Natural convective heat transfer from two thin vertically spaced two-dimensional isothermal plates where one is horizontal and the other is inclined

Abstract

A numerical study of natural convective heat transfer from two isothermal vertically aligned thin horizontal two-dimensional plates having the same width has been undertaken. The vertical distance between the two plates is relatively small and as a result, there is an interaction between the flows over the two plates which affect the heat transfer rates from the plates. One of the plates is horizontal and the other is inclined to the horizontal. Both the case where the bottom plate is horizontal and the top plate is inclined and the case where the bottom plate is inclined and the top plate is horizontal has been considered. The effect of the dimensionless vertical spacing between the plates and the angle of inclination to the horizontal of the inclined plane on the mean heat transfer rates from the individual surfaces of each plate and on the mean heat transfer rates from the entire surface of each plate have been studied. The mean flow has been assumed to be steady. The conditions considered include those under which turbulent flow can develop and the turbulence model with buoyancy force effects accounted for has been used in obtaining the solution. The heat transfer rates considered, expressed in terms of mean Nusselt numbers, will depend on the Rayleigh number, on the angle of inclination of the inclined plate, on whether it is the upper or lower plate that is inclined, on the dimensionless vertical spacing between the plates, and on the Prandtl number. Results have only been obtained for a Prandtl number of 0.74, i.e., the value for air at ambient conditions. Investigations of the effect of the plate inclination angle and of the dimensionless spacing between the plates on the variation of the Nusselt number with Rayleigh number have been undertaken for both the case where the top plate is inclined and for the case where the bottom plate is inclined. (AU)