Thermal Capacity Effect on Transient Free Convection Adjacent to a Vertical Surface in a Porous Medium

Abstract

In this paper we analyse how the presence of the thermal capacity of a vertical flat plate of finite thickness, which is embedded in a porous medium affects the transient free convection boundary-layer flow. At the time t = 0, the plate is suddenly loaded internally with a constant heat flux rate q″, so that a transient boundary-layer flow is initiated adjacent to the plate. Initially, the transient effects due to the imposition of the uniform heat flux rate at the plate are confined to a thin fluid region near to the surface and are described by a small time solution. These effects continue to penetrate outwards and eventually evolve into a new steady state flow. Analytical solutions have been derived for these transient (small time) and steady state (large time) flow regimes, which are then matched by a numerical solution of the full boundary-layer equations. It has been found that the non-dimensional fluid temperature (or fluid velocity) profiles are reduced when the thermal capacity effects, described by a parameter Q ^*, are reduced. For small values of Q ^*, the approach of these profiles to their steady state values is monotonic. However, for large values of Q ^*, the temperature profiles are observed to locally exceed (pass through a maximum value) the final steady state values at certain distances from the plate. In general, the maxima in the temperature profiles increase in size as Q ^* increases and the time taken to approach the steady state solutions increases significantly.