleigh and the gyrotactic numbers was found. Alloui et al. [6] investigated the effect of heating or cooling from below, of a square enclosure, on the development of gravitactic bioconvection. Here, the influence of thermoeffects on a bifurcation diagram and the flow structure were presented, reporting that the heating from below destabilizes the suspension and cooling from below stabilizes it. ...
... The numerical code was validated by comparing one case reported by Alloui et al. [6] for Ra = 10 3 , Ra T = 4 × 10 3 , Pe = Sc = Le = 1 and A = 1. The results presented in Figure 2 reproduce quantitatively and qualitatively the same iso-patterns of ψ, n, and θ, which represent dimensionless streamlines, microorganism concentration and temperature contours, respectively. ...
... The temperature contours are deformed by the swimming of the microorganisms. According to the results reported by Alloui et al. [6], the microorganisms have a uniform distribution preferentially on the right side. This behaviour can be seen in Figure 4. Case 3: the heat source is located in the left half of the upper wall of the cavity, (see Figure 2). ...
In this work, the dynamics of the bioconvection process of gravitactic microorganisms enclosed in a rectangular cavity, is analyzed. The dimensionless cell and energy conservation equations are coupled with the vorticity-stream function formulation. Then, the effects of the bioconvection Rayleigh number and the heating source on the dynamics of microorganisms are discussed. The results based in streamlines, concentration and temperature contours are obtained through numerical simulations considering eight different configurations of symmetrical and asymmetrical heat sources. It is concluded that microorganisms accumulate in the warmer regions and swim through the cooler regions to reach the surface. They form cells for each heat source, but at high concentrations, they form a single stable cell. The results presented here can be applied to control and to understand the dynamics of microorganisms with discrete heat sources.
... He obtained a relation between thermal Rayleigh number and bio-convection Rayleigh number. Alloui et al. [12] explored the impacts of cooling and heating from below on gravitactic bio-convection inside a square cavity. They focused on critical Rayleigh numbers in their numerical analysis and demonstrated that transition from subcritical to supercritical bifurcation occurs in the case of augmenting the thermal Rayleigh number from zero to 1708. ...
... The above solutions are then added to the equations (8)- (12) and then solved by the Newton Raphson method. ...
The paper reports the natural thermo-bio-convection of gyrotactic microorganisms in a square cavity with two smaller square heat sources inside the cavity. The flow is assumed to be two-dimensional, steady, buoyancy-driven, and Newtonian. The work investigates the influences of thermal Rayleigh number, bio-convection Rayleigh number, Lewis number, and Peclet number on the natural convection heat transfer, entropy generation, and micro-organism concentration. The governing equations are discreted by finite element method. The diffusion equation is used for the motion of microorganisms, and the energy equation is considered for the effects of temperature. The main finding of this study is that both thermal and bio-convection Rayleigh number improve thermo-bio-convection performance of gyrotactic microorganisms in a square cavity with two square heaters inside the cavity. For high thermal Rayleigh numbers (Rat = 105), increasing Rab from 10 to 100 causes 4.5% enhancement in average Nusselt number and average Sherwood number decreases by 4.5%. These findings are applicable in various fields of expertise such as ocean ecosystems, oil recovery and fuel cells.
... The bio-convection macroscopically means the convective motion of a fluid that is subjected to the generated gradient of density through plural swimming and also movement of microorganisms [31][32][33][34]. The self-impelled motile microorganisms boost the density of host fluid in a specific orientation so that results in the bio-convection flow. ...
... The self-impelled motile microorganisms boost the density of host fluid in a specific orientation so that results in the bio-convection flow. In general, it can be said that the microorganisms swimming is a reaction to the external force field, for instance, gravity or biochemical stimulus such as oxygen concentration gradient [34]. Nanoparticles are not self-impelled, quite contradictory to motile microorganisms, and their movement is the result of the effects of Brownian movement and thermophoresis in nanofluid. ...
The present paper has conducted the numerical analysis of a nanofluid consisting of microorganisms on the isothermal linear stretching sheet. The problem has been modeled under the influences of partial slip and heat absorption/generation at the sheet surface. The governing equations are converted to ordinary differential equations through a series of similarity transformations. Using a finite difference method, the resulting equations are discretized, and also they are linearized by applying the linearization technique of Newton. Results of temperature, velocity, concentration of nanoparticles, motile microorganisms' density and also coefficient of reduced skin friction, reduced Nu, reduced Shr, and reduced density numbers of the microorganisms are graphically demonstrated and a detailed description is given. The microorganisms dimensionless density increases as d increase, while decreases with increasing the values of Pe, Lb, Gr and O. Also, boundary layer thickness for motile microorganisms declines by increasing Lb and O. Finally, when the rates of heat generation(λ > 0) and absorbsion (λ < 0) increase, the microorganisms density increases and decreases, respectively.
... After that, Alloui et al. [24] studied the gravitactic behavior of microorganisms and found that as the swimming speed of microorganism's increases the value of the critical wave number is also increasing. Alloui and his co-author [25] carried out a numerical simulation and studied the development of bioconvection pattern in a rectangular enclosure. They gave an elegant analytical solution which shows that cooling from below stabilizes the system and heating from below destabilizes the system. ...
... From the above literature review and as far as the author's best knowledge, there is yet no analytical and numerically study of non-linear stability analysis of bio-thermal convection containing gravitactic microorganisms. All the researchers reported so far (Kuznetsov [20], Alloui et al. [23,25]) are considered only the linear stability analysis, whereas, in this article, we studied both linear and nonlinear stability analysis of bio-thermal convection containing gravitactic microorganisms in a fluid layer. The mathematical model is solved numerically for both linear and nonlinear stability analysis. ...
The bio-thermal convection in a suspension containing gravitactic microorganisms saturated by a fluid is investigated within the framework of linear and nonlinear stability theory. Energy method is used for nonlinear stability analysis. Effect of Péclet number (swimming speed of microorganisms) and bioconvection Rayleigh number (concentration of microorganisms) on the stability of the system is analyzed numerically by using the Galerkin weighted residual method. The subcritical region of instability for faster swimmers is large as compared to slowly swimmers. Bioconvection Rayleigh number destabilizes the onset of bio- thermal convection and this effect is more predominant for high speed of microorganisms. The Péclet number, bioconvection Rayleigh number increase the size of cell.
... The cooling or heating of bioconvection in a horizontal part of fluid with microorganisms by Nield and Kuznetsov [10]. Alloui et al. [11] studied the thermo-bioconvection in a suspension of gyrotactic microorganisms numerically. Xu and Pop [12] examined the combined bioconvection flow in a horizontal channel that contains nanofluid which include nanoparticles and gyrotactic microorganisms. ...
The effect of Joule heating is examined on fully developed mixed biocon-vection nanofluid flow with microorganisms in a horizontal channel in the presence of uniform external magnetic field. The passively controlled nanofluid model is used to model the flow problem. The governing partial differential equations are transformed into ordinary differential equations by using suitable similarity transformations. They are solved by using homotopy analysis method (HAM). The results are discussed for different combinations of pertinent parameters.
... They have considered the flow under a low Reynolds number with long wavelength approximation. According to [29][30][31][32][33], bioconvection is a macroscopic fluid motion triggered by a density difference brought on by a population of motile microorganisms swimming together. Selfpropelled motile microorganisms enhance the base fluid density in a particular direction to create the bioconvection flow. ...
This study investigates 2D bioconvection magneto-hydrodynamic (MHD) flow and heat transfer of the non-Newtonian (Casson) nanofluid model. The phenomenon of Brownian motion and thermophoresis containing gyrotactic microorganisms over a nonlinear surface is demonstrated pictorially under the simultaneous impact of thermal radiation and velocity slip. Herein, the flow is electrically conducting where different cases and the effect of convergence parameters such as chemical reactions and heat generation/absorption are studied. The transformed ODEs are tackled numerically by employing the Bvp4c scheme. This method contains three-stage Lobatto IIIa collocation formula that provides continuous solutions up to fifth-order accuracy. The salient features of relevant flow parameters are illustrated through tables and graphs, and the current results are compared with the previous ones, which claim considerable agreement. The main finding reveals an increase in the thermophoresis parameter (Nt) and radiation (R) parameters, uprising the temperature profile which leads to enhancement in the thermal boundary layer. Also, the impact of the magnetic parameter (M) shows decrement in the velocity profile because there exists a Lorentz force that suppresses fluid motion. The friction factor and local Nusselt number decrease for higher values of the Casson parameter (β), whereas increment is illustrated for the suction parameter (S).
... Song and Khan et al. [20][21][22] studied bioconvection analysis for Sutterby nanofluid over an axially stretched cylinder and configured by a rotating disk. Alloui et al. [23] examined the effect of bottom heating/cooling on the stability of bioconvection. Mansour et al. [24] inspected magnetohydrodynamic (MHD) mixed bioconvection in the presence of inclined external magnetic field. ...
In this article, we investigate the bioconvection in an inclined cavity comprising oxytactic microorganisms and nanofluid in the presence of Soret and Dufour in the porous medium. The governed nonlinear partial differential equations (PDE) of the model are reduced to a system of non-dimensional PDE. Further, a modified set of non-dimensional PDE with dimensionless parameters and boundary conditions are solved using the finite element method. The effects of relevant quantities on the streamlines, temperature gradient, iso-concentration of solute, nanoparticles and microorganisms concentration are examined in detail. The main conclusion is that the average Nusselt number and average Sherwood numbers of oxygen concentration and microorganisms are boosted with the inclination angle (ω=0∘−90∘).
... PI technique helps to improve any process in terms of energy efficiency, cost-effectiveness, compactness, safety, and sustainable energy productivity [1,2]. Such process intensification is influenced by the bioconvective flow containing nanoparticles and motile microorganisms (like bacteria and algae) [3]. The term 'bioconvection' corresponds to macroscopic convective motion, which is caused by the interactive responses of different stimuli (which is termed as taxes). ...
In many industries as well as medical science, process intensification dealing with proper mixing is dictated by the thermo-fluidic transport process, and mass transfer rate. Modeling as well as controlling such a device/system comprising multiphysical consequences and multifaceted geometries is a rather challenging task. In this exercise, an effort has been taken to explore the bioconvective heat and mass transfer phenomena of Cu-water nanofluid with the suspension of motile oxytactic microorganisms in a complex wavy porous enclosure heated at the left and cooled at the right imposing the magnetic field. The resulting mathematical model is converted into nonlinear partial differential equations (PDEs), which are then solved with a developed, validated computing code based on the finite volume-based technique. The investigation is conducted for various emerging parameters such as bioconvective Rayleigh number (Rb), Darcy number (Da), Darcy-Rayleigh number (Ra), Hartmann number (Ha), Peclet number (Pe), Lewis number (Le), oxygen diffusion ratio (χ), undulation numbers (n). This work focuses on the in-depth concept of flow-physics in the bioconvection environment by the wavy heated wall in a porous environment with the applied magnetic field. The various emerging parameters severely affect undergoing the thermo-magneto-bioconvective process, and reveal critical roles in the heat and mass transport dynamics. An undulation in the wavy wall raises bioconvection, heat, and mass transfer effects. The bioconvection effect is more at a low convection regime. It also showed that higher the bioconvection and mass transfer rate corresponds to lower heat transfer. It is worth remarking here that bioconvection always favors heat and mass transfer. The present investigation showed the extent of controllability of nano-bioconvective heat and mass transport phenomena. This concept and findings could be useful in the design of nano-bio-fuel cells and similar devices in sustainable and cleaner energy production.
... The self-driving mobile microorganisms desire to increase the volume of base fluid in the system by producing a bioconvective stream in one direction, according to Refs. [25][26][27][28][29] . Chemical or oxytactical properties, gyrotactic traits, and negative gravitational characteristics are used to classify motile microorganism A bottom-heavy microbe with gyrotaxis is the most frequent. ...
This paper investigates the influence of dispersion impact on mixed convection flow over a horizontal cone within a non-Darcy porous medium. Multiple convective boundary conditions are applied to address the heat, mass and motile microorganism transfer phenomena. This paper incorporates the dispersion effect for gyrotactic microorganisms due to biological and environmental applications. By imposing appropriate similarity transformations, the nonlinear partial differential equations governing flow, temperature, concentration, and microbe fields are reduced to a system of ordinary differential equations & then solved using the MATLAB BVP4C function. The computation of grid independence test is analyzed for different flow profiles to show the precision of the points. In a few instances, our present numerical data is compared with previously published works, leading to excellent agreement. The non-Darcy effect, as well as mixed convection values from 0.1 to 0.9 and buoyancy parameters from 0.2 to 0.8, all significantly affects the velocity profile. The reduction in the microorganism profile is brought on by the increase in the bioconvection Lewis parameter and bio convection peclet number between 0.3 and 1. In the absence of dispersion, the variation of Biot numbers between 0.5 and 2, favor heat, mass, and motile microorganism transfer the most in the range of mixed convection parameter 0.5 to pure forced convection 1. Thermal, solutal and microorganism dispersion coefficients a, b, c that lie between 17 and 13 and higher values of modified peclet number ranges from 2 to 10 cause increased dispersion effects which lower flow transfer rates mostly in forced convection regime.
... Motile microorganisms are heavier than their encompassing liquid and usually swim in the upward direction, which brings about producing different flow profiles into the system, as described briefly in Refs. [40][41][42][43][44][45][46] . The advantages of adding motile microorganisms to the suspension include improved mass transfer and microscale mixing. ...
The steady mixed convection flow towards an isothermal permeable vertical cylinder nested in a fluid-saturated porous medium is studied. The Darcy model is applied to observe bioconvection through porous media. The suspension of gyrotactic microorganisms is considered for various applications in bioconvection. Appropriate similarity variables are opted to attain the dimensionless form of governing equations. The resulting momentum, energy, concentration, and motile microorganism density equations are then solved numerically. The resulting dual solutions are graphically visualized and physically analyzed. The results indicate that depending on the systems' parameters, dual solutions exist in opposing flow beyond a critical point where both solutions are connected. Our results were also compared with existing literature.
... Since motile microorganisms are denser than the liquid they are surrounded by, they swim upwards, resulting in different flow profiles in the system according to Refs. [16][17][18][19][20]. Gyrotaxis is most commonly found in a bottom-heavy microorganism. ...
The problem of steady laminar mixed convection boundary layer flow along vertical thin needle with variable surface heat, mass and motile microorganism flux in the presence of gyrotactic microorganism is considered in this study. The dimensionless leading equations of continuity, momentum, concentraton and motile microorganism conservation are reduced to ordinary differential equations with the help of similarity transformations. The transformed governing equations are then numerically solved by using MATLAB BVP4C function. The research is reached to excellent argument by comparison in few cases between the results obtained from MATLAB and Maple algorithm with the help of dsolve command. Numerical calculations are carried out for various values of the dimensionless parameters of the problem which includes mixed convection parameter λ, power law index m, buoyancy parameters N 1 , N 2 Lewis parameter Le, bioconvection lewis parameter Lb, Bioconvection peclet number Pe and also the parameter a representing the needle size. It is also shown from the results that the surface (wall) temperature, surface fluid concentration, surface motile microorganism concentration and the corresponding velocity, temperature, concentration and motile microorganism profiles are significantly induced by these parameters. The results are pictured and discussed in detail.
... The effects of bio thermal convection in a suspension of gyrotactic microorganism in boundary layer flows were Corresponding author, Ph.D., E-mail: raakeshnitharwal@gmail.com studied by Nield and Kuzentsov (2006). Alloui et al. (2007) did numerical study of thermo bioconvection in a suspension of gravitactic microorganisms. Kuzentsov (2010,2011) described the nanofluid bioconvection in a suspension containing both gyrotactic and oxytactic microorganism with nanoparticles in a water-based fluid. ...
The paper presents the effects of temperature jump and concentration slip on inclined MHD bioconvection past a
vertical porous plate via porous media. The authors have examined how the presence of both nanoparticles and gyrotactic
microorganism impact the whole procedure. It is researched that the numerical scheme, called Runge-Kutta fourth fifth order
Fehlberg method (RKF45) has been used to solve the governing partial differential equations. The equations are reduced into
ordinary differential equations by using suitable similarity transformation. The effects of pertinent parameter for variation in the
velocity profile, velocity profile at far field, temperature profile, concentration profile and motile microorganism density profile
have been obtained. The results obtained from current study in the concluding part of the paper match to the pre researched data
which validate the authenticity of the study.
... Pedley et al. [4] initiated the use of the bioconvection term concerning microscopic convection due to motile microorganisms. A numerical solution of thermo-bioconvection suspended due to gyrotactic microorganisms was carried by Alloui et al. [5]. Khan et al. [6] investigated the combined effect on boundary layer flow with heat and mass exchange of waterbased nanofluid mixed with gyrotactic microorganisms in presence of magnetic field and Navier slip. ...
A study related to bioconvection of magnetohydrodynamic boundary layer flow, heat and mass exchange of Casson fluid containing gyrotactic microorganisms above a linearly stretching surface is considered. The Partial differential equations which govern the physical situation are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformations. Taylor’s series solution for momentum, energy, the diffusive concentration of nanofluid, and concentration of microorganism’s equations are obtained using the differential transform method and compared with numerical solutions. The effects of a range of non-dimensional parameters on bioconvection fluid flow and heat transfer are analyzed through graphs.
... In fluid dynamics, bioconvection [1][2][3] occurs when microorganisms, which are denser than water, swim upwards. The upper surface of the fluid becomes thicker due to the assemblage of microorganisms. ...
The double-diffusive tangent hyperbolic nanofluid containing motile gyrotactic microorganisms and magnetohydrodynamics past a stretching sheet is examined. By adopting the scaling group of transformation, the governing equations of motion are transformed into a system of nonlinear ordinary differential equations. The Keller box scheme, a finite difference method, has been employed for the solution of the nonlinear ordinary differential equations. The behaviour of the working fluid against various parameters of physical nature has been analyzed through graphs and tables. The behaviour of different physical quantities of interest such as heat transfer rate, density of the motile gyrotactic microorganisms and mass transfer rate is also discussed in the form of tables and graphs. It is found that the modified Dufour parameter has an increasing effect on the temperature profile. The solute profile is observed to decay as a result of an augmentation in the nanofluid Lewis number.
... Bioconvection systems have been studied depending on the mechanism of directional motion and these phenomena have been proposed in the literature by previous studies. [28][29][30][31][32][33][34][35] They focused on nanofluid comprising gyrotactic microorganisms and reaffirmed that the subsequent large-scale velocity of fluid caused by self-propelled motile microorganisms. ...
This article, describes two-dimensional magnetohydrodynamic steady incompressible viscous power law nanofluid comprising gyrotactic microorganisms adjacent to a vertical stretching sheet. The governing non-linear partial differential equations are lessened to a set of non-linear ordinary differential equation using similitude transformation. The non-dimensional boundary value problem is then solved under spectral relaxation method. The influences of different parameters such as buoyancy convection parameters [Formula: see text], magnetic field parameter M, power law parameter [Formula: see text], Prandtl number [Formula: see text], modified Prandtl number [Formula: see text], thermophoresis parameter [Formula: see text], Peclet number [Formula: see text], Lewis number [Formula: see text], Brownian motion parameter [Formula: see text], bioconvection Lewis number [Formula: see text], and bioconvection constant [Formula: see text] on flow convective characteristics phenomena are explored via plots and tables. The skin friction factor, rate of heat transfer, rate of mass transfer, and the density number of the motile microorganisms near the surface are also computed. Our results are compared with the existing results to support our model. Residual error analysis is determined for showing the convergence rate against iteration. Our result showed that the momentum thickness reduces as the value of [Formula: see text] induces and thermal boundary thickness increases as the value of [Formula: see text] induces. We also revealed that the density of the motile microorganisms [Formula: see text] is a reducing function of [Formula: see text] and concentration boundary layer induces with the increase of [Formula: see text], whereas its thickness close to the surface decreases with increasing of [Formula: see text]. Also, the stream line patterns are exhibited to the impact of physical sundry variables.
... They analyzed that the density of motile microorganisms decreases by augmenting the values of bio convection Schmidt and Peclet numbers. For the interest of readers, some other studies on gyrotactic microorganism are mentioned in [34,35]. ...
... Avraemnko [25] has studied gyrotactic microorganisms over a porous layer. Alloui et al. [26] have studied heat transfer effects on bioconvection suspension of gyrotactic microorganisms. Mahdy [27] has explored mixed convection nanofluid flow across an isothermal wedge. ...
This work consists of a theoretical boundary layer analysis of heat and mass transport in a viscous fluid-embracing gyrotactic micro-organism over a cylinder. The flow governing equations are modeled through boundary layer approximations. The governing non-linear partial differential equations are lessened to a set of nonlinear ordinary differential equations using similitude transformation. The boundary layer equations are elucidated numerically, applying the spectral relaxation method with the aid of the computational software MATLAB. The impact of several pertinent parameters on flow convective characteristic phenomena are explored through the use of graphs and tables and are discussed with in-depth physical descriptions. In addition, the friction factor, the rate of heat transfer, rate of mass transfer, and the density number of the motile microorganism are also presented with respect to the above controlled parameters. It is noticed that for the increasing values of the magnetic parameter with reductions and enhancements, the density of the motile microorganism is a declining function of, and the concentration field enhances with the strengthening of, whereas it reduces with the rise of. Furthermore, the streamline patters are emphasized for the impact of controlled flow variables. Current outcomes are compared with the available results from previous cases and are observed to be in agreement.
... They analyzed that the density of motile microorganisms decreases by augmenting the values of bio convection Schmidt and Peclet numbers. For the interest of readers, some other studies on gyrotactic microorganism are mentioned in [34,35]. ...
This communication addresses the entropy analysis of 3D flow of Maxwell nanofluid containing gyrotactic microorganism in the presence of homogeneous-heterogeneous reactions with improved heat conduction and mass diffusion models over a stretched surface. Improved models are presented by utilizing Cattaneo-Christov heat flux and generalized Fick's law. Governing equations which represents the given flow situation are modeled in the form of PDEs by applying boundary layer analysis, then suitable makeovers are engaged to transform prevailing PDEs into a set of transformed ODEs that are solved using optimal homotopy analysis process as a computational toolbox in Mathematica. Special cases of some published work are found to be in excellent agreement of our work. The impact of physical parameters on velocity, temperature, concentration, reaction rate, concentration of motile microorganism, and entropy generation are discussed graphically. Finally, the convergence of homotopic solution is presented in tabular form which confirms the reliability of proposed scheme. It is reported that entropy generation increases for higher values of radiation parameter and Brinkman number, whereas Bejan number is reduced for the higher values of radiation and magnetic parameters. Also, fluid temperature and concentration fields are reduced by augmented values of Prandtl and Schmidt numbers.
... Bé g et al. [17] considered the problem of natural convection magnetomicropolar biopolymer flow over a horizontal circular cylinder. Alloui et al. [18] analyzed the influence of heating/cooling from bottom on the stability of a suspension of motile gravitactic microorganisms in a shallow fluid layer. Alloui et al. [19] have also examined the impact of heating/cooling from below on the evolution of gravitactic bioconvection in a square cavity. ...
... The water based fluid consisting motile gyrotactic organisms studied numerically in Refs. [27][28][29]. The micro-organism which is self-impellent can improve the fluid density in a specific direction, which can cause bio-convection flow. ...
This research deals with Burgers nanofluid flow between two parallel and horizontal plates in the presence of gyrotactic microorganisms and under the impact of thermal radiation. The nanofluid flow is assumed in a steady state and medium between the plates is kept porous. The effects of the heat generation/absorption and nanoparticles on the flow are considered. The significant influences of Brownian motion and thermophores is have been taken in Nano-fluids model. The governing nonlinear PDEs of Burgers nanofluid relation are rendered into nonlinear ODEs using appropriate transformations and elucidated by the HAM (Homotopy analysis method). HAM is used to achieve the required goal. The convergence of the HAM technique is illustrated numerically. The features of the dimensionless velocity, temperature, concentration and nanoparticle motile microorganisms density with numerous thermo-physical, non-dimensional parameters are graphed and detailed investigation of these parameters are conducted. The current research specifies that the temperature profile of the nanofluid enhances for the augmented values of Brownian motion and thermophoresis parameters. Graphs for the local Nusselt number, Sherwood numbers and local density number of motile microorganisms are computed and analyzed. Moreover, the influence of various embedded parameters are shown and studied graphically in detail. Finally, we find some final key interpretations in the light of this research work.
... The water based fluid consisting motile gyrotactic organisms studied numerically in Refs. [27][28][29]. The micro-organism which is self-impellent can improve the fluid density in a specific direction, which can cause bio-convection flow. ...
This research deals with Burgers nanofluid flow between two parallel and horizontal plates in the presence of gyrotactic microorganisms and under the impact of thermal radiation. The nanofluid flow is assumed in a steady state and medium between the plates is kept porous. The effects of the heat generation/absorption and nanoparticles on the flow are considered. The significant influences of Brownian motion and thermophores is have been taken in Nano-fluids model. The governing nonlinear PDEs of Burgers nanofluid relation are rendered into nonlinear ODEs using appropriate transformations and elucidated by the HAM (Homotopy analysis method). HAM is used to achieve the required goal. The convergence of the HAM technique is illustrated numerically. The features of the dimensionless velocity, temperature, concentration and nanoparticle motile microorganisms density with numerous thermo-physical, non-dimensional parameters are graphed and detailed investigation of these parameters are conducted. The current research specifies that the temperature profile of the nanofluid enhances for the augmented values of Brownian motion and thermophoresis parameters. Graphs for the local Nusselt number, Sherwood numbers and local density number of motile microorganisms are computed and analyzed. Moreover, the influence of various embedded parameters are shown and studied graphically in detail. Finally, we find some final key interpretations in the light of this research work.
... The water based fluid consisting motile gyrotactic organisms studied numerically in Refs. [27][28][29]. The micro-organism which is self-impellent can improve the fluid density in a specific direction, which can cause bio-convection flow. ...
This research deals with Burgers nanofluid flow between two parallel and horizontal plates in the presence of gyrotactic microorganisms and under the impact of thermal radiation. The nanofluid flow is assumed in a steady state and medium between the plates is kept porous. The effects of the heat generation/absorption and nanoparticles on the flow are considered. The significant influences of Brownian motion and thermophores is have been taken in Nano-fluids model. The governing nonlinear PDEs of Burgers nanofluid relation are rendered into nonlinear ODEs using appropriate transformations and elucidated by the HAM (Homotopy analysis method). HAM is used to achieve the required goal. The convergence of the HAM technique is illustrated numerically. The features of the dimensionless velocity, temperature, concentration and nanoparticle motile microorganisms density with numerous thermo-physical, non-dimensional parameters are graphed and detailed investigation of these parameters are conducted. The current research specifies that the temperature profile of the nanofluid enhances for the augmented values of Brownian motion and thermophoresis parameters. Graphs for the local Nusselt number, Sherwood numbers and local density number of motile microorganisms are computed and analyzed. Moreover, the influence of various embedded parameters are shown and studied graphically in detail. Finally, we find some final key interpretations in the light of this research work.
... Uddin et al. studied the computational investigation of Stefan blowing and multipleslip effects on buoyancy-driven bioconvection nanofluid flow with microorganisms [37] and numerical solutions for gyrotactic bioconvection in nanofluid saturated porous media with Stefan blowing and multiple slip effects [38]. Different types of microorganisms, theoretical biconvection models, have been studied [39][40][41][42][43][44][45][46][47][48][49][50][51]. ...
This paper discusses the three-dimensional flow of the gyrotactic bioconvection of an Oldroyd-B nanofluid over a stretching surface. Theory of microorganisms is utilized to stabilize the suspended nanoparticles through bioconvection induced by the effects of buoyancy forces. Analytic solution for the governing nonlinear equations is obtained by using homotopy analysis method (HAM). The effects of involved parameters on velocity, temperature, nanoparticles concentration, and density of motile microorganisms are discussed graphically. The local Nusselt, Sherwood, and motile microorganisms numbers are also analyzed graphically. Several known results have been pointed out as the particular cases of the present analysis. It is found that the non-Newtonian fluid parameters, i.e., relaxation time parameter β1 and retardation time parameter β2 , have opposite effects on the velocity profile. The velocity of the fluid and boundary layer thickness decreases for increasing relaxation time while it decreases for increasing retardation time effects.
... Different types of micro-organisms, theoretical bio-convection models have been studied. [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56] In this paper we will consider the three-dimensional bioconvection flow of Maxwell nanofluid over a bi-directional stretching surface. The combined effects of MHD and heat source/sink are also analyzed. ...
This paper discusses the three-dimensional flow of Maxwell nanofluid containing
gyrotactic micro-organisms over a stretching surface. The effects of magnetic field
and heat source/sink are also considered. Theory of microorganisms is utilized to
stabilize the suspended nanoparticles through bioconvection induced by the effects
of buoyancy forces. HAM (homotopy analysis method) is used to acquire analytic
solution for the governing nonlinear equations. The effects of Deborah number, Hartmann
number, mixed convection parameter, buoyancy ratio parameter, bioconvection
Rayeigh number, stretching ratio parameter, brownian diffusion and thermophoresis
diffusion parameters, Prandtl number, Lewis number, micro-organisms concentration
difference parameter, bioconvection Peclet number and the bioconvection Lewis
number on velocity, temperature, density of motile microorganisms and nanoparticle
concentration are discussed graphically. The local Nusselt, Sherwood and motile
micro-organisms numbers are also analyzed graphically. The reduction of the boundary
layer thickness and velocity due to magnetic field is noted. The heat source/sink
parameter have opposite effects on the temperature profile. We found that In comparison
to the case of heat sink the thermal boundary layer thickness and temperature
increases in the case of heat source.
... Kuznetsov has studied the sta- bility of the gyrotactic micro-organisms in a suspension heated form below, and showed the interaction between bioconvection and nature convection by using a linear stability analysis manner [12]. Bilgen and his coauthors investigated the effect of heating or cooling on the development of gravitactic bioconvection in ver- tical cylinders with stress free sidewalls [13,14], they observed the transition from a subcritical bifurcation to a supercritical bifurca- tion when the thermal Rayleigh number was increased. Nield and Kuznetsov [15] presented a linear stability analysis of a sus- pension of gyrotactic microorganisms in fluid layer of finite depth, and pointed out the cooling from below stabilizes the suspension. ...
... [26][27][28][29] Bio-convection can be defined as the macroscopic fluid motion due to the density gradient which is resulting from communal swimming of motile microorganism. [30][31][32] In the bio-convection flow, the selfimpelled motile microorganism enhances the density of the base fluid in a specific direction. In general, the motile microorganisms are of three types namely: gyrotactic microorganism, negative gravitaxis, and oxytactic microorganism. ...
A computational simulation of two-dimensional magnetic-Carreau fluid in a suspension of gyrotactic microorganisms past a slendering sheet with variable thickness is investigated for slenderness parameters varied in the range of –0.2 to 1.0. Owing to the noticeable implication in various engineering applications, the effects of multiple slip is considered in the present simulation along with the Soret and the Dufour effects for the heat and mass transfer controlling process. The numerical values of the velocity, temperature, concentration, and the density of the motile organisms are computed by the robust Runge–Kutta-based Newton’s scheme. The thermal and concentration boundary layer are changed with the increase in the multiple slip parameters such as velocity slip, temperature slip, concentration slip, and diffusion slip parameters. With the rise in the Carreau fluid power index parameter, the velocity field increases while it declines with the velocity slip and magnetic field parameter. The increasing values of velocity slip, Dufour number, Soret number, and magnetic parameter boost up the density of the motile organism profiles for different slenderness parameter considered in the present study. The effect of the nondimensional factors on the skin friction, local Nusselt, local Sherwood, and the density numbers of the motile organisms are discussed with the assistance of the table for three different slenderness parameters. It is found that multiple slip parameters enable to control the heat and mass transfer rate. Finally, both the qualitative and quantitative comparisons of the present results with previous study are presented in the tabular form and are found to be in excellent agreement.
... The collective swimming of motile micro-organisms [1][2][3][4] yields the density gradient as a result the macroscopic fluid motion occurs and termed as bioconvection. To enhance the density of base fluid in specific direction so that the bioconvection flow is attained the self impelled motile micro-organisms is required. ...
The current pagination summarized the influence of bio-convection Schmidt number, bio-convection Peclet number and micro-organisms concentration difference parameter on the density of motile gyrotactic micro-organisms when they have interaction with the thermally stratified magneto-nanofluid flow past a vertical stretching surface. It is observed that the density of motile microorganisms is the decreasing function of the bio-convection Schmidt and Peclet numbers. It is trusted that the outcomes of present analysis will serve as a helping source for the upcoming developments regarding individualities of motile gyrotactic micro-organisms subject to boundary layer flows induced by stretching surfaces. Keywords: Motile gyrotactic micro-organisms, Temperature stratification, Viscous nanofluid, Vertical surface, MHD, Shooting method
... These microorganisms show different responses towards the stimulators, thus creating different bio-convection systems. Comprehensive studies discussing responses of different microorganisms towards external agents (light, magnetic field, oxygen etc.) are disclosed in [33][34][35][36][37][38][39][40][41][42][43][44][45][46] . ...
A numerical investigation of steady three dimensional nanofluid flow carrying effects of gyrotactic microorganism with anisotropic slip condition along a moving plate near a stagnation point is conducted. Additionally, influences of Arrhenius activation energy, joule heating accompanying binary chemical reaction and viscous dissipation are also taken into account. A system of nonlinear differential equations obtained from boundary layer partial differential equations is found by utilization of apposite transformations. RK fourth and fifth order technique of Maple software is engaged to acquire the solution of the mathematical model governing the presented fluid flow. A Comparison with previously done study is also made and a good agreement is achieved with existing results; hence reliable results are being presented. Evaluations are carried out for involved parameters graphically against velocity, temperature, concentration fields, microorganism distribution, density number, local Nusselt and Sherwood numbers. It is detected that microorganism distribution exhibit diminishing behavior for rising values of bio-convection Lewis and Peclet numbers.
... Bio-convection generated due to such responses has vast importance in bio-microsystems, biotechnology and enzyme biosensors, etc. Specifically this swimming property is useful to purify cultures, separation of fast swimming species from the slow swimmers and separation of living and dead cells. Related information on this topic can be seen by the developments [1][2][3][4][5][6][7][8][9][10][11] and many studies therein. ...
Here we have numerically examined the effects of EMHD in flow of nanofluid past a porous Riga surface with gyrotactic microorganism and nanoparticles. Modeling is presented via Grinberg term and a Lorentz force parallel to the wall of a Riga plate. The fluid is electrically conducting, and the Lorentz force decreases exponentially. Using shooting method, the obtained governing nonlinear coupled ODEs are solved. Physical impact of all the pertinent parameters are examined using graphs and tables. In particular, we discussed the behavior of temperature, velocity, motile microorganism density and nanoparticle concentration profile. Nusselt and Sherwood numbers are examined with the help of tables. This analysis motivates the recent researchers, and it provides a platform for further study on nanofluid flow with gyrotactic microorganism past a Riga plate. A comparison is also presented with previously published results as a special case of our study.
... The swimming properties are determined by hydrodynamic interactions between the beating patterns of a cilium or flagellum and the fluid, and a change in the swimming direction is due to some information processing including a behavioral response to the ambient environment. The behavioral response can be classified into several categories of -taxis such as chemotaxis (chemicals), gravitaxis (gravity), [1][2][3][4] and gyrotaxis (torque acting on the body). [5][6][7][8] Here, we focus on the photomovement of Euglena gracilis, a unicellular photosynthetic alga, whose body is approximately 10 µm wide and 50-100 µm long. ...
The motion of individual Euglena gracilis was experimentally analyzed. The flow field of E. gracilis during free swimming was visualized by the particle image velocimetry method to show that the time-averaged flow field is well represented by two Stokeslets, suggesting that the flow around E. gracilis is categorized as the typical puller type. The orbit of swimming E. gracilis in a uniform environment was also analyzed. The orbit was classified into two modes, “moving” and “stationary”, to obtain statistics on waiting time, swimming length during a single motion, and the directional change between two successive swimming directions. For the distribution of waiting time and swimming length, power laws were obtained. On the basis of the results, biased random walk models were constructed to discuss the long-time diffusion behavior of an individual motion. The swimming behavior of E. gracilis in a nonuniform light environment was analyzed by focusing on the directional change behavior, whereby a Markov chain model was proposed to reproduce the observed behavior.
... Bioconvection is used to describe the phenomenon of macroscopic convection motion of the fluid originated due to the density gradient created by collective swimming of microorganisms (such as bacteria and algae) [1][2][3][4][5][6]. These self-propelled motile microorganisms increase the density of the base fluid by swimming in a particular direction, thus causing bioconvection. ...
... They showed that their produced code gives good agreement with earlier works. Alloui et al. [6] investigated the effect of heating or cooling from below on the stability of a suspension of motile gravitactic microorganisms in a shallow fluid layer. They used the linear perturbation theory and observed that the thermo-effects may either stabilize or destabilize the suspension, and decrease or increase the wave length of the bioconvective pattern. ...
This article describes the steady magnetohydrodynamic mixed thermo-bioconvection in a square enclosure filled with a homogeneous and isotropic porous medium in the presences of oxytactic microorganisms. The model used for the oxytactic microorganisms is based on a continuum model of a suspension of oxytactic microorganisms. The mixed convection is resulting for the interaction between the buoyancy force and the moving of the top wall of the cavity with constant speed. The horizontal walls of the cavity are considered to be adiabatic while the vertical walls are differentially heated. The governing equations are solved using the finite volume method with SIMPLE technique. Comparisons with previously published works are performed and found to be in excellent agreements. It is found that the increase in both Richardson number and Hartmann number reduces the average Nusselt and Sherwood numbers.
... They discovered that the bioconvection Rayleigh number rises with the increase in Peclet number. Alloui et al. [7] numerically investigated bioconvection in two cases i.e., cooling and heating from below. As bioconvection is three-dimensional in nature, Ghorai and Hill [8] studied the gyrotactic bioconvection in this dimension. ...
The current study covers the relative study of non-aligned magnetohydrodynamic stagnation point flow of a nanofluid comprising gyrotactic microorganisms across a stretching sheet in the presence of nonlinear thermal radiation and variable viscosity. The governing equations transitioned as nonlinear ordinary differential equations with suited similarity transformations. With the assistance of Runge-Kutta based shooting method, we derived solutions. Results for oblique and free stream flow cases are exhibited through plots for the parameters of concern. In tabular form, heat and mass transfer rate along with the local density of the motile microorganisms are analyzed for some parameters. It is found that local density of the motile microorganisms is highly influenced by the Biot and Peclet numbers. Rising values of the magnetic field parameter, Biot number, thermal radiation parameter and thermophoresis parameter increase the thermal boundary layer. Bioconvection Peclet number and bioconvection Lewis number have tendency to reduce the density of the motile microorganisms. It is also found that thermal and concentration boundary layers become high in free stream flow when compared with the oblique flow.
... Bioconvection is defined as the macroscopic fluid motion because of the density gradient resulting from collective swimming of motile micro-organisms [41][42][43][44][45]. The self-impelled motile micro-organisms enhance the base fluid density in a particular direction in such a way that they cause the bioconvection flow. ...
The behavior of a water-based nanofluid containing motile gyrotactic micro-organisms passing an isothermal nonlinear stretching sheet in the presence of a non-uniform magnetic field is studied numerically. The governing partial differential equations including continuity, momentums, energy, concentration of the nanoparticles, and density of motile micro-organisms are converted into a system of the ordinary differential equations via a set of similarity transformations. New set of equations are discretized using the finite difference method and have been linearized by employing the Newton’s linearization technique. The tri-diagonal system of algebraic equations from discretization is solved using the well-known Thomas algorithm. The numerical results for profiles of velocity, temperature, nanoparticles concentration and density of motile micro-organisms as well as the local skin friction coefficient Cfx, the local Nusselt number Nux, the local Sherwood number Shx and the local density number of the motile microorganism Nnx are expressed graphically and described in detail. This investigation shows the density number of the motile micro-organisms enhances with rise of M, Gr/Re2, Pe and Ω but it decreases with augment of Rb and n. Also, Sherwood number augments with an increase of M and Gr/Re2, while decreases with n, Rb, Nb and Nr. To show the validity of the current results, a comparison between the present results and the existing literature has been carried out.
The appearance of gyrotactic microorganisms unsteady MHD nanofluid is explored numerically using a cylinder in this study for the two-dimensional scenario. Boundary layer approaches are used to simulate the basic equations of the flow. The novelty of this study is due to the analysis of gyrotactic microorganisms over a cylinder in terms of unsteady nanofluids. The recommended model can greatly improve the fields of thermal and industrial engineering, which is advantageous. Using appropriate variables, the primary mathematical model has been transformed into dimensionless form. Explicit finite difference method (EFDM) is used to model the current statement. Earlier to that a stability test has been performed to gather information on the restrictions of using appropriate parameters. The effects of flow patterns have been studied from a variety of angles. All the computed results and the consequences are analyzed and illustrated graphically. When the findings are contrasted with those from earlier inquiries into the specific situation, there is a significant degree of agreement. The addition of Brownian motion due to the cross-diffusion effect and the coupling parameter for the interaction of the dissipative heat promotes the nanofluid velocity throughout the region, further reverse influence is shown through the shear stress profiles. An important finding of the present investigation can be identified as, the profiles of the heat transport phenomenon increase significantly for the growing values of several parameters such as Brownian, thermophoresis, Eckert number and the resistivity of the magnetic parameter; however, enhanced Lewis number retards it significantly. Furthermore, the present investigation has great use in the field of medical sciences, chemical engineering, mechanical engineering, plasma research and so on.
This study aims to discover the application of bioconvection and heat absorption or omission aspect of 2D incompressible MHD Oldroyd-B nanofluid over the stagnation region. Directed by suitable similarity transformations, the system of PDEs is transformed into a system of coupled nonlinear ODEs. The results were made by using Runge–Kutta shooting technique. The Buongiorno model is capitalized while Oldroyd-B model is employed for portraying the viscoelastic behavior of the flow. In order to visualize the impact of relevant parameters on momentum boundary layer, temperature, concentration and microorganism profiles are computed graphically. Numerical outcomes for the local Nusselt number, Sherwood number, microorganism number and local skin friction number are calculated for different parametric situations to provide interesting features of the examination. Furthermore, it has been also observed from statistical point that the correlation coefficient of the local Nusselt number, Sherwood number, microorganism number and local skin friction number with various parametric situations are highly significant at the α=0.01 level of significance (p<0.0001 for a two-tailed test).
In the context of bioconvection, bacteria are swimming microorganisms. Actually, a microorganism’s species is related to a focused swimming cell in the convection model. Unsteady chemically reactive (Water–Copper (Cu)–Ferrous Oxide (Fe3O4)) hybrid nanofluid dynamics between two stretchable rotating disks at varied Lorentz force and viscous dissipation are unknown when the suspension of gyrotactic micro-organisms is taken into account. The paper’s novelty is addressing this gap, which is to examine the impact of chemical reactions on the unsteady bioconvective hybrid nanofluid flow between two stretchable rotating disks with viscous dissipation and the magnetic field. The use of Von-Karman similarity transformations allows for the conversion of governing equations into nonlinear ordinary differential equations. Based on the combination of Runge–Kutta fourth order and shooting methods, the final equations are calculated. A major finding of this study is Reynolds number escalates both axial and radial velocities but decreases the tangential velocity. The temperature increases with the rise in both Eckert number and heat source parameters. The concentration decreases with the rise in Schmidt number and chemical reaction parameter.
This paper deals with a study on the magnetohydrodynamic boundary layer flow and transfer of heat and mass of a viscous nanofluid comprising gyrotactic microorganisms. The flow is supposed to take place on a sheet, which stretches or shrinks asymmetrically in its own plane, where the line of symmetry of the stagnation motion and that of the stretching/shirking surface are in general not aligned. The governing non-linear partial differential equations and auxiliary conditions are transformed to a set of non-linear ODEs with the suitable boundary conditions by using similarity transformation. The resulting equations are solved numerically employing spectral relaxation method (SRM) through the use of MATLAB. We take some initial guesses, which satisfy the boundary condition for the iterative spectral relaxation technique. The influences of assorted parameters such as velocity ratio parameter α, source/sink parameter Q, Prandtl number Pr, magnetic field parameter M, Peclet number Pe, Lewis number Le, Bioconvection Lewis number Lb, Brownian motion parameter Nb, thermophoresis parameter Nt, Eckert number Ec, local Eckert numbers (Ecx and Ecy) and bioconvection constant σ are investigated. Transfer of mass and heat and the impact of microorganisms present in the fluid are explored through graphs and tables and the results are discussed in details. Variation in the skin-friction, heat transfer rate and the density number of the motile microorganism is also investigated. Residual error analysis is also performed for establishing the convergence rate against iteration. The study reveals that the velocity enhances, but the temperature reduces with rise in the strength of the magnetic field, while the thickness of the motile microorganisms is reduced as the Peclet number increases.
Bioconvection plays an inevitable role in introducing sustainable and environment-friendly fuel cell technologies. Bio-mathematical modelling of such designs needs continuous refinements to achieve strong agreements in experimental and computational results. Actually, microorganisms transport a miscellaneous palette of ingredients in manufacturing industrial goods particularly in fertilizer industries. Heat transfer characteristics of molecular structure are measured by a physical phenomenon which is allied with the transpiration of heat within matter. Motivated by bio-inspired fuel cells involved in near-surface flow phenomena, in the present article, we examine the transverse swimming of motile gyrotactic microorganisms numerically in a rheological Jeffery fluid near a stretching wall. The leading physical model is converted in a nonlinear system of ODEs through proper similarity alterations. A numerical technique called shooting method with R-K Fehlberg is applied via mathematical software and graphical presentations are obtained. The influence of all relative physical constraints on velocity, temperature, concentration, and volume fraction of gyrotactic microorganisms is expressed geometrically. It is found that heat and mass flux at the surface as well as density of motile microorganism’s declines for Brownian motion and thermophoresis parameter. Comparison in tabular form is made with existing literature to validate the results for limiting cases with convective boundary conditions.
In recent research, it is worth mentioning that bioconvection usage has shown significant promise for environmentally friendly, sustainable “green” fuel cell technologies. In this context, the present problem definitely gives a boost to a deeper analysis of the Oldroyd-B fluid model in the presence of gyrotactic microorganisms. This study analyses oblique Oldroyd-B fluid with mixed convection on an elastic surface with interactive properties and gyrotactic microorganisms under the influence of suction/injection with zero heat and mass. The principal physical model is converted in a nonlinear system of ODEs employing proper similarity equations. The impact of all relative physical constrictions on velocity, temperature, concentration, and volume fraction of gyrotactic microorganisms is expressed geometrically. Physical scales like skin friction measurements, heat transfer rate, and mass transfer rate at the surface are calculated numerically.
Bioconvection has shown significant promise for environmentally friendly, sustainable “green” fuel cell technologies. The improved design of such systems requires continuous refinements in biomathematical modeling in conjunction with laboratory and field testing. Motivated by exploring deeper the near-wall transport phenomena involved in bio-inspired fuel cells, in the present paper, we examine analytically and numerically the combined free-forced convective steady boundary layer flow from a solid vertical flat plate embedded in a Darcian porous medium containing gyrotactic microorganisms. Gyrotaxis is one of the many taxes exhibited in biological microscale transport, and other examples include magneto-taxis, photo-taxis, chemotaxis and geo-taxis (reflecting the response of microorganisms to magnetic field, light, chemical concentration or gravity, respectively). The bioconvection fuel cell also contains diffusing oxygen species which mimics the cathodic behavior in a proton exchange membrane (PEM) system. The vertical wall is maintained at iso-solutal (constant oxygen volume fraction and motile microorganism density) and iso-thermal conditions. Wall values of these quantities are sustained at higher values than the ambient temperature and concentration of oxygen and biological microorganism species. Similarity transformations are applied to render the governing partial differential equations for mass, momentum, energy, oxygen species and microorganism species density into a system of ordinary differential equations. The emerging eight order nonlinear coupled, ordinary differential boundary value problem features several important dimensionless control parameters, namely Lewis number (Le), buoyancy ratio parameter i.e. ratio of oxygen species buoyancy force to thermal buoyancy force (Nr), bioconvection Rayleigh number (Rb), bioconvection Lewis number (Lb), bioconvection Péclet number (Pe) and the mixed convection parameter ([Formula: see text] spanning the entire range of free and forced convection. The transformed nonlinear system of equations with boundary conditions is solved numerically by a finite difference method with central differencing, tridiagonal matrix manipulation and an iterative procedure. Computations are validated with the symbolic Maple 14.0 software. The influence of buoyancy and bioconvection parameters on the dimensionless temperature, velocity, oxygen concentration and motile microorganism density distribution, Nusselt, Sherwood and gradient of motile microorganism density are studied. The work clearly shows the benefit of utilizing biological organisms in fuel cell design and presents a logical biomathematical modeling framework for simulating such systems. In particular, the deployment of gyrotactic microorganisms is shown to stimulate improved transport characteristics in heat and momentum at the fuel cell wall.
The transient mixed convection boundary layer analysis of incompressible flow over an isothermal vertical cylinder is embedded in a saturated porous medium in the vicinity for Gyrotactic microorganism effects. The mathematical model used for the bioconvective nanofluid incorporates the effects of Brownian motion, thermophoresis, and gyrotactic microorganisms. Moreover, the resulting governing nonsimilarity equations are changed into partial differential equations and solved numerically. The results are explained graphically for various physical parameters. It is determined that bioconvection parameter boosts the heat transfer rates and the thickness of the motile microorganism reduces the mass transfer rates. Expanding bioconvection Lewis number leads to decrease in heat transfer rates and the density of the motile microorganism, whereas the mass transfer rates decelerate the flow field. The investigation is pertinent to the nanobiopolymer manufacturing processes.
The aim of the present paper is to establish the detailed numerical results for bioconvection boundary-layer flow of a two-phase dusty nanofluid. The dusty fluid contains gyrotactic microorganisms along an isothermally heated vertical wall. The physical mechanisms responsible for the slip velocity between the dusty fluid and nanoparticles, such as thermophoresis and Brownian motion, are included in this study. The influence of the dusty nanofluid on heat transfer and flow characteristics are investigated in this paper. The governing equations for two-phase model are non-dimensionalized and then solved numerically via two-point finite difference method together with the tri-diagonal solver. Results are presented graphically for wall skin friction coefficient, rate of heat transfer, velocity and temperature profiles and streamlines and isotherms. To ensure the accuracy, the computational results are compared with available data and are found in good agreement. The key observation from the present analysis is that the mass concentration parameter, , extensively promotes the rate of heat transfer, , whereas, the wall skin friction coefficient, , is reduced by loading the dust parameters in water based dusty nanofluid.
Thisarticle is an investigation on effect of heat convection on nanofluid flow over a moving Riga plate of variable thickness. In the present study motile density of gyrotactic microorganisms submerged in nanofluid is also examined under the influence of bio-convection, mass flux and heat convection. The physical problem is mathematically modeled and obtained nonlinear system of partial differential equation. The obtained highly nonlinear system of coupled partial differential equations is converted into ordinary differential equations using suitable transformation. The highly nonlinear system is tackled numerically by means of implicit finite difference scheme Keller Box. Emphasis is given to the nanofluidic transport towards Riga plate in the presence of heat convection and mass flux condition. Influence of meaningful physical parameters of interest are examined and studied on fluid velocity, nanoparticle temperature and concentration along with motile microorganism density graphically. Reliability and efficiency of presented numerical scheme is validated by comparative tables. It is concluded that nanofluid velocity is an increasing function of microorganism concentration and modified magnetic parameter while it seems to decrease with increase in buoyancy ratio, Grashof number and wall thickness.
The prime purpose of this analysis is to investigate the effect of variable thermophysical properties of nanofluid on bioconvection boundary layer flow past a uniformly heated vertical cone. The governing equations with associated boundary conditions for this phenomenon are cast into a non-dimensional form via continuous transformations, which are then solved by using the implicit finite difference method. How does the phenomena of heat transfer is effected due to the temperature-dependent thermophysical properties of the fluid is the question investigated in this manuscript. Comprehensive numerical computations are carried out for wide range of the parameters that are describing the flow characteristics. The influence of the governing physical parameters on the distribution of velocity and temperature profiles, wall skin friction and local rate of heat transfer is explored. Tabular comparison with some special cases of published data is done and good agreement is found. It is recorded that, the variable thermophysical properties of the fluid are more likely to promote the rate of heat transfer, Qw as compared to fluid having constant properties.
This investigation reveals effect of induced magnetic field on stagnation point flow over a stretching sheet containing gyrotactic microorganisms. The nonlinear system of coupled differential equations is transformed and solved numerically with the help of shooting method along with Runge-Kutta method of order 5. The solution accuracy is set up to 6 decimal places. Main focus is to examine influence of induced magnetic field and thermal radiation on fluid flow and microorganism density. The behavior of fluid velocity, temperature, concentration and microorganism density for distinct values of pertinent physical parameters is examined. The results are displayed through graphs and tables. Main findings of present analysis are abridged in concluding remarks. It is concluded that bioconvection plays a vital role in reducing temperature and concentration profiles. Moreover, Microorganism density rises with the rise in Peclet number Pe,magnetic parameter ϵ,Brownian motion parameter Nb and thermophoresis parameter Nt while it reduces for rise in Lewis number. Present results are validated by comparative analysis and they are found to be in good agreement.
Using the continuum model of Pedley et al. [J. Fluid Mech. 195, 223 (1988)] for bioconvection in a suspension of swimming, gyrotactic micro-organisms, the existence and stability of periodic arrays of two-dimensional plumes in deep chambers are investigated. The system is governed by the Navier-Stokes equations for an incompressible fluid coupled with a micro-organism conservation equation. These equations are solved numerically using a conservative finite-difference scheme. In sufficiently deep chambers, the plumes are sometimes unstable to varicose or meandering modes. A linear stability analysis for an infinitely deep plume predicts the growth rates of these instabilities and agrees well with the numerical results.
Using the continuum model of Pedley, Hill & Kessler (1988) for bioconvection in a suspension of swimming, gyrotactic micro-organisms, we investigate the existence and stability of a two-dimensional plume in tall, narrow chambers with stress-free sidewalls. The system is governed by the Navier Stokes equations for an incompressible fluid coupled with a micro-organism conservation equation. These equations are solved numerically using a conservative finite-difference scheme. In sufficiently deep chambers, the plume is always unstable to both varicose and meandering modes. A linear stability analysis for an infinitely long plume predicts the growth rates of these instabilities, explains the mechanisms, and is in good agreement with the numerical results.
The onset of thermosolutal convection and finite-amplitude flows, due to vertical gradients of heat and solute, in a horizontal rectangular enclosure are investigated analytically and numerically. Dirichlet or Neumann boundary conditions for temperature and solute concentration are applied to the two horizontal walls of the enclosure, while the two vertical ones are assumed impermeable and insulated. The cases of stress-free and non-slip horizontal boundaries are considered. The governing equations are solved numerically using a finite element method. To study the linear stability of the quiescent state and of the fully developed flows, a reliable numerical technique is implemented on the basis of Galerkin and finite element methods. The thresholds for finite-amplitude, oscillatory and monotonic convection instabilities are determined explicitly in terms of the governing parameters. In the diffusive mode (solute is stabilizing) it is demonstrated that overstability and subcritical convection may set in at a Rayleigh number well below the threshold of monotonic instability, when the thermal to solutal diffusivity ratio is greater than unity. In an infinite layer with rigid boundaries, the wavelength at the onset of overstability was found to be a function of the governing parameters. Analytical solutions, for finite-amplitude convection, are derived on the basis of a weak nonlinear perturbation theory for general cases and on the basis of the parallel flow approximation for a shallow enclosure subject to Neumann boundary conditions. The stability of the parallel flow solution is studied and the threshold for Hopf bifurcation is determined. For a relatively large aspect ratio enclosure, the numerical solution indicates horizontally travelling waves developing near the threshold of the oscillatory convection. Multiple confined steady and unsteady states are found to coexist. Finally, note that all the numerical solutions presented in this paper were found to be stable.
Bioconvection is a result of the negative gravitactic behavior of microorganisms. When the top-heavy density gradient generated by gravitaxis grows sufficiently large, an overturning convection occurs leading to a formation of characteristic patterns, which involve highly concentrated aggregation of cells into extended two-dimensional structures. Although gravity is a crucial factor, few experiments have been done with reference to gravity as an experimental variable. In order to gain an insight into the hydrodynamic as well as biological dependence of the convective motion on gravity, we investigated changes in bioconvective patterns of Tetrahymena under altered gravity acceleration generated by a long-arm centrifuge. Bioconvective patterns recorded of three different cell strains (T. pyriformis, T. thermophila and its behavioral mutant, TNR) were analyzed quantitatively using space-time plot and Fourier analysis. For example, under subcritical conditions, when T. pyriformis (1.0 x 10(6) cells ml(-1)) was placed in a 2 mm-deep chamber, no spatial pattern was observed at 1 g. When the suspension was centrifuged, however, patterns began to appear as acceleration increased over a critical value (1.5 g), and then remained steady. The formation was reversible, i.e. the patterns disappeared again as acceleration decreased. Under supracritical conditions, i.e. when a suspension of the same density was placed in a 4 mm-deep chamber, a steady state pattern was formed at 1 g. The pattern spacing in the steady state was observed to decrease stepwise in response to step increases in acceleration. Fourier analysis demonstrated that for TNR the mean wave number changed almost simultaneously with step changes in acceleration, whereas the responses were less sharp in the wild-type strains. This may suggest that the locomotor phenotype of the cell, such as its avoiding response ability, has a crucial role in bioconvective pattern formation. These findings are discussed in relation to former theoretical studies.
Presents introductory skills needed for prediction of heat transfer and fluid flow, using the numerical method based on physical considerations. The author begins by discussing physical phenomena and moves to the concept and practice of the numerical solution. The book concludes with special topics and possible applications of the method.
Numerical experiments were carried out on the pattern formation of bioconvection that is observed in cultures of motile aquatic microorganisms. New features were revealed on how the bioconvective system evolves and how the number of falling fingers is selected at each stage of evolution. At the onset of convection, the relevant dynamical regime is that of the Rayleigh–Taylor instability. Then, readjustment of the wavenumber occurs as the adjacent convection cells combine with each other. The trajectory in (total kinetic energy, total potential energy) space shows that evolution of the system proceeds in the direction of intensifying the downward advection of microorganisms and reducing the total potential energy of the system. Finally the system reaches a stationary state, where the aspect ratio of the convection cells resembles that of Be´nard–Rayleigh convection and is optimum for the efficient downward advection of microorganisms. Furthermore, it is demonstrated that trajectories of the two cases deviate from this major evolution. In the case where the diffusion time of the system is large, the system shows remarkable oscillation and repeats the Rayleigh–Taylor instability intermittently. In the case where the viscous effect is large, the system ceases to evolve before reaching the optimum mode.
Patterns formation of gravitactic microorganism in a vertical cylinder is described by the Navier–Stokes equation coupled with the microorganism conservation equation. The control volume method is used to solve numerically these equations. It is found that when the Peclet number is decreased, the critical Rayleigh number also decreases to approach the value corresponding to Bénard convection under fixed-flux heating condition. However, at high Peclet numbers, the development convection is very different from that of Bénard convection. The most fundamental difference is that, while Bénard convection is a supercritical instability, the gravitactic bioconvection is shown to be a subcritical bifurcation from the diffusion state.
This paper examines the stability in viscous liquid of a steady regime in which the temperature decreases with uniform gradient between a lower horizontal surface which is heated and an upper horizontal surface which is cooled. The problem has been treated both experimentally and theoretically by Benard, Brunt, Jeffreys, Low and Rayleigh, and it is known that instability will occur at some critical value of gh3Delta rho /rho knu , h denoting the thickness of the fluid layer, Delta rho /rho the fractional excess of density in the fluid at the top as compared with the fluid at the bottom surface, k the diffusivity and nu the kinematic viscosity. The critical value depends upon the conditions at the top and bottom surfaces, which may be either 'free' or constrained by rigid conducting surfaces. The theoretical problem is solved here under three distinct boundary conditions, and greater generality than before is maintained in regard to the 'cell pattern' which occurs in plan. In addition an approximate method is described and illustrated, depending on a stationary property akin to that of which Lord Rayleigh made wide application in vibration theory. Within the assumptions of the approximate theory (i.e. with neglect of terms of the second order in respect of the velocities) a particular size is associated with every shape of cell (such that 'a2' takes a preferred value), but no particular shape is more likely than another to occur in a layer of indefinite extent (section 31). The explanation of the apparent preference for a hexagonal cell pattern (section 5) must presumably be sought in a theory which takes account of second-order terms. This conjecture if correct goes some way towards explaining the rather indefinite nature of observed cell-formations (cf. Low 1930, figure 10).
Bioconvection observed in a culture of motile micro-organisms was analyzed numerically. The governing equations are the Navier-Stokes equations with the Boussinesq approximation and a diffusion equation for the motile micro-organism. A transition from a static condition to periodic oscillation was observed according to the increase of the Rayleigh number. It was found that the system of bioconvection could be led into chaotic conditions via a single-frequency oscillatory behavior to a sequence of period-doubling bifurcations by increasing the Rayleigh number, which is analogous to Bénard convection.
In this paper, we investigate the effect of heating or cooling from below on the stability of a suspension of motile gravitactic microorganisms in a shallow fluid layer. The linear perturbation theory is used to obtain the stability diagram and the critical conditions for the onset of convection. It is found that the thermo-effects may either stabilize or destabilize the suspension, and decrease or increase the wavelength of the bioconvective pattern.
This paper studies thermo-bioconvection, a macroscopic convective motion induced in a fluid layer by the combined effect of density stratification caused by the upswimming of oxytactic microorganisms and heating from below. Both agencies affecting the density are destabilizing; therefore, monotonic instability is expected. Oscillatory instability may be possible in the case of cooling from below.
Experiments by Kessler on bioconvection in laboratory suspensions of bacteria (Bacillus
subtilis), contained in a deep chamber, reveal the development of a thin upper
boundary layer of cell-rich fluid which becomes unstable, leading to the formation of
falling plumes. We use the continuum description of such a suspension developed by
Hillesdon et
al. (1995) as the basis for a theoretical model of the boundary layer and
an axisymmetric plume. If the boundary layer has dimensionless thickness λ [double less-than sign] 1, the
plume has width λ1/2. A similarity solution is found for the plume in which the cell
flux and volume flux can be matched to those in the boundary layer and in the bulk of
the suspension outside both regions. The corresponding model for a two-dimensional
plume fails to give a self-consistent solution.
A model for collective movement and pattern formation in layered suspensions of negatively geotactic micro-organisms is presented. The motility of the organism is described by an average upward swimming speed U and a diffusivity tensor D. It is shown that the equilibrium suspension is unstable to infinitesimal perturbations when either the layer depth or the mean concentration of the organisms exceeds a critical value. For deep layers the maximum growth rate determines a preferred pattern size explicitly in terms of U and D. The results are compared with observations of patterns formed by the ciliated protozoan Tetrahymena
pyriformis.
The effect of gyrotaxis on the linear stability of a suspension of swimming, negatively buoyant micro-organisms is examined for a layer of finite depth. In the steady basic state there is no bulk fluid motion, and the upwards swimming of the cells is balanced by diffusion resulting from randomness in their shape, orientation and swimming behaviour. This leads to a bulk density stratification with denser fluid on top. The theory is based on the continuum model of Pedley, Hill & Kessler (1988), and employs both asymptotic and numerical analysis. The suspension is characterized by five dimensionless parameters: a Rayleigh number, a Schmidt number, a layer-depth parameter, a gyrotaxis number G, and a geometrical parameter measuring the ellipticity of the micro-organisms. For small values of G, the most unstable mode has a vanishing wavenumber, but for sufficiently large values of G, the predicted initial wavelength is finite, in agreement with experiments. The suspension becomes less stable as the layer depth is increased. Indeed, if the layer is sufficiently deep an initially homogeneous suspension is unstable, and the equilibrium state does not form. The theory of Pedley, Hill & Kessler (1988) for infinite depth is shown to be appropriate in that case. An unusual feature of the model is the existence of overstable or oscillatory modes which are driven by the gyrotactic response of the micro-organisms to the shear at the rigid boundaries of the layer. These modes occur at parameter values which could be realized in experiments.
When a suspension of the bacterium Bacillus
subtilis is placed in a chamber with its upper surface open to the atmosphere, complex bioconvection patterns form. These arise because the cells (a) are denser than water, and (b) swim upwards on average so that the density of an initially uniform suspension becomes greater at the top than at the bottom. When the vertical density gradient becomes large enough an overturning instability occurs which evolves ultimately into the observed patterns. The cells swim upwards because they are oxytactic, i.e. they swim up gradients of oxygen, and they consume oxygen. These properties are incorporated in conservation equations for the cell and oxygen concentrations, which, for the pre-instability stage of the pattern formation process, have been solved in a previous paper (Hillesdon, Pedley & Kessler 1995). In this paper we carry out a linear instability analysis of the steady-state cell and oxygen concentration distributions. There are intrinsic differences between the shallow-and deep-chamber cell concentration distributions, with the consequence that the instability is non-oscillatory in shallow chambers, but must be oscillatory in deep chambers whenever the critical wavenumber is non-zero. We investigate how the critical Rayleigh number for the suspension varies with the three independent parameters of the problem and discuss the most appropriate definition of the Rayleigh number. Several qualitative aspects of the solution of the linear instability problem agree with experimental observation.
The motion of Paramecium caudatum has been investigated at various temperatures by measuring the transient behavior of spatial distribution in the diffusion process of organisms that, by electric stimulus, are initially gathered at a single place in the glass culture cell. The spatial distribution through the course of diffusion has a nearly Gaussian profile. Dispersion was obtained at 1 sec intervals and increased linearly with time. The time dependence of the dispersion gave a diffusion coefficient for the random motion of the organisms. The results show that the diffusion coefficient has a maximum at the temperature at which the paramecia were cultivated.
The aim of this paper is to investigate the effect of heating from below on the stability of a suspension of motile gyrotactic microorganisms in a fluid layer of finite depth. This problem is relevant to a number of geophysical applications, such as investigation of the dynamics of some species of thermophiles (heat-loving microorganisms) living in hot springs. It is established that heating from below makes the system more unstable and helps the development of bioconvection. By performing a linear stability analysis, a correlation for the critical bioconvection Rayleigh number is obtained.
This paper investigates the combined effect of density stratification due to oxytactic upswimming and heating from below on the stability of a suspension of motile oxytactic microorganisms in a shallow fluid layer. Different from traditional bioconvection, thermo-bioconvection has two destabilizing mechanisms that contribute to creating the unstable density stratification. This problem may be relevant to a number of geophysical applications, such as the investigation of the dynamics of some species of thermophiles (heat loving microorganisms) living in hot springs. By performing a linear stability analysis, we obtained a correlation between the critical value of the bioconvection Rayleigh number and the traditional, “thermal” Rayleigh number. It is established that heating from below makes the system more unstable and helps the development of bioconvection.
A linear stability analysis is applied to investigate the onset of bioconvection in a horizontal layer of fluid containing a suspension of motile microorganisms with heating or cooling from below. With cooling from below the stabilizing effect of the thermal stratification is opposed to the destabilizing effect resulting from the congregation of the microorganisms, and oscillatory convection is possible in certain circumstances. The stability criterion is found in terms of a thermal Rayleigh number, a bioconvection Rayleigh number, a bioconvection Péclet number, a gyrotactic number, and a measure of the cell eccentricity, together with (in the case of oscillatory convection) a Prandtl number and a Lewis number.
Bioconvection patterns are usually observed in the laboratory in shallow suspensions of randomly, but on average upwardly, swimming micro-organisms which are a little denser than water, but have also been found in situ in micropatches of zooplankton [Kils (1993), 1993. Bull. Mar. Sci. 53, 160–169]. The mechanism of upswimming differs between bottom-heavy algae and oxytactic bacteria. Rational continuum models have been formulated and analysed in each of these cases for low cell volume fraction. These will be described, as will new theoretical and experimental developments, including nonlinear analysis of the patterns, dispersion in shear flows, measurements of algal cell swimming behaviour, and new attempts to set up a model for more concentrated suspensions. The paper will review all work in this area since 1992, the year of the publication of the article "Hydrodynamic phenomena in suspensions of swimming micro-organisms" by Pedley and Kessler [1992b. Annu. Rev. Fluid Mech. 24, 313–358].
Bioconvection occurs as the result of the collective behaviour of many microorganisms swimming in a fluid and is realized as patterns similar to those of thermal convection which occur when a layer of fluid is heated from below. We consider the phenomenon of pattern formation due to gyrotaxis, an orientation mechanism which results from the balance of gravitational and viscous torques acting on bottom-heavy micro-organisms. The continuum model of Pedley et al. (1988, J. Fluid. Mech.
195, 223–237) is used to describe the suspension. The system is governed by the Navier-Stokes equations for an incompressible fluid coupled with a micro-organism conservation equation. These equations are solved numerically using a conservative finite-difference scheme. To examine the dependence of the horizontal pattern wavelengths on the parameters, we consider two-dimensional solutions in a wide chamber using rigid side walls. The wavelengths of the numerical computations are in good agreement with the experimental observations and we provide the first computational examples of the commonly seen ‘bottom-standing’ plumes.
'Bioconvection' is the name given to pattern-forming convective motions set up in suspensions of swimming micro-organisms. 'Gyrotaxis' describes the way the swimming is guided through a balance between the physical torques generated by viscous drag and by gravity operating on an asymmetric distribution of mass within the organism. When the organisms are heavier towards the rear, gyrotaxis turns them so that they swim towards regions of most rapid downflow. The presence of gyrotaxis means that bioconvective instability can develop from an initially uniform suspension, without an unstable density stratification. In this paper a continuum model for suspensions of gyrotactic micro-organisms is proposed and discussed; in particular, account is taken of the fact that the organisms of interest are non-spherical, so that their orientation is influenced by the strain rate in the ambient flow as well as the vorticity. This model is used to analyse the linear instability of a uniform suspension. It is shown that the suspension is unstable if the disturbance wavenumber is less than a critical value which, together with the wavenumber of the most rapidly growing disturbance, is calculated explicitly. The subsequent convection pattern is predicted to be three-dimensional (i.e. with variation in the vertical as well as the horizontal direction) if the cells are sufficiently elongated. Numerical results are given for suspensions of a particular algal species (Chlamydomonas nivalis); the predicted wavelength of the most rapidly growing disturbance is 5-6 times larger than the wavelength of steady-state patterns observed in experiments. The main reasons for the difference are probably that the analysis describes the onset of convection, not the final, nonlinear steady state, and that the experimental fluid layer has finite depth.
In three-dimensional bioconvection, the regions of rising and sinking fluid are dissimilar. This geometrical effect is studied for axisymmetric bioconvection in a cylindrical cell with stress-free (i.e. normal velocity and tangential stress vanish) lateral and top boundaries, and rigid bottom boundary. Using the continuum model of Pedley et al. (1988, J. Fluid Mech.195, 223-237) for bioconvection in a suspension of swimming, gyrotactic microorganisms, the structure and stability of an axisymmetric plume in a deep chamber are investigated. The system is governed by the Navier-Stokes equations for an incompressible fluid coupled with a microorganism conservation equation. These equations are solved numerically using a conservative finite-difference scheme. Comparisons are made with two-dimensional bioconvection.
- N A Hill
- T J Pedley
N.A. Hill, T.J. Pedley, Bioconvection, Fluid Dyn. Res. 37 (2005) 1-20.