MHD Slip Flow and Heat Transfer with Ohmic Heating between a Rotating Solid Disk and Stationary Permeable Disk

Abstract

In this paper, the axially-symmetric MHD (magnetohydrodynamic) slip fluid flow and heat transfer between a rotating disk and a stationary permeable disk has been examined. The physical system is comprised of a free-fluid region with an underlying fluid-saturated porous bed with a solid base. The fluid flow within the free-fluid region is modeled using the Navier-Stokes equation, whereas the flow within the porous bed is described using the Brinkman equation. The governing equations of fluid flow and heat transfer, along with the associated boundary conditions, are reduced to a system of ordinary differential equations using suitable similarity transformations. A series expansion technique is then employed in order to obtain analytical approximations for the velocity and temperature distributions. The results produced in this study are presented in graphical form. Unless otherwise stated, the following non-dimensional values are used for the numerical calculations: Hartmann number M=1, Reynolds number R=0.1, Darcy parameter beta=0.05, thermal conductivity ratio lambda=0.5, Eckert number Ec=10, slip parameter N^*=0.05, eta=1, and Prandtl numbers Pr_1=Pr_2=10. The influence of the Darcy parameter, Hartmann number and thermal conductivity ratio on the flow velocity and fluid temperature are investigated.