Thermally Developing Region of a Parallel Plate Channel Partially Filled with a Porous Material with the Effect of Axial Conduction and Viscous Dissipation: Uniform Wall Heat Flux

Abstract

The present investigation has been undertaken to assess the effect of axial conduction and viscous dissipation on heat transfer characteristics in the thermally developing region of a parallel plate channel with porous insert attached to both the walls of the channel. Both the walls are kept at uniform heat flux. The fully developed flow field in the porous region corresponds to Darcy–Brinkman equation and the clear fluid region to that of plane Poiseuille flow. The effect of parameters, Brinkman number, Br, Darcy number, Da, Peclet number, Pe, and a porous fraction, γp have been studied. The numerical solutions have been obtained for, 0.005 ≤ Da ≤ 1.0, 0 ≤ γp ≤ 1.0 and −1.0 ≤ Br ≤ 1.0 and Pe = 5, 25, 50, 100 and neglecting axial conduction (designated by Ac = 0) by using the numerical scheme successive accelerated replacement (SAR). There is an unbounded swing in the local Nusselt number because of viscous dissipation.