Transient natural convection in a cavity with walls of finite thickness

Abstract

Numerical studies are made of transient natural convection in a square cavity. The top and bottom end walls are thermally insulated The vertical solid side walls are affinite thickness and affinite thermal conductivity. Flow is driven, from the motionless isothermal initial state, by impulsively increasing (decreasing) the temperature at the outer surface of one (the other) vertical side wad. Numerical solutions are sought to the time-dependent Navier-Stokes equations for the fluid and the solid regions. The ratios of thermophysical properties between solid and fluid are the significant parameters. As the thermal capacity ratio increases, the development of flow in the fluid region is retarded. The conductive and convective timescales are estimated. The effects of the thermal conductivity ratio and of the thickness of the side wad are delineated. The effect of the system Rayleigh number on transient heat transport is analyzed. The applicability of the approximate one-dimensional thermal conductance model to the transient features is scrutinized.