Effects of temperature-dependent viscosity and variable thermal conductivity on MHD non-Darcy mixed convective diffusion of species over a stretching sheet

A numerical model is presented to study the effects of temperature-dependent viscosity and variable thermal conductivity on mixed convection problem. Two important types of wall heating conditions namely, prescribed surface temperature and prescribed wall heat flux which arise in polymer industries are considered. The problem is solved numerically by using the fifth-order Runge–Kutta Fehlberg method with shooting technique. It is found that the Prandtl number is to decrease the skin friction coefficient, local Nusselt number and local Sherwood number. The effects of non-uniform heat source/sink and porous parameter are analyzed on velocity, temperature, skin friction co-efficient, Nusselt and Sherwood numbers.     

Mixed convection magnetohydrodynamic heat and mass transfer past a stretching surface in a micropolar fluid-saturated porous medium under the influence of Ohmic heating,Soret and Dufour effects

A numerical model is developed to examine the combined effects of Soret and Dufour on mixed convection magnetohydrodynamic heat and mass transfer in micropolar fluid-saturated Darcian porous medium in the presence of thermal radiation, non-uniform heat source/sink and Ohmic dissipation. The governing boundary layer equations for momentum, angular momentum (microrotation), energy and species transfer are transformed to a set of non-linear ordinary differential equations by using similarity solutions which are then solved numerically based on shooting algorithm with Runge–Kutta–Fehlberg integration scheme over the entire range of physical parameters with appropriate boundary conditions. The influence of Darcy number, Prandtl number, Schmidt number, Soret number and Dufour number, magnetic parameter, local thermal Grashof number and local solutal Grashof number on velocity, temperature and concentration fields are studied graphically. Finally, the effects of related physical parameters on local Skin-friction, local Nusselt number and local Sherwood number are also studied. Results showed that the fields were influenced appreciably by the Soret and Dufour effects, thermal radiation and magnetic field, etc.     

Effect of Hall currents and chemical reaction on hydromagnetic flow of a stretching vertical surface with internal heat generation/absorption

The problem of steady, laminar, hydromagnetic, simultaneous heat and mass transfer by laminar flow of a Newtonian, viscous, electrically conducting and heat generating/absorbing fluid over a continuously stretching surface in the presence of the combined effect of Hall currents and mass diffusion of chemical species with first and higher order reactions is investigated. The fluid is permeated by a strong transverse magnetic field imposed perpendicularly to the plate on the assumption of a small magnetic Reynolds number. Certain transformations are employed to transform the governing differential equations to a local similarity form which are solved numerically. Comparisons with previously published work have been conducted and the results are found to be in good agreement. A parametric study is performed to illustrate the influence of the magnetic field parameter, Hall parameter, the coefficients of space-dependent and temperature-dependent internal heat generation/absorption, the chemical reaction parameter and order of reaction on the fluid velocity, temperature and concentration distributions. Numerical data for the local skin-friction coefficient, the local Nusselt number and the local Sherwood number have been tabulated for various values of parametric conditions.     

MHD non-Darcy mixed convective diffusion of species over a stretching sheet embedded in a porous medium with non-uniform heat source/sink, variable viscosity and Soret effect

The effects of temperature dependent viscosity and non-uniform heat source/sink on non-Darcy MHD mixed convection boundary layer flow over a vertical stretching sheet embedded in a fluid-saturated porous media is studied in this paper. Boundary layer equations are transformed into ordinary differential equations using self-similarity transformation which are then solved numerically using fifth-order Runge-Kutta-Fehlberg method with shooting technique for various values of the governing parameters. The effects of variable viscosity, porosity, electric field parameter, non-uniform heat source/sink parameters, Soret number and Schmidt number on concentration profiles are analyzed and discussed. Favorable comparisons with previously published work on various special cases of the problem are obtained. Numerical results for variation of the local Sherwood number with buoyancy parameter, Schmidt number, and Soret number are reported graphically to show some interesting aspects of the physical parameters.     

Soret and Dufour effects on MHD slip flow with thermal radiation over a porous rotating infinite disk

In this investigation, thermal radiation effect over an electrically conducting, Newtonian fluid in a steady laminar magnetohydrodynamic convective flow over a porous rotating infinite disk with the consideration of heat and mass transfer in the presence of Soret and Dufour diffusion effects is investigated. The partial differential equations governing the problem under consideration are transformed by a similarity transformation into a system of ordinary differential equations which are solved numerically using fourth order Runge–Kutta based shooting method. The effects of the magnetic interaction parameter, slip flow parameter, Soret number, Dufour number, Schmidt number, radiation parameter, Prandtl number and suction parameter on the fluid velocity, temperature and concentration distributions in the regime are depicted graphically and are analyzed in detail. The corresponding skin-friction coefficients, the Nusselt number and the Sherwood number are also calculated and displayed in tables showing the effects of various parameters on them.     

Nonsimilar boundary layer analysis of double-diffusive convection from a vertical truncated cone in a porous medium with variable viscosity

This work presents a boundary layer analysis about variable viscosity effects on the double-diffusive convection near a vertical truncated cone in a fluid-saturated porous medium with constant wall temperature and concentration. The viscosity of the fluid is assumed to be an inverse linear function of the temperature. A boundary layer analysis is employed to derive the nondimensional nonsimilar governing equations, and the transformed boundary layer governing equations are solved by the cubic spline collocation method to yield computationally efficient numerical solutions. The obtained results are found to be in good agreement with previous papers on special cases of the problem. Results for local Nusselt and Sherwood numbers are presented as functions of viscosity-variation parameter, buoyancy ratio, and Lewis number. For a porous medium saturated with a Newtonian fluid with viscosity proportional to an inverse linear function of temperature, higher value of viscosity-variation parameter leads to the decrease of the viscosity in fluid flow, thus increasing the fluid velocity as well as the local Nusselt number and the local Sherwood number.     

Nonsimilar solutions for double-diffusion boundary layers on a sphere in micropolar fluids with constant wall heat and mass fluxes

This work presents nonsimilar boundary layer solutions for double-diffusion natural convection near a sphere with constant wall heat and mass fluxes in a micropolar fluid. A coordinate transformation is employed to transform the governing equations into nondimensional nonsimilar boundary layer equations and the obtained boundary layer equations are then solved by the cubic spline collocation method. Results for the local Nusselt number and the local Sherwood number are presented as functions of the vortex viscosity parameter, Schmidt number, buoyancy ratio, and Prandtl number. Higher vortex viscosity tends to retard the flow, and thus decreases the local convection heat and mass transfer coefficients, raising the wall temperature and concentration. Moreover, the local convection heat and mass transfer coefficients near a sphere in Newtonian fluids are higher than those in micropolar fluids.     

Effect of double stratification on MHD free convection in a micropolar fluid

This paper analyzes the flow and heat and mass transfer characteristics of the free convection on a vertical plate with variable wall temperature and concentration in a doubly stratified micropolar fluid. A uniform magnetic field is applied normal to the plate. The governing non-linear partial differential equations are transformed into a system of coupled non-linear ordinary differential equations using similarity transformations and then solved numerically using the Keller-box method. The numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. The non-dimensional velocity, microrotation, temperature and concentration are presented graphically for various values of magnetic parameter, coupling number, thermal and solutal stratification parameters. In addition, the Nusselt number, the Sherwood number, the skin-friction coefficient, and the wall couple stress are shown in a tabular form.     

Viscous dissipation and Joule heating effects on MHD-free convection from a vertical plate with power-law variation in surface temperature in the presence of Hall and ion-slip currents

An analysis is presented to study the effects of viscous dissipation and Joule heating on MHD-free convection flow past a semi-infinite vertical flat plate in the presence of the combined effect of Hall and ion-slip currents for the case of power-law variation of the wall temperature. The fluid is permeated by a strong transverse magnetic field imposed perpendicularly to the plate on the assumption of a small magnetic Reynolds number. The governing differential equations are transformed by introducing proper non-similarity variables and solved numerically. The effects of various parameters on the velocity and temperature profiles as well as the local wall shear stresses and the local Nusselt number are presented graphically and in tabular form. It is found that the magnetic field acts as a retarding force on the tangential flow but has a propelling effect on the induced lateral flow. The skin-friction factor for the tangential flow and the local Nusselt number decrease but the skin-friction factor for the lateral flow increases as the magnetic field increases. The skin-friction factor for the tangential and lateral flows are increased while the local Nusselt number is decreased if the effect of viscous dissipation, Joule heating and heat generation are considered. The opposite trend was observed as the temperature power coefficient n is increased. Also, the skin-friction factor for the tangential flow and the local Nusselt number are increased due to the Hall and ion-slip currents, whereas the skin-friction factor for the tangential flow increases when Hall values increase to one and decreases for values of Hall greater than one, but reduces by rising ion-slip values.     

Non-Darcy free convection flow over a horizontal cylinder in a saturated porous medium with variable viscosity,thermal conductivity and mass diffusivity

In this paper, the effects of variable viscosity and thermal conductivity on coupled heat and mass transfer by free convection about a permeable horizontal cylinder embedded in porous media using Ergun mode are studied. The fluid viscosity and thermal conductivity and are assumed to vary as a linear function of temperature while the mass diffusion is assumed to vary as linear function of concentration. The surface of the horizontal cylinder is maintained at a uniform wall temperature and a uniform wall concentration. The transformed governing equations are obtained and solved by using the implicit finite difference method. Numerical results for dimensionless temperature and concentration profiles as well as Nusselt and Sherwood numbers are presented for various values of parameters namely, Ergun number, transpiration parameter, Rayleigh and Lewis numbers and buoyancy ratio parameter.     

Study of hydromagnetic heat and mass transfer flow over an inclined heated surface with variable viscosity and electric conductivity

The effects of variable electric conductivity and temperature dependent viscosity on hydromagnetic heat and mass transfer flow along a radiate isothermal inclined permeable surface in a stationary fluid in the presence of internal heat generation (or absorption) are analyzed numerically presenting local similarity solutions for various values of the physical parameters. The research shows that the difference in the results between variable Prandtl number and constant Prandtl number are significant when fluid viscosity strongly dependents on the temperature. The results also show that skin friction coefficient, Nusselt number and Sherwood number are lower for the fluids of constant electric conductivity than those of the variable electric conductivity.     

竖直平板嵌入非Darcy多孔介质时,数值研究流过平板的不稳定MHD自然对流中的Dufour和Soret效应

就竖直平板嵌入非Darcy多孔介质中,导电流体流过平板时作不稳定的二维磁流体(MHD)双扩散对流,数值研究了Dufour和Soret效应对流动的影响.用Crank-Nicolson型的隐式有限差分法,按三对角矩阵处理,求解无量纲的非线性控制方程.详细地研究了问题中出现的各种参数对不稳定无量纲的速度、温度和浓度曲线的影响.进一步地,给出并分析了表面摩擦因数、Nus-selt数和Sherwood数随时间的变化.研究结果表明,不稳定速度、温度和浓度分布曲线,受Dufour和Soret的影响十分显著.随着Dufour数的增加或者Soret数的减小,表面摩擦因数和Sherwood数都在减小,而Nusselt数在增加.研究发现,当磁场参数增加时,边界层中的速度和温度在减小.     

Natural convection boundary layer flow of fluid with temperature-dependent viscosity from a horizontal elliptical cylinder with constant surface heat flux

This study deals with the temperature-dependent viscosity effects on the natural convection boundary layer on a horizontal elliptical cylinder with constant surface heat flux. The mathematical problem is reduced to a pair of coupled partial differential equations for the temperature and the stream function, and the resulting nonlinear equations are solved numerically by cubic spline collocation method. Results for the heat transfer characteristics are presented as functions of eccentric angle for various values of viscosity variation parameters, Prandtl numbers and aspect ratios. Results show that an increase in the viscosity variation parameter tends to accelerate the fluid flow near the surface and increase the maximum velocity, thus decreasing the velocity boundary layer thickness. As the viscosity variation parameter is increased, the surface temperature tends to decrease, thus increasing the local Nusselt number. Moreover, the local Nusselt number of the elliptical cylinder increases as the Prandtl number of the fluid is increased.     

The effect of variable viscosity on MHD viscoelastic fluid flow and heat transfer over a stretching sheet

An analysis has been carried out to study the momentum and heat transfer characteristics in an incompressible electrically conducting non-Newtonian boundary layer flow of a viscoelastic fluid over a stretching sheet. The partial differential equations governing the flow and heat transfer characteristics are converted into highly non-linear coupled ordinary differential equations by similarity transformations. The effect of variable fluid viscosity, Magnetic parameter, Prandtl number, variable thermal conductivity, heat source/sink parameter and thermal radiation parameter are analyzed for velocity, temperature fields, and wall temperature gradient. The resultant coupled highly non-linear ordinary differential equations are solved numerically by employing a shooting technique with fourth order Runge–Kutta integration scheme. The fluid viscosity and thermal conductivity, respectively, assumed to vary as an inverse and linear function of temperature. The analysis reveals that the wall temperature profile decreases significantly due to increase in magnetic field parameter. Further, it is noticed that the skin friction of the sheet decreases due to increase in the Magnetic parameter of the flow characteristics.     

MHD flow and heat transfer of a micropolar fluid over a stretching surface with heat generation (absorption) and slip velocity

In this work, the effects of slip velocity on the flow and heat transfer for an electrically conducting micropolar fluid over a permeable stretching surface with variable heat flux in the presence of heat generation (absorption) and a transverse magnetic field are investigated. The governing partial differential equations describing the problem are converted to a system of non-linear ordinary differential equations by using the similarity transformation, which is solved numerically using the Chebyshev spectral method. The effects of the slip parameter on the flow, micro-rotation and temperature profiles as well as on the local skin-friction coefficient, the wall couple stress and the local Nusselt number are presented graphically. The numerical results of the local skin-friction coefficient, the wall couple stress and the local Nusselt number are given in a tabular form and discussed.     

Effects of Soret Dufour,chemical reaction and thermal radiation on MHD non-Darcy unsteady mixed convective heat and mass transfer over a stretching sheet

A study has been carried out to analyze the combined effects of Soret (thermal-diffusion) and Dufour (diffusion-thermo) on unsteady MHD non-Darcy mixed convection over a stretching sheet embedded in a saturated porous medium in the presence of thermal radiation, viscous dissipation and first-order chemical reaction. Energy equation takes into account of viscous dissipation, thermal radiation and Soret effects. The governing differential equations are transformed into a set of non-linear coupled ordinary differential equations and solved using similarity analysis with numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing nonlinear boundary value problem is based on shooting algorithm with Runge–Kutta–Fehlberg integration scheme over the entire range of physical parameters. The effects of various physical parameters on the dimensionless velocity, temperature and concentration profiles are depicted graphically and analyzed in detail. Favorable comparisons with previously published work on various special cases of the problem are obtained. Numerical results for local skin-friction, local Nusselt number, and local Sherwood number are tabulated for different physical parameters.     

Convective heat and mass transfer in three-dimensional mixed convection flow of viscoelastic fluid in presence of chemical reaction and heat source/sink

Heat and mass transfer effects in the three-dimensional mixed convection flow of a viscoelastic fluid with internal heat source/sink and chemical reaction have been investigated in the present work. The flow generation is because of an exponentially stretching surface. Magnetic field normal to the direction of flow is considered. Convective conditions at the surface are also encountered. Appropriate similarity transformations are utilized to reduce the boundary layer partial differential equations into the ordinary differential equations. The homotopy analysis method is used to develop the solution expressions. Impacts of different controlling parameters such as ratio parameter, Hartman number, internal heat source/sink, chemical reaction, mixed convection, concentration buoyancy parameter and Biot numbers on the velocity, temperature and concentration profiles are analyzed. The local Nusselt and Sherwood numbers are sketched and examined.     

Heat and mass transfer in MHD free convection from a moving permeable vertical surface by a perturbation technique

Numerical results are presented for heat and mass transfer effect on hydromagnetic flow of a moving permeable vertical surface. An analysis is performed to study the momentum, heat and mass transfer characteristics of MHD natural convection flow over a moving permeable surface. The surface is maintained at linear temperature and concentration variations. The non-linear coupled boundary layer equations were transformed and the resulting ordinary differential equations were solved by perturbation technique [Aziz A, Na TY. Perturbation methods in heat transfer. Berlin: Springer-Verlag; 1984. p. 1–184; Kennet Cramer R, Shih-I Pai. Magneto fluid dynamics for engineers and applied physicists 1973;166–7]. The solution is found to be dependent on several governing parameter, including the magnetic field strength parameter, Prandtl number, Schmidt number, buoyancy ratio and suction/blowing parameter, a parametric study of all the governing parameters is carried out and representative results are illustrated to reveal a typical tendency of the solutions. Numerical results for the dimensionless velocity profiles, the temperature profiles, the concentration profiles, the local friction coefficient and the local Nusselt number are presented for various combinations of parameters.     

Similarity solution in MHD: Effects of thermal diffusion and diffusion thermo on free convective heat and mass transfer over a stretching surface considering suction or injection

An analysis is carried out to study free convective heat and mass transfer of an incompressible, electrically conducting fluid over a stretching sheet in the presence of suction and injection with thermal-diffusion (Soret) and diffusion-thermo (Dufour) effects. The similarity solutions are obtained using scaling transformations. Furthermore, the similarity equations are solved numerically by using shooting technique with fourth-order Runge–Kutta integration scheme. A comparison with previously published work is performed and the results are found to be in good agreement. Numerical results of the local skin friction coefficient, the local Nusselt number and the local Sherwood number as well as the velocity, the temperature and the concentration profiles are presented for different physical parameters. The result indicates: (i) for fluids with medium molecular weight (H₂, air), Dufour and Soret effects should not be neglected; and (ii) the suction and injection parameter has significant impact in controlling the rate of heat transfer in the boundary layer.     

粘性导电流体在磁场作用下流过多孔通道时传热传质振荡流的数值解——用于病理状态动脉中血液的流动

当血管内壁出现多孔性结构时,流过多孔性血管的血液将作不稳定的MHD流动.研究血液在其中的传热传质问题,考虑了与时间相关的渗透率和振荡引起的吸入速度,并数值地求解该问题.对分析中出现的参数取不同数值时,图形给出了速度、温度、浓度场,以及表面摩擦因数、Nusselt数和Sherwood数的计算结果.研究表明,血液流动受磁场和Grashof数的影响明显.