International Journal of Engineering Science Invention Research & Development; Vol. I Issue III September 2014 www.ijesird.com e-ISSN: 2349-6185 P. R. Sharma and Kalpna Sharma ijesird, Vol. I (III) September 2014/ 65 UNSTEADY MHD TWO-FLUID FLOW AND HEAT TRANSFER THROUGH A HORIZONTAL CHANNEL P. R. Sharma*, Kalpna Sharma°, *Department of Mathematics, University of Rajasthan, Jaipur (India), Email: profprsharma@yahoo.com ° Department of Mathematics, Manipal University Jaipur, Jaipur (India), Email: kalp_aali@yahoo.co.in . ABSTRACT- An unsteady MHD flow of two viscous immiscible incompressible electrically conducting fluids and heat transfer through a horizontal channel with isothermal non-conducting permeable plates in the presence of transverse magnetic field is investigated. The partial differential equations governing the flow and heat transfer are transformed to ordinary differential equations and closed-form solutions are obtained in both fluids. Numerical results for velocity and temperature fields are presented graphically and the numerical values of skin-friction and Nusselt number have been tabulated. The effect of different parameters like viscosity ratio, phase angle, Hall parameter, thermal conductivity ratio and Prandtl number on velocity field, temperature field, skin friction and Nusselt number are discussed. Keywords: MHD, isothermal, electrically conducting fluid, skin friction, Nusselt number I INTRODUCTION Study of flow through and past a porous medium constitutes a comparatively recent development in fluid mechanics, with applications in Science, Engineering and Technology. More specifically, the existence of a fluid layer adjacent to a layer of fluid saturated porous medium is a common occurrence in both geophysical and engineering environments. Modeling of such systems requires understanding of the convective interaction between the fluid layer and the adjacent fluid saturated porous medium. Some of the geothermal sources e.g. One in the Gulf of California, lie very close to the surface and under a body of water. These situations may be molded as fluid superposed, porous layers. Packham and Shail (1971) studied stratified laminar flow of two immiscible fluids. Soundalgekar and Bhat(1971) considered oscillatory MHD flow and heat transfer through a channel. Magnetohydrodynamic heat transfer in two phase flow between parallel plates was discussed by Lohrasbi and Sahai (1988). Zaturska et al. (1988) analyzed flow of viscous fluid driven along a channel by suction at porous walls. Two- dimensional flow of a viscous fluid in a channel with porous walls was considered by Cox (1991). Malashetty and Leela (1991) investigated magneto hydrodynamic heat transfer in two fluid flow. Malashetty and Leela (1992) studied magneto hydrodynamic heat transfer in two phase of flow. Berman (1993) investigated laminar flow in channels with porous walls. Attaia and Kotb (1996) considered MHD flow between two parallel plates with heat transfer. Malashetty and Chamkha (2000) reported analytical solutions for flow of two immiscible fluids in porous and non-porous channels. Malashetty et al. (2004) studied fully developed flow and heat transfer in a horizontal channel containing an electrically conducting fluid sandwiched between two fluid layers. Umawathi et al. (2004) considered fully developed flow and heat transfer in a horizontal channel containing an electrically conducting fluid sandwiched between two fluid layers. Umawathi and Mateen (2004) analyzed unsteady two-fluid flow and heat transfer in a horizontal channel. Pilecks and Socolowsky(2005) considered viscous two-fluid flows in perturbed unbound domains. Umawathi et al. (2006) analyzed oscillatory Hartman two-fluid flow and heat transfer in a horizontal channel. Tsuyoshi and Shu-Ichiro (2008) studied two-fluid magneto hydrodynamic simulation of converging hi flows in the interstellar medium. Linga and Sreedhar (2009) analyzed unsteady two-fluid flow and heat transfer of conducting fluids in channels under transverse magnetic field. Magnetic fields for fluid motion were discussed by Weston et al (2010). Kumar et al (2012) discussed the unsteady MHD free convective flow through porous medium sandwiched between viscous fluids. II FORMULATION OF THE PROBLEM Consider a two-dimensional unsteady flow of two viscous immiscible incompressible electrically conducting fluids through horizontal parallel permeable non-conducting plates, extending in the * x - and * y - directions in the presence of transverse magnetic field of uniform intensity B 0 region – I(o≤ * y ≤h) is filled with a viscous incompressible fluid having density 1  , dynamic viscosity 1  , specific heat at constant pressure 1 p C , thermal conductivity 1  and region -II (-h ≤ y ≤ 0) is filled with a different viscous incompressible fluid having density 2  , dynamic viscosity 2  , specific heat at constant pressure 2 p C and thermal conductivity 2  . The flow in both regions of the channel is assumed to be fully developed and is driven by a common pressure