Transient Natural Convection on a Vertical Flat Plate Embedded in a High-Porosity Medium

Abstract

This paper provides an analysis of the non-Darcian effect on transient natural convection of a vertical flat plate embedded in a high-porosity medium. The plate surface is either maintained at an uniform wall temperature (UWT), or subjected to an uniform heat flux (UHF), and convective, boundary and inertia effects are considered. The local volume-averaged principles and certain empirical relations have been utilized to establish the governing equations. The coupled nonlinear partial differential equations are solved with a numerical integration technique using a cubic spline. Along with transient mean and local Nusselt numbers at the plate, representative transient velocity and temperature profiles are presented. Both effects for non-Darcian flow model are shown to be more pronounced in high-porosity medium and, hence, reduce the heat transfer rate.