Buoyancy‐driven flow of a viscous incompressible fluid in an open‐ended rectangular cavity with permeable horizontal surfaces

Abstract

Purpose

The purpose of this paper is to consider the unsteady natural convection flow of a viscous incompressible fluid, which is induced by differential heating on the solid vertical boundary of an open‐ended rectangular cavity with the two horizontal surfaces which are permeable and maintained at the temperature of ambient fluid. Attention is focused on how the flow and heat transfer is affected by variations of the buoyancy force, as well as by the permeability of the surfaces.

Design/methodology/approach

An upwind finite‐difference method in conjunction with a successive over‐relaxation iteration technique is used to solve the governing boundary layer equations. To do this, the first and second derivatives were approximated by central differences and were used in the vorticity, energy and Poisson equations. To preserve the conservative property, the finite‐difference forms of the vorticity and energy equations were written in conservative form for the convective terms.

Findings

Local rate of heat transfer from the heated surface increases owing to an increase in the value of Ra. In the region near the bottom surface, the heat transfer from the left vertical surface decreases, but that increases in the region near the upper surface. Due to blowing of fluid through the permeable surfaces, the rate of heat transfer is higher than the situation where fluid is being withdrawn. This difference was found to be higher in the case of larger value of Ra.

Research limitations/implications

The analysis is valid for unsteady, two‐dimensional natural convection flow of a viscous fluid filled in an open‐ended rectangular enclosure. An extension to three‐dimensional flow case is left for future work.

Practical implications

The method is very useful to analyze solar receiver systems, fire research, electronic cooling, brake housing of an aircraft and many environmental geothermal processes.

Originality/value

The results of this study may be of some interest to engineers interested in heat transfer in ventilated rooms or enclosures.

Citation

Hossain, M.A., Asghar, S. and Subba Reddy Gorla, R. (2010), "Buoyancy‐driven flow of a viscous incompressible fluid in an open‐ended rectangular cavity with permeable horizontal surfaces", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 20 No. 7, pp. 759-772. https://doi.org/10.1108/09615531011065557