919 Indian Journal of Science and Technology Vol. 3 No. 8 (Aug 2010) ISSN: 0974- 6846 Research article “Heat transport” Senthilkumar et al. ©Indian Society for Education and Environment (iSee) http://www.indjst.org Indian J.Sci.Technol. Oscillatory MHD free convective flow through a porous medium with mass transfer, Soret effect and chemical reaction N.Ahmed and H. Kalita Dept. of Mathematics, Gauhati University, Guwahati 781014, Assam, India. saheel_nazib@yahoo.com Abstract An attempt is made to investigate the problem of an oscillatory MHD free convective flow through a porous medium with mass transfer, Soret effect and chemical reaction when the temperature as well as concentration at the plate varies periodically with time about a steady mean. Analytical solutions to the coupled non-linear equations governing the flow and heat and mass transfer are obtained by using regular perturbation technique. The influence of the different parameters entering in to the problem viz. the Hartmann number M, the Grashof number for heat transfer r G , the Grashof number for mass transfer m G , Soret number 0 S , the plate velocity U , chemical reaction h C etc. on temperature distribution, species concentration, velocity distribution, skin-friction and the rates of heat and mass transfer at the plate are discussed graphically. 2000 Mathematics subject classification: 76 D, 76 W 05 Keywords: Free convection, MHD, thermal diffusion, chemical reaction. Nomenclature A is the suction parameter; B r is the magnetic induction vector; 0 B is strength of the applied magnetic fluid; C is the species concentration of the fluid; h C chemical reaction parameter; p C is the specific heat at constant pressure; W C is the species concentration of the fluid at the plate; C ∞ is the species concentration far away from the plate; M D is the coefficient of chemical molecular diffusivity; T D is the coefficient of chemical thermal diffusivity; E is the Eckert number; m G is the Grashof number for mass transfer; r G is the Grashof number for heat transfer; g is the acceleration due to gravity; K is the permeability of the porous medium; k is the thermal conductivity; M is the Hartmann number; P is the Prandtl number; Q is the heat source parameter; S is the Schmidt number; 0 S is the Soret number; T is the fluid temperature; W T is the temperature of the fluid at the plate; T ∞ is the fluid temperature far away from the plate; t is the time; U is the non- dimensional plate velocity; U is the dimensional plate velocity; u is the x component of the non dimensional fluid velocity in the boundary layer; 0 v is the mean suction velocity; (, ,0) uv are the components of the fluid velocity; y is the non dimensional distance from the plate; (, , ) x yz are the Cartesian coordinates. Greek symbols α is the heat source strength; β is the coefficient of volume expansion for heat transfer; β is the coefficient of volume expansion for mass transfer; ρ is the fluid density; μ is the coefficient of viscosity; υ is the kinematic viscosity; σ is the electrical conductivity; θ is the non dimensional temperature; φ is the non dimensional species concentration; ω is the frequency parameter; ε is the small reference parameter; ξ is the coefficient first order chemical reaction; λ is the reciprocal of the Soret number. Introduction The MHD free convective flow and heat transfer problems through porous medium have attracted the attention of a number of scholars due to its importance in many branches of science and technology such as fiber and granular insulations, geothermal system etc. In engineering, its application has been found in MHD pumps, MHD bearing etc. Convection in porous media is applied in geothermal energy recovery, oil extraction; thermal energy storage and flow throw filtering devices. The phenomena of mass transfer are also very common in the theory of stellar structure and in chemical engineering in particular. In many times, it has been observed that the foreign mass reacts with the fluid and in such a situation chemical reaction plays an important role in chemical industry. Many researchers carried out the study of free convective effects on flow past a vertical surface with different boundary conditions (Vedhanayagam et al., 1980; Kolar & Sastri, 1988; Camargo et al., 1996; Ahmed & Kalita, 2008). The problems of natural convection flow through porous medium past a plate were investigated by Kim & Vafai (1989) and Harris & Ingham (1997).The combined heat and mass transfer effect on MHD free convective flow through porous media was investigated by (Chaudhary & Jain, 2007). However in the above mentioned works, the thermal– diffusion (Soret) effect was not taken into account. This assumption is justified when the concentration level is very low. The flux of mass caused due to temperature