Free convective flow in a square enclosure partly filled with a high conductivity porous layer

摘要

In order to assess, in a very basic way, the possibility of using high conductivity porous inserts to enhance heat transfer rates in natural convective flows, a numerical study of natural convective heat transfer across a square enclosure with one vertical wall heated to a uniform high temperature and with the opposite vertical wall cooled to a uniform lower temperature and with the remaining two walls adiabatic has been undertaken. There is a rectangular porous layer adjacent to the hot vertical wall, this layer, in general, filling part of the enclosure and with the remainder of the enclosure being filled with pure fluid. The porous layer is assumed to be saturated with this fluid. The flow has been assumed to be laminar and two-dimensional. Fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces, this being treated by means of the Boussinesq type approximation. The flow in the porous layer has been treated using the Darcy model. The governing equations have been written in terms of dimensionless variables and the resultant dimensionless equations have been solved using a well-tested finite-difference method. The solution has, as parameters, the dimensionless thickness of the porous layer, the Darcy number, the Rayleigh number, the Prandtl number, the ratio of the effective thermal conductivity of the porous layer to the thermal conductivity of the fluid and the ratio of the kinematic viscosities of the porous and fluid layers. Results have been obtained for a Prandtl number of 0.7 and a viscosity ratio of 1. The variation of the mean heat transfer rate across the enclosure with dimensionless porous layer thickness for various combinations of Rayleigh number and Darcy number for fixed conductivity ratios between 1 and 10 has been considered. The results show that enhancement of the heat transfer rate is possible in some situations.