Numerical Investigation of Transient Free Convective Flow in Vertical Channel Filled with Porous Material in the Presence of Thermal Dispersion

Abstract

The present work consists of a numerical investigation of transient free convective flow in vertical channel formed by two infinite vertical parallel plates filled with porous material in the presence of thermal dispersion. The governing coupled-nonlinear equations of momentum and energy transport are solved numerically using the implicit finite difference method, while the approximate analytical solution is also presented to find the expression for velocity, temperature, skin friction, and rate of heat transfer for the steady fully developed flow using the perturbation technique. The main objective is to investigate the effects of the dimensionless time, Darcy number, thermal dispersion, and Prandtl number on the fluid flow and heat transfer characteristics. Solutions are presented in graphical form and given in terms of fluid velocity, fluid temperature, skin friction, and rate of heat transfer for various parametric values. The significant result from this study is that velocity and temperature is enhanced with increase in thermal dispersion parameter and time. Furthermore, excellent agreement is found between the steady-state solution and the transient solution at large values of time.