FREE CONVECTION HEAT TRANSFER BETWEEN A PERMEABLE VERTICAL WALL AND A POWER-LAW FLUID

Abstract

The problem of natural convection flow of a power-law fluid past a vertical porous wait, taking into consideration the effects of the inertia terms and watt injection or suction on the Nusselt number, has been analyzed. The system of partial differential equations was transformed to a coupled nonlinear set of ordinary differential equations for the isothermal wall and the constant wall heat flux case by using a generalized Rayleigh number that shows the dependence on the power-law index n more explicitly. The resulting two-point boundary-value problem was linearized and solved iteratively using Keller's box method. It was confirmed that inclusion of the inertia terms is more important for flow situations with low to moderate Prandtt numbers than for polymeric liquids with very high Prandtl numbers. The results indicate that both suction and injection at wall Reynolds numbers less than unity have a significant effect on the velocity and temperature profiles and ultimately on the Nussett number.