Natural Convection Heat Transfer

Abstract

A numerical and experimental investigation for natural convection heat transfer from a pipe embedded in a semi-infinite, liquid-saturated porous medium is carried out. The surface of the medium is assumed to be impermeable. The governing equations for Darcy flow are solved using finite element method. The finite element formulation is based on a two-dimension Galerkin approach. Extensive series of numerical solutions are conducted over a wide range of the governing parameters 2 h/R8, 10 Ra250, where h/R, and Ra are the burial depth/pipe radius ratio, and the Darcy-Rayleigh number, respectively. The effects of these parameters on both the temperature and flow fields and on the pipe surface heat transfer rate are analyzed. Experiments are conducted on an electrically heated brass pipe buried in a liquid-saturated porous medium enclosed in a vertical container to validate the present predictions. Sand grains with nominal diameter 2.7 mm saturated with water are used as the porous medium. The experimental data are compared with both the present predictions and with those available in the literature and fair agreement is noticed. Correlating equations for the average Nusselt number are obtained as functions of Darcy-Rayleigh number and the pipe burial depth ratio.