Buoyancy driven heat transfer in cavities subjected to thermal boundary conditions at bottom wall

Abstract

Natural convection in cavities is studied numerically using a finite volume based computational procedure. The enclosure used for flow and heat transfer analysis has been bounded by adiabatic top wall, constant temperature cold vertical walls and a horizontal bottom wall. The bottom wall is subjected to uniform/sinusoidal/linearly varying temperatures. Nusselt numbers are computed for Rayleigh numbers (Ra) ranging from 103 to 107 and aspect ratios (H/L) 0.5 and 1. Air is taken as working fluid (Pr = 0.7). Results are presented in the form of stream lines, isotherm plots and average Nusselt numbers. It is observed from this study that the uniform temperature at the bottom wall gives higher Nusselt number compared to the sinusoidal and linearly varying temperature cases. The average Nusselt number increases monotonically with Rayleigh number for both aspect ratio 1 and 0.5 for bottom wall and side walls. For the case of aspect ratio 1, the average Nusselt number for a given Rayleigh number increases at the bottom wall compared to aspect ratio 0.5. However, the average Nusselt number increases as the aspect ratio decreases from 1 to 0.5 for side wall except for uniform temperature case.