Effect of Wall Conduction on Natural Convection in an Enclosure With a Centered Heat Source

Abstract

This study presents a numerical investigation of the effects of wall conduction on laminar natural convection heat transfer in a two-dimensional rectangular enclosure. The heat transfer is driven by a constant-temperature heat source in the center of the enclosure. The time dependent governing equations in the primitive form are solved numerically by the use of a finite-volume method. The numerical algorithm is first validated by comparing our predictions with those of Kim and Viskanta for a square cavity surrounded by four conducting walls. A parametric study is then conducted to examine the effects of wall conduction on the natural convection heat transfer. The parameters include the Rayleigh number, wall thickness, wall thermal conductivity ratio and diffusivity ratio. In addition, the effects of varying thermal boundary conditions on the outside walls are reported. Results indicate that the qualitative features of natural convection heat transfer in the laminar range are not significantly altered by the inclusion of wall conduction. However, the quantitative results may be significantly modified by the wall conductance. In general, the wall conduction reduces the rate of heat dissipation from the enclosure. The average Nusselt number decreases as the wall thickness ratio is increased and/or the wall thermal conductivity is reduced. Results also indicate that it may be possible to define an effective Rayleigh number that includes the effects of wall thickness and conductivity.