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The present article describes the unsteady flow of a couple stress via a ternary hybrid nanofluid on a stretching surface with porous media. The nanofluid exhibits important properties for increasing heat transmission, and it is widely used in manufacturing and industrial applications. The basic similarity equations have been discovered to accommod...
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... the present work, we use nonNewtonian coupling. Moreover, it should be noted that the water containing spherical aluminum oxide, cylindrical single wall CNT, and platelet graphene nanoparticles, as shown in Figure 1, is transported. Table 1 shows the thermal characteristics of these three nanofluids. ...
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... ternary hybrid nanoparticles within the nanofluid increase as the volume fraction of the nanoparticles increases, allowing for an increased area for improved heat conduction. As can be seen in Figure 11, this raises the velocity of the nanofluid. Figure 12 shows the impact of ( ) θ η on η for various values of Λ for the stretching surface. ...
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... can be seen in Figure 11, this raises the velocity of the nanofluid. Figure 12 shows the impact of ( ) θ η on η for various values of Λ for the stretching surface. ( ) θ η decreases with an increase the value of Λ , and it is observed that the boundary layer thickness also reduces in the stretching surface. ...
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... ) θ η decreases with an increase the value of Λ , and it is observed that the boundary layer thickness also reduces in the stretching surface. Figure 13 indicates the impact of ( ) θ η on η for various values of the Biot number for the stretching case. Here, it seen that ( ) θ η decreases as the value of the Biot number increases. ...
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... performance of nanofluids is affected by both the drop in particle volume fraction and the increase in temperature in the flow pattern. Figure 14 show the temperature distribution ( ) θ η versus the similarity variable η for various values of the mass transpiration Vc for the stretching surface. This means that the thickness of the thermal boundary layer under suction is thinner than under blowing. ...
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... means that the thickness of the thermal boundary layer under suction is thinner than under blowing. Figure 15 show the temperature distribution ( ) θ η versus the similarity variable η for various values of the thermal radiation NR for the stretching surface. Thermal radiation, therefore, increases the thermal diffusivity of nanofluids; for emerging radiation parameter values, heat will be added to the regime, and temperatures will rise as a result. ...
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... has the effect of dampening or enhancing heat transmission in a linear manner. Figure 16a,b show the streamline flow patterns for suction and injection situations, respectively. For suction and injection scenarios, we look at different line patterns. ...
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... suction and injection scenarios, we look at different line patterns. The streamline flow pattern for the stretched boundaries is shown in Figure 16a,b for varied levels of mass transpiration Vc while other parameters remain constant. When wall suction occurs at specific locations, as predicted by the physical theory, the flow field becomes regularized. ...
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... the other hand, blowing (flow injection) eliminates the streamline in the circular shape. Figure 17 indicates the effect of the skin friction coefficient on the stretching/shrinking surface λ as a function of couple stress Λ , respectively. ...
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... it is noticed that the couple stress parameter is the reciprocal of thickness decreasing of the boundary layer occurs via the same process. While skin friction is linearly proportional to the thickness of the boundary layer, it is estimated to have an inverse proportionality λ , as depicted in Figure 17. In addition, upward pulling couple stress parameters will draw fluid toward the negative y direction and reduce skin friction. ...
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... thickness of the boundary layer will decrease when the suction parameter, which measures the strength of wall suction, is increased, and as a result, the gradient of the velocity on the wall will also increase. This impact will enhance skin friction, as shown in Figure 17. Figure 18 shows the effect of the skin friction coefficient on couple stress Λ as a function of the stretching/shrinking surface λ , respectively. ...
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... impact will enhance skin friction, as shown in Figure 17. Figure 18 shows the effect of the skin friction coefficient on couple stress Λ as a function of the stretching/shrinking surface λ , respectively. Here, it should be noted that the process of the decrease of the boundary layer's thickness and the stretching/shrinking surface parameter are the same. ...
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... it should be noted that the process of the decrease of the boundary layer's thickness and the stretching/shrinking surface parameter are the same. Skin friction is thought to have an inverse relationship with boundary layer thickness, as shown in Figure 18, even though the two are linearly proportional λ . Additionally, fluid will be drawn toward the negative y direction, and the skin friction will be decreased by the upward pulling couple stress parameters. ...
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The present study investigates the effect of mass transpiration on heat absorption/generation, thermal radiation and chemical reaction in the magnetohydrodynamics (MHD) Darcy–Forchheimer flow of a Newtonian fluid at the thermosolutal Marangoni boundary over a porous medium. The fluid region consists of H2O as the base fluid and fractions of TiO2–Ag...
Citations
... (iv) Induced magnetic field impact is disregarded in this work. Given the aforementioned presumptions, the appropriate conditions and fundamental equations required for this investigation are outlined below (Sneha et al. [37] and Pal and Mondal [38]): Through the utilisation of (5), the expression (3) may be reformulated as relates to a spherical shape, while 5.7 n relates to a platelet shape. Pal and Mondal [38] provided the succeeding similarity transmutations for converting governing equations: ...
The study of fluid flow over an inclined flat plate finds applications in a diverse range of engineering fields including aerodynamics, energy production and automotive design. This study theoretically investigates the steady and radiative flow of a ternary hybrid nanofluid (Water + TiO 2 + CoFe 2 O 4 + MgO ) with couple stress, using the Darcy-Forchheimer model. The flow occurs through a tilted flat plate and is subjected to irregular heat source parameter and entropy generation. The problem’s equations have been transformed into a collection of ordinary differential equations (ODEs), which has been skillfully resolved using the bvp4c solver. Graphs are utilized to elucidate outcomes for two instances of shape components, namely platelet and spherical. An escalation in the couple stress parameter (S) is demonstrated to be inversely related to the fluid velocity, resulting in a drop. Specifically, when 0.5 ≤ S ≤ 3, the friction factor exhibits a decline, with rates of 0.306201851 (for Platelet shape) and 0.304466755 (for Spherical shape). An intriguing observation reveals an augmentation in the generation of entropy as the volumetric fraction of TiO 2 rises. Upon investigation, it has been determined that when the Eckert number ( Ecn ) increases within the range of 0 ≤ Ecn ≤ 0.3, there is a significant reduction in the Nusselt number. Specifically, the decline is measured to be 0.328685192 for the platelet shape and 0.308939422 for the spherical shape. The utility of the Forchheimer number in regulating the fluid’s motion has been unveiled.
... Walter's B ternary nanoliquids (Ag-SWCNTs-graphene/water) and second-grade nanoliquids (Ag-SWCNTs-graphene) were studied in two dimensions for the effects of nonlinear thermal radiation by Marianna et al. [19]. The unstable pair stress flow via a tri-hybrid nanofluid on a stretching and contracting surface with a porous medium was reported by Sneha et al. [20]. Tri-hybrid nanofluid was created by combining three distinct microspheres: graphene, single-wall carbon nanotubes, and Al 2 O 3 . ...
This investigation aims to determine the existence of a dual solution in magnetohydrodynamic (MHD) thermal radiative tri-hybrid nanofluid flow over an exponential shrinking surface by considering mass suction effects at the surface. Furthermore, the impacts of Smoluchowski temperature and Maxwell velocity effects are taken into account. The products on various flow fields are examined for three different types of fluid: mono nanofluid ($Fe_3O_4$/$H_2O$), hybrid nanofluid ( $Fe_3O_4$-$Al_2O_3$/$H_2O$), and tri-hybrid nanofluid ($Fe_3O_4$-$Al_2O_3$-$Cu$/$H_2O$). Estimating entropy production is also included in the current work. The similarity transformation is used to translate the nonlinear partial differential equations (PDEs) into a set of ordinary differential equations (ODEs). The numerical MATLAB function bvp4c is utilized in the construction and solution of governing higher-order nonlinear ODEs. The stability of these numerical solutions is achieved by finding the lowest eigenvalue because of the duality present in the solutions. A minimum eigenvalue that is positive denotes the upper stable solution branch, whereas a minimal eigenvalue that is negative indicates the bottom unstable solution branch. A tabular and graphic analysis is conducted on the impact of emergent factors on temperature, skin friction coefficient, Nusselt number, entropy generation, etc. The results also demonstrate that when mono nanofluid changes to hybrid nanofluid and hybrid nanofluid to tri-hybrid nanofluid, the velocity and profile improve. It has been demonstrated that the fluid's temperature and the pace at which heat is transferred are greatly influenced by the thermal radiation parameter. The magnetic field aggravates flow in the case of a stable solution. The production of entropy is also accelerated considerably by thermal radiation. The current optimization technique offers a new and beneficial insight into the production of plastic films, heat exchangers, polymer sheets, crude oil, and electronic devices. Therefore, it is advised to use the results to create an industrial device setup.
... Mahmood et al. [19] shown the great usefulness of Cu-T iO 2 -Al 2 O 3 / polymer ternary hybrid nanofluid unstable stagnation point flow near stretching/shrinking surfaces, including heat generation/ absorption and velocity slip. On a stretching and contracting surface with porous media, Sneha et al. [20] described the unsteady flow of pair stress via a ternary hybrid nanofluid. They combined three different microspheres-Al 2 O 3 , single wall carbon nanotubes, and graphene-into a ternary hybrid nanofluid. ...
... If we take τ = 0 we obtain the steady-state solution f (η) = f 0 (η), and θ(η) = θ 0 (η), of Eqs. (19)- (20). Hence, f 0 (η) and θ 0 (η) are the model problem's basic steady-state solution, and γ is the unknown eigenvalue needed to determine. ...
This investigation aims to determine the existence of a dual solution in magne-tohydrodynamic (MHD) mixed convective radiative ternary hybrid nanofluid flow in a permeable Darcy-Forchheimer porous medium over an exponential shrinking surface by considering velocity & thermal slips and suction effects at the surface. The impacts for three types of fluid, namely, the mono nanofluid ( Cu/H 2 O ), hybrid nanofluid ( Cu-Ag/H 2 O ), and ternary hybrid nanofluid ( Cu-Ag-Al 2 O 3 /H 2 O ) are analyzed on different flow fields. The current work also addresses estimating entropy production to light on its innovative use in coolant applications. The nonlinear partial differential equations (PDEs) are converted into a set of ordinary differential equations (ODEs) using similarity transformation. Governing higher-order nonlin-ear ODEs are constructed and solved using the bvp4c numerical MATLAB function. Due to the presence of duality in the numerical solutions, the stability of these solutions is performed by locating the lowest eigenvalue. A positive minimum eigenvalue represents the upper stable solution branch, while a negative minimal eigenvalue represents the lower unstable solution branch. The effects of emergent variables on entropy generation and velocity, temperature, skin friction coefficient, and Nusselt number are analyzed graphically and in tabular form. The findings also show that the velocity profile improves when mono nanofluid transitions to hybrid nanofluid. However, it swiftly degrades for a ternary hybrid nanofluid medium for both solution branches. The temperature rises as we transition from mono to hybrid and from hybrid to ternary nanofluid medium. It has been shown that the thermal radiation Preprint submitted to 26 October 2023 parameter significantly influences the fluid’s temperature and the heat transfer rate. In the event of a stable solution, the increment in the Forchheimer number slows the flow of the liquid and is exacerbated by the magnetic field. Thermal radiation also significantly speeds up the creation of entropy. The present optimization method provides a fresh, advantageous perspective on the manufacture of polymer sheets, glass fiber, crude oil, plastic films, heat exchangers, and electronic gadgets. Hence, the obtained results are recommended for developing industrial device setup.
... Additionally, there is a substantial increase of 88.12% in the streamline patterns, as well as notable enhancements in Nusselt numbers and isotherms. The article by Sneha et al. [29] elucidates the dynamics of an unsteady flow involving a couple of stresses through the implementation of a ternary hybrid nanosuspension on a stretching sheet accompanied by porous material. Few other significant works using ternary hybrid nanofluids are presented in papers by Hafeez et al. [30], Adnan and Ashraf [31], Al Oweidi et al. [32], Puneeth et al. [33], and Mahmood and Khan [34]. ...
In this study, mathematical modeling of the energy transfer and flow characteristics of ternary nanoliquid in a square enclosure is performed. In the cavity considered, the left and bottom borders are warmed uniformly or non-uniformly when the rest of the borders are cooled. The robust finite element method with quads and triangles as elements is used to work out the control equations of the problem. The current study is validated against previously published works, and good agreement is shown. The isolines are investigated for various Rayleigh numbers at uniform and non-uniform thermal boundary conditions. The impact of ternary hybrid nanofluids on the mean Nusselt number at hot borders is explored in dependence on the Rayleigh number and nanoparticle concentration. A comparative study of different fluids for the mean Nusselt number at heated borders is also conducted and analyzed with appropriate graphs and tables. It has been shown that ternary nanofluids can be more effective compared to mono- and hybrid nanofluids, with a more essential growth of the energy transport rate with nanoadditives concentration.
... Souayeh et al. [20] studied flow of metallic (Ag + Au + Cu/H 2 O) ternary hybrid nanofluid on an exponentially stretching sheet and found that Brownian motion parameter and activation energy increase the temperature profile. Unsteady couple stress flow of ternary hybrid nanofluids using porous media was explored by Sneha et al. [21]. They studied impacts of various shapes of nanoparticles on fluid flow. ...
... Adun et al. [27] investigated various aspects of ternary hybrid nanofluid and their effect on fluid. The effect of ternary hybrid nanoparticles on radiative couple stress fluid moving subjected to a porous medium along with convective boundary conditions was investigated in detail by Sneha et [28]. Goud et al. [29] investigated variable thermal conductivity impact on THNF moving inside the dovetail fin. ...
... TETHNF Hamilton and Crosser nanofluid model are bestowed by Refs. [27,28]: ...
... Convective energy transport in a ternary nanofluid that is moving over a stretching plate was theoretically explored by Manjunatha et al. [26]. Other related recent works can be found in [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. ...
In the field of convective energy transfer, natural convection is one of the most studied phenomena, with applications ranging from heat exchangers and geothermal energy systems to hybrid nanofluids. The aim of this paper is to scrutinize the free convection of a ternary hybrid nanosuspension (Al2O3-Ag-CuO/water ternary hybrid nanofluid) in an enclosure with a linearly warming side border. The ternary hybrid nanosuspension motion and energy transfer have been modelled by partial differential equations (PDEs) with appropriate boundary conditions by the single-phase nanofluid model with the Boussinesq approximation. The finite element approach is applied to resolve the control PDEs after transforming them into a dimensionless view. The impact of significant characteristics such as the nanoparticles’ volume fraction, Rayleigh number, and linearly heating temperature constant on the flow and thermal patterns combined with the Nusselt number has been investigated and analyzed using streamlines, isotherms, and other suitable patterns. The performed analysis has shown that the addition of a third kind of nanomaterial allows for intensifying the energy transport within the closed cavity. The transition between uniform heating to non-uniform heating of the left vertical wall characterizes the heat transfer degradation due to a reduction of the heat energy output from this heated wall.
... Adun et al. [16] investigated various aspects of ternary hybrid nanofluid and their effect on fluid. Sneha et al. [17] conducted an in-depth examination of the influence that ternary nanocomposites have now upon radiative couple stress liquid traveling through a permeable material. Goud et al. [18] investigated variable thermal conductivity impact on THNFs moving inside the dovetail fin. ...
... Physical BCs are linked with the system of PDEs TETHNF Hamilton and Crosser nanofluid model are bestowed by Refs. [17,18]: ...
Ethanol and biodiesel, which both belong to the first generation of biofuel technology, are the two most popular forms of biofuels now in use. In order to create next-generation biofuels using waste, cellulosic biomass, and algae-based resources, the Bioenergy Technologies Office (BETO) is working with business. The present article is designed to study the effect of tetra hybrid nanoparticles with the utilization of the novel Hamilton and Crosser model and catalytic reaction on binary fluid with the consideration of ethanol biofuel as a base fluid. Ethanol comprising tetra hybrid nanoparticles and heterogeneous catalytic reaction amplifies thermal conductivity and significantly increases brake thermal efficiency and reduces brake-specific fuel consumption in diesel engines. Therefore, the aim of this article is a theoretical checkup that is related to heat and mass transport of biofuel flow considering binary fluid accompanied with autocatalysis reaction and novel tetra hybrid nanoparticles on biofluid flow subjected to a Riga wedge. Transportation of heat via nonuniform heat source/sink, thermal radiation, and thermal conductivity are in our consideration. The mathematics of the assumed problem generates the system of non-linear partial differential equations from basic equations of momentum, energy, and mass. The usage of non-dimensional variables gave a system of non-linear ODEs with boundary conditions which are further dealt with in the Lobatto111A scheme. The results are obtained for stretching/shrinking wedge with several parameters. From obtained results, it is observed that the velocity field diminishes owing to magnification in Weissenberg number and Casson fluid parameter. The temperature field diminishes by amplifying heat generation, thermal radiation, and variable thermal conductivity parameter. Concentration distribution escalates by rising homogeneous reaction parameters.
... Currently, Maranna [9] scrutinizes the role of heat radiation, mass suction or blowing, as well as Marangoni barrier constraints, on the stream of ternary nanoparticles in a permeable material. Besides straightening surfaces with penetrable materials, there is an unstable motion of coupled stress through a tnfs, as researched by Sneha [10]. Furthermore, because of their significant qualities that increase heat transfer rates, nanoparticles are frequently used in production and for industrial purposes. ...
Due to its extensive applicability and employment in different systems, the study of thermal transport is a significant area of research. The main goal of this investigation is to analyse the impact of thermal radiation as well as the Navier-Stokes condition upon the two-dimensional flow of second-grade as well as Walter's B ternary nanoliquids through a permeable shrinking flat surface. The phrase “ternary nanofluid” refers to a suspension of three different types of nanoparticles, notably silver (Ag), SWCNTs, and graphene particles, in water as the base fluid. The inverse Darcy phenomenon has an effect on the momentum equation as well. The energy equation also accounted for nonlinear thermal radiations as well as heat source and sink components. The phenomenon is portrayed as a nonlinear system of partial differential equations. The model equations are transformed into a non-dimensional series of ordinary differential equations by replacing similarity. Afterwards, the transformed ODEs were tackled analytically in order to establish an analytical solution of the energy equation in terms of a confluent hyper-geometric function by utilizing similarity conversion. This research reveals that the velocity field is reduced significantly by the slip parameter. The benefits of a few emerging factors, such as the viscoelastic parameter, inverse Darcy number, slip parameter, solid volume fraction, radiation, Prandtl number, and skin friction coefficient effects on solution, have been displayed through plots and discussed. Additionally, it has been concluded from this analysis that ternary nanofluids have a higher thermal flow rate than hybrid or standard nanofluids.
... Khan et al. [14] looked at a nanofluid made of silver and water and found that the silver nanofluid was a better conductor and moved heat well. Several noteworthy works on nanofluids are provided in the following references [15][16][17][18][19]. Daniel et al. [20] investigated a solution for nanofluid flow stretching when the MHD electrical effect is executed with ohmic heating. ...
Citation: Lund, L.A.; Chandio, A.F.; Vrinceanu, N.; Yashkun, U.; Shah, Z.; Alshehri, A. Darcy-Forchheimer Magnetized Nanofluid flow along with Heating and Dissipation Effects over a Shrinking Exponential Sheet with Stability Analysis. Micromachines 2023, 14, 106. https:// Abstract: Nanoparticles have presented various hurdles to the scientific community during the past decade. The nanoparticles dispersed in diverse base fluids can alter the properties of fluid flow and heat transmission. In the current examination, a mathematical model for the 2D magnetohydro-dynamic (MHD) Darcy-Forchheimer nanofluid flow across an exponentially contracting sheet is presented. In this mathematical model, the effects of viscous dissipation, joule heating, first-order velocity, and thermal slip conditions are also examined. Using similarity transformations, a system of partial differential equations (PDEs) is converted into a set of ordinary differential equations (ODEs). The problem is quantitatively solved using the three-step Lobatto-three formula. This research studied the effects of the dimensionlessness, magnetic field, ratio of rates, porosity, Eckert number, Prandtl number, and coefficient of inertia characteristics on fluid flow. Multiple solutions were observed. In the first solution, the increased magnetic field, porosity parameter, slip effect, and volume percentage of the copper parameters reduce the velocity field along the η-direction. In the second solution, the magnetic field, porosity parameter, slip effect, and volume percentage of the copper parameters increase the η-direction velocity field. For engineering purposes, the graphs show the impacts of factors on the Nusselt number and skin friction. Finally, the stability analysis was performed to determine which solution was the more stable of the two.
