TRANSIENT NATURAL CONVECTION OF WATER NEAR ITS DENSITY EXTREMUM IN A RECTANGULAR CAVITY FILLED WITH POROUS MEDIUM

Abstract

A numerical study is performed to analyze the transient flow field and heat transfer behavior of cold water in a rectangular enclosure filed with a porous medium. The numerical method was employed by the SIMPLE-C algorithm. The accurate nonlinear relation between density and temperature developed by Gebhart and Mollendorf was used. The numerical results show that, for R < 0 · 5, the size of the clockwise vortex beside the high-temperature surface increases as time increases. The clockwise vortex occupies almost the whole space when the steady state is reached. For R = 0 · 5, the size of the clockwise vortex adjacent to the high-temperature surface increases as time increases. However, two counterrotation vortices having the same strength and size exist in the space when steady state is reached. For R > l, only one counterclockwise vortex exists in the space the entire time. For τ > 10⁻³, the heat transfer rate increases with increase in Darcy number for the entire time. However, as time increases, the heat transfer rate on the high-temperature surface decreases and that on the low-temperature surface increases.