Effects of Variable Thermal Conductivity and Grashof Number on Non-Darcian Natural Convection Flow of Viscoelastic Fluids with Non Linear Radiation and Dissipations

Abstract

Effects of variable thermal conductivity, porosity and Grashof number on natural convection of viscoelastic fluid flow and heat transfer are studied and discussed. The nonlinear radiation and dissipations are taken into consideration. The fluid flows through non-Darcy porous medium which lies between two heated vertical plates that are kept at constant, but different, temperatures. High order accurate finite difference schemes are introduced to solve the governing equations. The coupled nonlinear differential equations are linearized and iterations are used to approximate that linearized terms. The finite difference method transforms the coupled linearized differential (momentum and energy) equations to a linear system of algebraic equations. An error analysis is introduced by refinement of mesh size and comparisons with available previous results. Effects of fluid and heat parameters on the velocity field, temperature, skin friction factor and Nusselt number are tabulated and plotted. The present results and comparisons show that the numerical solution is of excellent agreement with previous analytical and numerical solution.