The effect of water density extremum on heat transfer within a cylinder containing a heat-generating porous media

Abstract

A numerical model was used to investigate the effect of the density extremum of water in a cylinder containing a heat-generating porous media. The modeled vertical cylinder had an adiabatic bottom surface with isothermal sides and top. The density of water was varied with temperature, as was the heat generation rate, aspect ratio, and boundary temperature to reveal the affects upon heat transfer and maximum temperatures. Results of the explicit finite difference model using Darcy's formulation for the momentum equations indicate that the uniform internal heat generation rate and the surface area to volume ratio determine maximum temperatures and steady-state flow patterns. At very low heat generation rates, the boundary temperature does not significantly affect the location of the maximum velocity unless the boundary temperature is at the extremum temperature of 4°C. When larger internal heat generation rates are considered, and as the surface area to volume ratio decreases, the effect of boundary temperature becomes less significant. Because the density extremum of water is so near its melting point of 0°C, the effect of the maximum density is essentially negligible for boundary temperatures above the melting point of water.