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Impact of oxytactic microorganisms and variable species diffusivity on blood-gold Reiner–Philippoff nanofluid
Abstract
Currently, researchers across the world achieved theoretical and experimental works to investigate the significance of nanofluid due to their diverse application in heat transport phenomena. Nanofluids are actually the suspension of nanoparticles in the base liquid. Embedding nanoparticles in the base fluid enhances thermal conductivity and heat transfer rate. The present article shed light on the influence of gold nanoparticles along with oxytactic microorganisms on radiative Reiner–philippoff fluid due to extendable sheet. Suitable transformation convert the partial differential equations (PDEs) are renovated into nonlinear ordinary differential equations (ODEs) and furthermore tackled these equations numerically via bvp4c Matlab builtin scheme. Further the investigations are carried out in the presence of molecular diffusivity, oxytactic microorganisms and nonlinear thermal radiation. The effect of influential parameters on heat transfer, mass transfer, motile density of microorganisms profile are investigated with the assistance of tables and graphs. Embedding the nanoparticles and nonlinear thermal radiation amplifies the heat transfer process and motile density profile depreciates owing to an augmentation in Peclet number. The novel outcomes of this investigation will advance the field of nanomaterials.
... Numerical results for velocity and heat profiles have been identified at different values of the pertinent variables. Table 4 of the present study as the value obtained in that table is in good agreement with that reported by [40,42]. ...
... Table 3 Quantity of − ′(0) at = = = 1, = 2 for several values of Rd and S Cortell [43] Ferdows et al. [44] Waini et al. [45] Noor Amalina [40] Present Result 0 −0. 5 Table 4 Quantity of (0) at = 0 and = 1 for several values of and . Sajid et al. [42] Noor et al. [ Table 7 In the absence and presence of thermal radiation, the magnitude of the Nusselt number ...
Reiner–Philippoff (RP) fluid flow above a heated sheet concluded the model of Cattaneo–Christov heat flux for Darcy-Forchheimer is implemented in this work. The influences of thermal radiation, heat source/sink, velocity, and thermal slip boundary conditions are also deliberated. The transformations are used to convert obtained PDEs into a set of ordinary differential equations, and they are solved numerically using the shooting method (RK-4) solver with the help of the computational software MATLAB. The dimensionless temperature and velocity numbers are further developed. More engineering curiosity of local Nusselt and Skin frictions are tabulated, depicted, and interpreted.
... Shear thinning (Pseudo-plastic), shear thickening (dilatant) and Newtonian behavior are all represented by the Reiner-Philippoff fluid. The same group also includes fluids like Sisko, Power-law etc. [11]. All models examined here have a three-parameter, time-independent counterpart that at low shear rates behaves like non-Newtonian fluids and at high shear rates like Newtonian fluids. ...
Here, the mass-based hybridity method and the Reiner-Philippoff model are used in tandem to investigate the forced convection of Au-Cu/blood nanofluid flow over a nonlinear shrinking/stretching sheet with radiation and suction influences. It is claimed that the masses of base fluid (blood) and nanoparticles (Au and Cu) as an alternative to the nanoparticles volume fraction, according to the Tiwari-Das single-phase algorithm can be numerically implemented in the present problem using the finite difference method in the MATLAB software. The Prandtl number was chosen to 10, and the blood mass was set to 100 gr. Further, the range of nanopar-ticles is from 0 gr to 40 gr, the mutable sheet parameter is between −1.3 to 2, and for the Reiner-Phillippoff parameter its range varies from 0.1 to 1. In addition, it is proven that the governing equations of the present problem possess dual similarity solutions in a certain range of governing parameters. Findings show that the Reiner-Philippoff parameter limits the range of the suction impact of the shrinking sheet for which at least a solution is available. Results indicate that an increase in the suction parameter from 0 to 2 leads to an increment of about 109 % and 226 % for skin friction and heat transfer rate, respectively. Moreover, the dual solutions of this research only exist for the case in which the suction parameter of the surface sheet is greater than its critical value. Finally, in the numerous engineering applications where cooling technologies are crucial, new models for nanofluid hybridity can surely be very beneficial. ARTICLE HISTORY
... Quantity of at = = 0 for several values of and .Sajid et al.(T. Sajid, Tanveer, Munsab, & Sabir, 2020) ...
Study of chemical reaction along with magnetic effect is significant in industrial process now a days. Magnetohydrodynamics (MHD) over Reiner-Philippoff (R-P) fluid flow passing through a stretching sheet and variable thickness with homogeneous-heterogeneous reactions is investigated in this article. With similarity transformations, partial differential equations are modified into dimensionless system of ordinary differential equations. Numerical results are obtained by the shooting technique along with the R-K method by using computational software MATLAB. The physical analysis of appropriate parameters in the velocity and concentration profiles is discussed in detail and shown graphically. It is summarized with critical observations that the inclining values of the wall thickness parameter cause the reduction in velocity and homogeneous reactions. At the same time, contrary behaviour is observed for heterogeneous reactions. The effect of MHD is noted to resist the velocity and concentration profiles for homogeneous reactions. However, the opposite behaviour is noted for heterogeneous reactions.
... Tassaddiq and Al-Hussain [12] explored Casson Hybrid nanoparticles flow with up-and-down tackiness in a thin film. Sajid et al. [13] examined the effect of ox tactic organisms and the diffusivity of different species on bloodgold interactions. Reiner Philippoff nanofluid. ...
The main aim of the current framework is to scrutinize the importance of gold and silver nanoparticles submerge in the human blood as a base fluid in the presence of magnetohydrodynamics (MHD) inside a stenotic artery. The primary reason for adopting gold and silver nanoparticles as nanomaterials for drug delivery is because they exhibit potential drug transport and imaging properties. The temperature and the velocity of the blood gradually decline as increment the size of the nano particles of gold. Furthermore, the effects of heat source-sink and thermal radiation are considered. To convert the partial differential equations (PDEs) into dimensionless ordinary differential equations (ODEs), a method of suitable similarity transformations has been utilized and then solved by using the bvp4c built in solver in MATLAB mathematical software to get the numerical solutions as well as the graphical results. Higher order ordinary differential equations (ODEs) are than tackled via shooting scheme. The outcomes of physical controlling parameters via temperature and velocity profiles are elaborated through graphs. The thermal distribution profile shows increasing behavior for the raising variations of Biot number and thermal radiation parameter. The current approach has the potential to be highly beneficial for efficient drug delivery in blood.
... The study revealed that an increase in the linear and nonlinear thermal and solutal convection parameters indicates an increase in flow rates. We refer the reader to other research work in this direction, see Mallikarjuna et al. [8], Sajid et al. [9], Yam et al. [10], Xiong et al. [11], Khan et al. [12], and Ahmed et al. [13]. In other non-Newtonian studies, Khan and Nadeem [14] investigated the dual solution of a Maxwell MHD nanofluid flow over a contracting surface. ...
Magneto-thermomechanical applications range from magnetic resonance imaging to electric diodes and the design of dielectric grease. To contribute significantly to the biomedical industry for proper prediction and treatment of diseases such as cancer, stenosis, and technological advancement in the design of electronic tools. This study presents the significance of magneto-thermomechanical modeling of Reiner-Philippoff fluid flow subject to thermal radiation influence. The Reiner-Philippoff fluid encapsulates the properties of shear-thinning, shear-thickening, and Newtonian fluids in different viscosity regimes. The mainstream velocity u e is considered in its generalized form as well as taking into account the influence of thermal radiation and thermal conductivity. To obtain the computational model analysis, a numerical tool via the bivariate spectral collocation method is deployed on the resulting transformed PDEs. Upon validation of the method, the profile distributions of respective boundary layers with respect to the Bingham number, magneto-thermomechanical parameter, and Reiner-Philippoff fluid parameter are analyzed and discussed. The results of the engineering quantities of skin friction and Nusselt number are presented in graphical and tabular form. Among the findings of this study is that the Newtonian fluid is a turning point for skin drag force and heat transfer rate. Besides, the ferrohydrodynamic parameter recedes the velocity of shear-thinning fluid the most, although, boosts its (shear-thinning fluid) heat transfer coefficient. ARTICLE HISTORY
This paper presents thorough computational and theoretical analyses of steady forced convective flow over a rotating disc submerged in a water-based nanofluid containing microorganisms. It delves into the examination of boundary layer flow characteristics of a viscous nanofluid, considering Stefan blowing effects and multiple slip conditions influenced by a magnetic field. Notably, the study accounts for novel aspects such as thermal radiation and both constructive and destructive chemical reactions. The movement of nanoparticles is elucidated based on thermophoresis and microscopic behaviors, while changes in volume fraction do not affect the thermo-physical properties of the nanofluid. To address the altered nonlinear set of differential equations, an effective numerical approach, the Keller-Box method, is implemented for critical and efficient solutions. These appropriate transformations are defined and applied. When compared to blowing suction, it shows a better enhancement in the rate of heat transfer, mass, and microorganisms. Some of the main observations are there is a decrease in wall skin friction in the directions of radial and tangential as magnetic field strength is increased. The evaluation of thermal boundary layer thickness and temperature is noted for the radiation parameter (Rd) improvement. The present analysis has applications in electromagnetic micro-pumps and nanomechanics. As to the applications in the science and engineering fields, technologies such as micro-electromechanical systems-based microfluidic devices and microfluidic-related technologies will be accepted.
The current study provides the numerical solutions of the language-based model through the artificial intelligence (AI) procedure based on the scale conjugate gradient neural network (SCJGNN). The mathematical learning language differential model is characterized into three classes, named as unknown, familiar, and mastered. A dataset is generalized by using the performance of the Adam scheme, which is used to reduce to mean square error. The AI based SCJGNN procedure works by taking the data with the ratio of testing (12%), validation (13%), and training (75%). An activation log-sigmoid function, twelve numbers of neurons, SCJG optimization, hidden and output layers are presented in this stochastic computing work for solving the learning language model. The correctness of AI based SCJGNN is noted through the overlapping of the results along with the small calculated absolute error that are around 10–06 to 10–08 for each class of the model. Moreover, the regression performances for each case of the model is performed as one that shows the perfect model. Additionally, the dependability of AI based SCJGNN is approved using the histogram, and function fitness.
In this discussion, the influence of carbon nanotubes on fluid flow is explored with the aim of optimizing, facilitating and improving heat transfer and stabilizing the flowing base fluid in modern technology. The current fluid model called Reiner-Philippoff is characterized as pseudo-plastic, dilatant and Newtonian fluid subject to the viscosity variation, making it easy to navigate between fluid rheologies. As a result, the importance of lacing the Reiner-Philippoff fluid flow enhanced by magnetohydrodynamics with single-wall carbon nanotube (SWCNT) and multi-wall carbon nan-otube (MWCNT) over a stretching sheet has been investigated. The governing mathematical model of the multi-variable differential equation has been transformed into a one-variable differential equation using a workable similarity transformation. The spectral local linearization method (SLLM) is employed to gain insight into the governing flow parameters, and the results are presented using tables and graphs. Prior to presenting the results of this study, the convergence and accuracy of the SLLM used for gaining insight into the governing flow parameters were established. Among the findings of this study is that the modified magnetic parameter supports the growth of the momentum boundary layer thickness for both SWCNT and MWCNT. The effective Prandtl number decreases the flow resistance more in the SWCNT compared to MWCNT.
The bioconvective flows are truly connected to real-life and engineering development. So, the models of biomicrosystems and biocells are considered for the technical analysis in this paper. Our intention for the current analysis was to theoretically examine electrical conduction flow into mass and heat transfer by an extensive gyrotactic microorganism into an inclined magnetic field toward a vertical stretching sheet with nonlinear solar radiation with different solar thermal appliances. The effect on velocity slip and Joule heating was again studied in detail. This classical problem on Navier Stokes equations to the current imitation was decreased to ordinary differential equations by applying the comparison method. The numerical solutions were changed by boundary value problem (BVP) to clarify the subject into finite difference numerical scheme by applying MATLAB. The important results show that the density of motile microorganisms reduces to the bioconvection Lewis number and Peclet number, although reverse performance was noticed for the bioconvection Rayleigh number. Further, solar radiation fosters heat transport. In this paper, complete analysis is provided for potential functions of solar thermoelectric cells, solar ponds, solar thermal power fabrication, etc.
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.
The aim of the study is to explore nonlinear mixed convection flow of nanomaterials (Prandtl–Eyring nanoliquid) with activation energy. Analysis of cross-diffusion (Soret and Dufour) impacts is addressed. Features of nanoliquid are analysed with thermophoresis and Brownian diffusion. Consideration of proper variables yields ordinary differential equations. Relevant system is tackled via numerical scheme. Significant outcomes are depicted graphically and elaborated in the relevance of sundry variables. Moreover, analysis of temperature and velocity gradients at the surface versus various variables of interest is tabulated and inspected.
The principle aim of the current communication is to scrutinize the impact of distinguished effects like variable thermal conductivity and variable molecular diffusivity on non-Newtonian Reiner–Philippoff fluid moving over a stretchable surface. The process of heat transfer is carried out in the presence of nonlinear thermal radiation, variable thermal conductivity, and heat generation/absorption. Furthermore, the study of mass transfer phenomena is carried out in the existence of variable molecular diffusivity. The PDEs regarding our model are renovated into ODEs by utilizing similarity transformation. Furthermore, the dimensionless model is tackled with the help of the RK4 method in conjunction with the shooting technique. The effects of different physical parameters that emerged during the numerical simulation on mass transfer rate, heat transfer rate, and velocity field are portrayed in the form of tables and graphs. It is noteworthy that an elevation in the heat source/sink parameters causes a reduction in the temperature profile. Moreover, a positive variation in the species diffusivity parameter augments the mass fraction field. A variation in the fluid parameter is found to be significantly affecting the shear thinning and shear thickening behaviour of the fluid. Reliability of the numerical outcomes is judged by comparing the obtained outcomes with the already available literature. The article is unique in its sense that the heat and mass transfer analysis of Reiner–Philippoff fluid under the aforementioned effects has not been investigated yet.
This paper is concerned with the investigation of variable viscosity bioconvection flow of nanofluid containing motile gyrotactic microorganisms over a nonlinear stretching sheet in the presence of nonlinear thermal radiation, chemical reaction, internal heat source, and suction/injection effects. The homotopy analysis method has been developed for solving the governing nonlinear differential equations of the boundary layer flow of nanofluid over a stretching sheet. The scaling group transformation (a special form of Lie group transformation) has been applied to find the similarity variable η. Figures are drawn by using Mathematica software to analyze the results that correspond to some important physical parameters and bioconvection parameters on velocity, temperature, nanoparticle concentration, and density of gyrotactic microorganisms. It is found that the influence of variable viscosity on velocity profiles showed that there is an increase in the velocity profiles of nanofluid and the reverse effect is observed on its temperature distribution. It is seen that the thermal radiation parameter increases the temperature distribution, whereas it decreases the nanoparticle concentration distribution. It is also found that the inverse Darcy number reduces the velocity profile, whereas it enhances the temperature distribution. This work may find applications in advanced nanomechanical bioconvection energy conversion devices, bio-nanocoolant systems, etc.
We have presented a comparison between steady and unsteady magnetohydrodynamic boundary layer flow, heat transfer features of Au–kerosene‐based nanoliquid over a stretching surface by taking variable viscosity, variable thermal conductivity, and slip boundary conditions in this study. Appropriate similarity translations are engaged to reduce nonlinear partial differential equations into a set of ordinary differential equations. These equations along with boundary conditions are elucidated numerically by finite‐element technique. Influence of several pertinent parameters on velocity, temperature, and concentration scatterings, in addition to that, the values of Nusselt number, skin‐friction coefficient, and Sherwood number are scrutinized in detail and the outcomes are exhibited through plots and tables. It is perceived that the values of Nusselt number, skin‐friction coefficient, and Sherwood number intensify in both steady–unsteady cases as the values of volume fraction parameter ( ϕ ) rise.
Currently, various researchers achieved theoretical and experimental works to scrutinize the influence of nanofluid in diverse forms of heat exchangers. In any engineering applications heat exchangers are critical components. Nanofluids are colloidal assortment of non-metallic or metallic particles suspended in base liquid. This study communicates a critical analysis of heat transport application of nanofluid. We established a model for unsteady flow of Maxwell nanofluid with the aspect of thermal radiation due to stretched cylinder. Moreover, heat source/sink is considered. Appropriate conversions yield the ordinary differential equations (ODEs) and then solved via homotopic methodology. Graphical outcomes of the velocity, temperature and concentration fields for influential parameters are plotted and discussed physically. The achieved outcomes specify that the temperature and concentration distribution increases for the higher unsteadiness parameter, curvature parameter and Maxwell parameter. Moreover, both thermophoresis and Brownian motion parameters enhances the thermal energy transport in flow.
The present work deals with the three-dimensional hybrid Cu-Al2O3/water nanofluid flow towards a stretching/shrinking sheet with the presence of velocity slip and convective conditions. A permeable sheet is considered to maintain the shrinking flow through an adequate wall mass suction. The nonlinear governing boundary layer coupled with energy equations are transformed into the ordinary differential equations using similarity transformation. Numerical computations are performed with the aid of boundary value problem solver (bvp4c) in the Matlab software and the results are presented in the tables and graphs. The boundary layer separation occurs in the shrinking flow region. An upsurge of slip and copper nanoparticle volume fraction parameters can increase the range of first and second solutions whereas Biot parameter give zero impact on delaying the boundary layer separation. However, an increase of Biot and slip parameters can boost the heat transfer rate while opposite result is obtained with the augmentation of the copper solid volume fraction. The stability of both solutions are examined, and it is validated that the first (upper branch) solution is more stable than second solution.
We have investigated the influence of hybrid nanoparticles on various physical quantities in a water-based hybrid nanofluid involved in a steady and fully developed forced convective flow generated over a stretched surface. Nonlinear thermal radiation and melting heat transfer analysis are featured in this work. To obtain the solution of the governing equations, a standard transformation and numerical procedure are implemented. Then, a comprehensive discussion of the effects of the flow regime on several governing parameters is presented. The results indicated that increasing magnetic strength \(M\) and nanoparticle volume fraction \(\phi_{1}\) lead to a thicker thermal boundary layer. A similar trend takes place with increasing nonlinear thermal radiation while the reverse is noticed for Eckert number. The entropy generation rate increases with the increase in Brinkman number and Bejan number reduces with increasing Eckert number. The obtained results of this model closely match with those available in the literature as a limiting situation. It is demonstrated that hybrid nanofluids exhibit lower entropy generation rates. The results of this study are of importance in the assessment of the effect of some essential design parameters on heat transfer and, consequently, in the optimization of industrial processes.
The aim of present study is to explore the heat and mass transfer properties in 2D transient flow of Maxwell nanofluid under the influence of magnetic field induced by stretching cylinder. The effects of heat sink/source, convective heat transport at surface and non-linear thermal radiation are contemplated for the analysis of heat transport mechanism in the flow of nanoliquid. Additionally, the aspect of chemical reaction is also reported in the solutal energy transport. The haphazard motion of nanoparticles and thermophoresis effect are studied using well-known Buongiorno theory for nanofluid. In the view of suitable transformations, the governing partial differential equations (PDEs) are transformed into non-linear ordinary differential equations (ODEs). Homotopic approach has been used to compute the series solutions of non-linear differential system. The acquired results are portrayed graphically for pertinent parameters and discussed with physical justification. It is found that the velocity, temperature and concentration fields boost up for higher value of magnetic parameter. The large value of unsteadiness parameter boosts up the both thermal and solutal energy transport in nanoliquid. Moreover, the increase in Brownian motion parameter enhances the temperature field but declines concentration fields. For the confirmation of these results, comparison tables are structured for different parameters.
In thoughtfulness of researchers and technologists in the arena of nanoscience and nanotechnology owing to reduced thermal properties of the usual base fluids, a new-fangled sort of fluids acknowledged as nanofluids have been established, which contains nanoparticles deferred in a hostfluid. For instance, nanofluids have superior heat transport enactment, because deferred nanoparticles have better thermal conductivity allied with base liquid. Here elaborated 3D flow of a Carreau nanoliquid is influenced by a bidirectional stretched surface. To visualize the properties of Brownian motion and thermophoresis on the Carreau nanoliquid, the Buongiorno's relation is exploited in a more proficient tactic. Variable thermal conductivity with the possessions of heat source/sink is pondered for heat transfer mechanisms. Suitable conversion is used to change the PDEs into non-linear ODEs. Numerically, bvp4c scheme is prompted to crack the resulting ODEs. The discrete behaviors for shear thinning/thickening of nanoliquid temperature and concentration field are described and deliberated in aspect for somatic parameters. It is exposed that the Carreau liquid temperature declines for Prandtl number and conflicting trends are being noted for Brownian and thermophoresis parameters. Moreover, heat transfer amount diminishes for higher Brownian and thermophoresis parameters. An assessment between two different approaches namely, bvp4c and homotopy analysis method, is also presented in tabular form which ensure that our outcomes are more precise.