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.     

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.     

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.     

Influence of double stratification on MHD free convection with Soret and Dufour effects in a Darcian porous media

The heat and mass transfer characteristics of natural convection about a vertical surface embedded in a doubly stratified saturated porous medium subjected to a magnetic field is studied, taking into account the Dufour and Soret effects. It is found that the similarity solution exists for the case of uniform surface heat and mass flux conditions when the thermal and solutal stratification of the medium are assumed to have power function form x^1/3. The resulting set of ordinary coupled nonlinear differential equations is solved numerically using shooting technique. Nusselt and Sherwood numbers are tabulated for various values of the involved parameters. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

流经有热辐射的无限垂直多孔平板时非稳定MHD流动的Soret和Dufour效应

不可压缩粘性导电流体,流经无限垂直多孔平板,平板存在振荡吸入速度和热辐射时,研究流动参数对自由对流和传质的非稳定磁流体动力学流动的Dufour(扩散热)和Soret(热扩散)效应.应用有限单元法,数值求解该问题的速度、温度和浓度场,还得到了表面摩擦、传热传质率的表达式.数值结果以图表方式给出,对外表致冷的平板(Gr0)和外表加热的平板(Gr0),给出了该方程中所遇参数的影响.     

MHD mixed convection of a viscous dissipating fluid about a permeable vertical flat plate

The problem of steady laminar magnetohydrodynamic (MHD) mixed convection heat transfer about a vertical plate is studied numerically, taking into account the effects of Ohmic heating and viscous dissipation. A uniform magnetic field is applied perpendicular to the plate. The resulting governing equations are transformed into the non-similar boundary layer equations and solved using the Keller box method. Both the aiding-buoyancy mode and the opposing-buoyancy mode of the mixed convection are examined. The velocity and temperature profiles as well as the local skin friction and local heat transfer parameters are determined for different values of the governing parameters, mainly the magnetic parameter, the Richardson number, the Eckert number and the suction/injection parameter, f_w. For some specific values of the governing parameters, the results agree very well with those available in the literature. Generally, it is determined that the local skin friction coefficient and the local heat transfer coefficient increase owing to suction of fluid, increasing the Richardson number, Ri (i.e. the mixed convection parameter) or decreasing the Eckert number. This trend reverses for blowing of fluid and decreasing the Richardson number or decreasing the Eckert number. It is disclosed that the value of Ri determines the effect of the magnetic parameter on the momentum and heat transfer.     

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.     

MHD free convective flow through porous medium in the presence of hall current, radiation and thermal diffusion

An unsteady free convective flow through porous media of viscous, incompressible, electrically conducting fluid through a vertical porous channel with thermal radiation is studied. A magnetic field of uniform strength is applied perpendicular to the vertical channel. The magnetic Reynolds number is assumed very small so that the induced magnetic field effect is negligible. The injection and suction velocity at both plates is constant and is given by v ₀. The pressure gradient in the channel varies periodically with time along the axis of the channel. The temperature difference of the plates is high enough to induce the radiative heat. Taking Hall current and Soret effect into account, equations of motion, energy, and concentration are solved. The effects of the various parameters, entering into the problem, on velocity, temperature and concentration field are shown graphically.     

Uniform suction/blowing effect on flow and heat transfer due to a stretching cylinder

The present paper presents a numerical solution of flow and heat transfer outside a stretching permeable cylinder. The governing system of partial differential equations is converted to ordinary differential equations by using similarity transformations, which are then solved numerically using the Keller-box method. The main purpose of the present study is to investigate the effects of the governing parameters, namely the suction/injection parameter, Prandtl number, and Reynolds number on the velocity and temperature profiles as well as the skin friction coefficient and the Nusselt number. The results are shown graphically. The values of the skin friction coefficient and the Nusselt number are presented in tables.     

Lie group analysis for thermal-diffusion and diffusion-thermo effects on free convective flow over a porous stretching surface with variable stream conditions in the presence of thermophoresis particle deposition

A study has been carried out to obtain the solutions for heat and mass transfer from natural convection flow along a vertical surface with temperature-dependent fluid viscosity embedded in a porous medium due to thermal-diffusion (Soret) and diffusion-thermo (Dufour) effects. This paper concerns with a steady two-dimensional flow of incompressible fluid over a vertical stretching sheet. The fluid viscosity is assumed to vary as a linear function of temperature. A scaling group of transformations is applied to the governing equations. The impact of thermophoresis particle deposition with chemical reaction in the presence of thermal-diffusion and diffusion-thermo effects plays an important role on the temperature and concentration boundary layer. The results thus obtained are presented graphically and discussed.     

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.     

Similarity solutions for mixed convection boundary layer flow over a permeable horizontal flat plate

The effects of suction and injection on steady laminar mixed convection boundary layer flow over a permeable horizontal flat plate in a viscous and incompressible fluid is investigated in this paper. The similarity solutions of the governing boundary layer equations are obtained for some values of the suction and injection parameter f₀, the constant exponent n of the wall temperature as well as the mixed convection parameter λ. The resulting system of nonlinear ordinary differential equations is solved numerically for both assisting and opposing flow regimes using a finite-difference scheme known as the Keller-box method. Numerical results for the reduced skin friction coefficient, the reduced local Nusselt number, and the velocity and temperature profiles are obtained for various values of the parameters considered. Dual solutions are found to exist for the opposing flow.     

Combined effects of non-uniform heat source/sink and thermal radiation on heat transfer over an unsteady stretching permeable surface

The present paper is concerned with the study of flow and heat transfer characteristics in the unsteady laminar boundary layer flow of an incompressible viscous fluid over continuously stretching permeable surface in the presence of a non-uniform heat source/sink and thermal radiation. The unsteadiness in the flow and temperature fields is because of the time-dependent stretching velocity and surface temperature. Similarity transformations are used to convert the governing time-dependent nonlinear boundary layer equations for momentum and thermal energy are reduced to a system of nonlinear ordinary differential equations containing Prandtl number, non-uniform heat source/sink parameter, thermal radiation and unsteadiness parameter with appropriate boundary conditions. These equations are solved numerically by applying shooting method using Runge–Kutta–Fehlberg method. Comparison of numerical results is made with the earlier published results under limiting cases. The effects of the unsteadiness parameter, thermal radiation, suction/injection parameter, non-uniform heat source/sink parameter on flow and heat transfer characteristics as well as on the local Nusselt number are shown graphically.     

On the linear stability analysis of a Maxwell fluid with double-diffusive convection

The problem of double-diffusive convection and cross-diffusion in a Maxwell fluid in a horizontal layer in porous media is re-examined using the modified Darcy–Brinkman model. The effect of Dufour and Soret parameters on the critical Darcy–Rayleigh numbers is investigated. Analytical expressions of the critical Darcy–Rayleigh numbers for the onset of stationary and oscillatory convection are derived. Numerical simulations show that the presence of Dufour and Soret parameters has a significant effect on the critical Darcy–Rayleigh number for over-stability. In the limiting case some previously published results are recovered.     

Influence of temperature-dependent viscosity and thermal radiation on MHD forced convection over a non-isothermal wedge

An analysis has been carried out to study heat transfer characteristics of an incompressible Newtonian electrically conducting and heat generating/absorbing fluid having temperature-dependent viscosity over a non-isothermal wedge in the presence of thermal radiation. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The wedge surface is assumed to be permeable so as to allow for possible wall suction or injection. The effects of viscous dissipation, Joule heating, stress work and thermal radiation are included in the model. The governing differential equations are derived and transformed using a non-similarity transformation. The transformed equations are solved numerically by applying a fifth-order Runge-Kutta-Fehlberg scheme with shooting technique. Favorable comparisons with previously published work on various special cases of the problem are obtained. Numerical results for the velocity and temperature profiles for a prescribed magnetic field parameter as well as the development of the local skin-friction coefficient and local Nusselt number with the magnetic field and radiation parameters are presented graphically and in tabulated form to elucidate the influence of the various physical parameters.     

壁面马赫数分布规律可控的新型内收缩基准流场设计方法

根据有旋特征线理论,设计出了沿程马赫数下降规律可控的轴对称基准流场,分析了基准流场的几何参数(前缘压缩角及中心体半径)的影响规律,发现选取较小的前缘压缩角和中心体半径有利于得到性能优良的基准流场;然后在设计状态Ma=6时研究了三种典型的马赫数下降规律对这种轴对称流场性能的影响。最后考虑了粘性的影响,并进行了粘性修正探索,结果表明,采用附面层位移厚度修正方法后,基准流场的壁面压力分布和无粘情况吻合良好。      

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.     

Dual solutions in mixed convection boundary-layer flow with suction or injection

The effect of suction/injection on the laminar mixed convectionboundary-layer flow about a vertical wall in an incompressibleviscous fluid is considered. The similarity solutions are obtainedfor some values of the suction/injection parameter as well asthe mixed convection parameter for three particular cases: uniformtemperature, uniform heat flux and stagnation flow. The resultingsystem of non-linear ordinary differential equations is solvednumerically for both assisting and opposing flow regimes usinga finite-difference scheme known as the Keller box method. Numericalresults are obtained for the skin friction coefficient and localNusselt number as well as velocity and temperature profiles.The effects of the involved parameters on the skin frictioncoefficient and the local Nusselt number characteristics arediscussed. It is found that dual solutions exist for assistingflow, besides that usually reported in the literature for opposingflow.     

Analytical approach to heat and mass transfer in MHD free convection from amoving permeable vertical surface

An analytical study is performed on heat and mass transfer in MHD‐free convection from a moving permeable vertical surface and the results are compared with previous works on this phenomenon to test the validity. The coupled equations of boundary layer are transformed from their non‐linear form to ordinary form using similarity transformation and then are solved by a newly developed method, homotopy analysis method. Having different base functions, homotopy analysis method provides us with great freedom in choosing the solution of a nonlinear problem. Solving the boundry layer equations, the effects of different parameters such as magnetic field strength parameter (M), Prandtl number (Pr), Schmidt number (Sc), buoyancy ratio and suction/blowing parameter (f_w) on velocity, temperature, and concentration profiles are taken into consideration. Obtained results show that increment of magnetic field strength parameter (M) leads to decrease in velocity profile. Copyright © 2011 John Wiley & Sons, Ltd.     

Convective heat transfer in a conducting fluid over a permeable stretching surface with suction and internal heat generation/absorption

We consider a convective flow in a porous medium of an incompressible viscous conducting fluid impinging on a permeable stretching surface with suction, and internal heat generation/absorption. Using a similarity transformation the governing equations of the problem are reduced to a coupled third-order nonlinear ordinary differential equations. We first examine a number of special cases for which we may obtain exact solutions. We then obtain analytical solutions (by the Homotopy Analysis Method) and numerical solutions (by a boundary value problem solver), in order to further study the behavior of the nonlinear differential equations, for various values of the physical parameters. Our numerical solutions are shown to agree with the available results in the literature. We then employ the numerical results to bring out the effects of the suction parameter, heat source/sink parameter, stretching parameter, porosity parameter, the Prandtl number and the free convection parameter on the flow and heat transfer characteristics. In the absence of suction and free convection, our findings are in agreement with the corresponding numerical results of Attia [H.A. Attia, On the effectiveness of porosity on stagnation point flow towards a stretching surface with heat generation, Comput. Mater. Sci. 38 (2007) 741-745].