Natural convection in a porous cavity with spatial sidewall temperature variation

Abstract

Purpose

To study the natural convention in a square porous cavity induced by heating one of the sidewalls and the other sidewall is cooled, while the horizontal walls are adiabatic. The heated wall is assumed to have spatial sinusoidal temperature variations about a constant mean value.

Design/methodology/approach

The Darcy model is used in the mathematical modeling of the natural convection in porous cavity. A finite volume method based on QUICK scheme is used to solve numerically the non‐dimensional governing equations.

Findings

It is found that the average Nusselt number varies based on the hot wall temperature. It increases with an increase in the amplitude, while the maximum average Nusselt number occurs at the wave number of k=0.75 for Rayleigh number based on the permeability of the medium of 500 and 1000 and at k=0.70 for a Rayleigh number of 10‐200.

Research limitations/implications

The effects of the amplitude (0‐1.0) and the wave number (0‐5) of the heated sidewall temperature variation on the natural convection in the cavity are investigated for Raleigh number 10‐1000.

Practical implications

The spatial sinusoidal temperature variation occurs in the applications when a cylindrical heater or a periodic array of heaters placed on a flat wall.

Originality/value

This paper is providing the details of the heat transfer inside the cavity which can be used in thermal design.

Citation

Saeid, N.H. and Mohamad, A.A. (2005), "Natural convection in a porous cavity with spatial sidewall temperature variation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 15 No. 6, pp. 555-566. https://doi.org/10.1108/09615530510601459