Hydromagnetic simultaneous heat and mass transfer by mixed convection from a vertical plate embedded in a stratified porous medium with thermal dispersion effects A. J. Chamkha, A.-R. A. Khaled Abstract The problem of steady, laminar, hydromagnetic simultaneous heat and mass transfer by mixed convection ¯ow over a vertical plate embedded in a uniform porous medium with a strati®ed free stream and taking into ac- count the presence of thermal dispersion is investigated for the case of power-law variations of both the wall temperature and concentration. Certain transformations are employed to transform the governing differential equations to a local similarity form. The transformed equations are solved numerically by an ef®cient implicit, iterative, ®nite-difference scheme. The obtained results are checked against previously published work on special cases of the problem and are found to be in excellent agreement. A parametric study illustrating the in¯uence of the magnetic ®eld, porous medium inertia effects, heat generation or absorption, lateral wall mass ¯ux, concen- tration to thermal buoyancy ratio, and the Lewis number on the ¯uid velocity, temperature and concentration as well as the Nusselt and the Sherwood numbers is con- ducted. The results of this parametric study is shown graphically and the physical aspects of the problem are discussed. List of symbols B Mixed convection parameter (B Ra x =Pe) B o Magnetic ®eld strength C Concentration at any point in the ¯ow ®eld C 1 Concentration at the free stream C w Concentration at the wall D Mass diffusivity D s Porous medium thermal dispersion parameter (D s cu 1 d=a) e Buoyancy ratio (e b c C w C 1 =b T T w T 1 F Inertia coef®cient of the porous medium f Dimensionless stream function f w=aPe 1=2 g Gravitational acceleration h Local convective heat transfer coef®cient h m Local mass transfer coef®cient K Permeability of the porous medium k e Porous medium effective thermal conductivity Le Lewis number (Le a=D) M Square of the Hartmann number M rB o K=qt Nu Local Nusselt number Nu hx=k e Pe Local Peclet number Pe u 1 x=a Q o Heat generation or absorption coef®cient Ra x Local Raleigh number Ra x g b T KT w T 1 x=ta S Strati®cation parameter Sh Local Sherwood number Sh h m x=D T Temperature at any point T w Wall temperature T 1 Free stream temperature u Tangential or x-component of velocity u 1 Free stream velocity v Normal or y-component of velocity V o Dimensionless wall mass transfer coef®cient V o 2V w x=au 1 1=2 V w Wall mass transfer velocity x Distance along the plate y Distance normal to the plate Greek symbols C Dimensionless porous medium inertia coef®cient C 2FK u 1 =qt a Molecular thermal diffusivity a e Effective thermal diffusivity of the porous medium a d Thermal diffusivity of the porous medium due to thermal dispersion b c Concentration expansion coef®cient b T Thermal expansion coef®cient d Dimensionless heat absorption parameter d Q o xa=u 1 / Transformed concentration / C C 1 =C w C 1 c Thermal dispersion constant g Coordinate transformation in terms of x and y g y=xPe 1=2 t Fluid kinematic viscosity w Stream function h Transformed temperature h T T 1 =T w T 1 q Fluid density r Fluid electrical conductivity 1 Introduction Simultaneous heat and mass transfer from different ge- ometries embedded in porous media has many engineer- ing and geophysical applications such as geothermal reservoirs, drying of porous solids, thermal insulation, Originals Heat and Mass Transfer 36 (2000) 63±70 Ó Springer-Verlag 2000 63 Received on 17 November 1998 A. J. Chamkha, A.-R. A. Khaled Department of Mechanical and Industrial Engineering Kuwait University P.O. Box 5969 Safat, 13060 Kuwait