Effects of slip condition and Newtonian heating on MHD flow of Casson fluid over a nonlinearly stretching sheet saturated in a porous medium

Ullah, Imran; Shafie, Sharidan; Khan, İlyas

doi:10.1016/j.jksus.2016.05.003

Cited by 128 publications

(68 citation statements)

References 36 publications

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“…Under the above‐made conditions and assumptions, the respective governing equations of the momentum, diffusion, and concentration take the following form:

\frac{\partial u}{\partial t} = v true(1 + \frac{1}{β} true) \frac{\partial^{2} u}{\partial y^{2}} - true(σ \frac{{B_{0}}^{2}}{ρ} + \frac{ν}{μ_{0}} true) u + g β_{T} (T - T_{\infty}) + g β_{C} true(C - C_{\infty} true),

\frac{\partial T}{\partial t} = α \frac{\partial^{2} T}{\partial y^{2}} + \frac{D_{m} K_{T}}{C_{S} C_{P}} \frac{\partial^{2} C}{\partial y^{2}},

\frac{\partial C}{\partial t} = D_{m} \frac{\partial^{2} C}{\partial y^{2}} + \frac{D_{m} K_{T}}{T_{m}} \frac{\partial^{2} T}{\partial y^{2}} - L true(C - C_{\infty} true) .

…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…They found that the heat transfer capacity of the base fluid water is the least amongst the base fluids chosen. Ullah et al had explored the effects of convective boundary condition and slip parameter hydromagnetic Casson fluid flow in a porous medium past stretching sheet. Mixed convection Casson fluid flow about a sphere in the presence of chemical reaction in the system had been discussed by El‐Kabeir et al Recently, Shaw et al carried out the study on the Soret and Dufour effect, thermal and solutal Marangonic convection of a chemically reactive Casson fluid past a stretching sheet.…”

Section: Introductionmentioning

confidence: 99%

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Unsteady MHD chemically reactive double‐diffusive Casson fluid past a flat plate in porous medium with heat and mass transfer

Das

Mahanta

Shaw

et al. 2019

Heat Trans. Asian Res.

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In this paper, an attempt has been made to analyze the effects of various parameters, such as Soret and Dufour effects, chemical reaction, magnetic field, porosity on the fluid flow, and heat and mass transfer of an unsteady Casson fluid flow past a flat plate. Convective boundary conditions in heat and mass transfer and slip constant on velocity have been taken into account for analysis. The governing equations of the model have been solved numerically using the MATLAB program bvp4c. The impact of various parameters of the model on the velocity, temperature, and concentration profiles has been analyzed through different graphs. To get an insight into the physical quantities of engineering interest, viz, skin friction, Sherwood number, and Nusselt number, their numerical values have been computed for various parameters. The range of the parameters used in numerical computations are Pr (0.3-0.8), ( β 0.5-1.5), M (1-5), A (0.5-1.5), L (0.1-0.9) 0 , D (0.2-4) f , Sr (0.3-6.3), and Sc (0.05-0.15). It has been noticed from the tabulated values that the skin friction gets enhanced with the increase in the thermal and solutal Grashof number,whereas its reverse effects have been observed with an increase in the Biot number. In limiting case, the present study is also compared with the available results in the literature.

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“…Under the above‐made conditions and assumptions, the respective governing equations of the momentum, diffusion, and concentration take the following form:

\frac{\partial u}{\partial t} = v true(1 + \frac{1}{β} true) \frac{\partial^{2} u}{\partial y^{2}} - true(σ \frac{{B_{0}}^{2}}{ρ} + \frac{ν}{μ_{0}} true) u + g β_{T} (T - T_{\infty}) + g β_{C} true(C - C_{\infty} true),

\frac{\partial T}{\partial t} = α \frac{\partial^{2} T}{\partial y^{2}} + \frac{D_{m} K_{T}}{C_{S} C_{P}} \frac{\partial^{2} C}{\partial y^{2}},

\frac{\partial C}{\partial t} = D_{m} \frac{\partial^{2} C}{\partial y^{2}} + \frac{D_{m} K_{T}}{T_{m}} \frac{\partial^{2} T}{\partial y^{2}} - L true(C - C_{\infty} true) .

…”

Section: Mathematical Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Unsteady MHD chemically reactive double‐diffusive Casson fluid past a flat plate in porous medium with heat and mass transfer

Das

Mahanta

Shaw

et al. 2019

Heat Trans. Asian Res.

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“…The influence of thermal radiation on viscous incompressible between oblique walls was examined by Adnan et al [33]. For further useful study regarding Newtonian, non-Newtonian, and nanofluids while considering the various flow conditions in different geometries are presented in [34][35][36][37][38][39][40][41][42][43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

Applications of Nanofluids for the Thermal Enhancement in Radiative and Dissipative Flow over a Wedge

et al. 2019

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The colloidal analysis for H2O and EG (Ethylene Glycol) by considering the influence of radiative heat flux and viscous dissipation is not performed so far. This study is performed to fill up this gap. Therefore, the flow of water and ethylene glycol functionalized magnetite nanoparticles over a moving wedge is examined. For thermal enhancement, two different magnetite nanoparticles, namely CoFe 2 O 4 (Cobalt ferrite) and Mn − ZnFe 2 O 4 ( Mn − Zn ferrite), diluted in the base fluids. Self-similar flow model of a nonlinear nature, containing the volume fraction of nanoparticles is obtained by using compatible similarity variables. For mathematical treatment of the model, the Runge-Kutta scheme is utilized, coupled with shooting techniques. The results for flow characteristics and significant physical parameters are graphically examined. A comprehensive comparative analysis has been made, which proved the reliability of the study.

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“…Recently, many other researchers have considered non‐Newtonian fluids like the Oldroyd‐B fluid, micropolar, and Casson fluid . The Casson fluid is a shear thinning fluid, which shows yield stress . When the applied shear stress is not much more than the yield stress, then the behavior of the Casson fluid is like a solid.…”

Section: Introductionmentioning

confidence: 99%

Steady incompressible magnetohydrodynamics Casson boundary layer flow past a permeable vertical and exponentially shrinking sheet: A stability analysis

Lund

Omar

Khan

2019

Heat Trans. Asian Res.

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Steady incompressible magnetohydrodynamic mixed convection boundary layer flow of a Casson fluid on an exponentially vertical shrinking sheet using the non-Newtonian heating equation is investigated in this paper. There are three main objectives of this study, namely, to develop a new mathematical model, to obtain multiple solutions, and to perform stability analysis. The governing partial differential equations have been changed into nonlinear ordinary differential equations. The resultant equations of boundary value problems are then converted into the equivalent initial value problems using the shooting method before they can be solved using Runge-Kutta of order four. The numerical results are obtained and found to be in good agreement with the published literature. The results also indicate that the velocity boundary layer becomes thinner as the magnetic, slip, and Casson parameters increase. Dual solutions for temperature and velocity distributions are obtained. Furthermore, the results suggest that the presence of the force of buoyancy (opposing flow case) would cause the occurrence of dual solutions. However, based on the stability analysis, only the first solution is stable. K E Y W O R D S Casson fluid, dual solution, exponentially shrinking, magnetohydrodynamics, stability analysis

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Effects of slip condition and Newtonian heating on MHD flow of Casson fluid over a nonlinearly stretching sheet saturated in a porous medium

Cited by 128 publications

References 36 publications

Unsteady MHD chemically reactive double‐diffusive Casson fluid past a flat plate in porous medium with heat and mass transfer

Unsteady MHD chemically reactive double‐diffusive Casson fluid past a flat plate in porous medium with heat and mass transfer

Applications of Nanofluids for the Thermal Enhancement in Radiative and Dissipative Flow over a Wedge

Steady incompressible magnetohydrodynamics Casson boundary layer flow past a permeable vertical and exponentially shrinking sheet: A stability analysis

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