A Numerical Study of Conjugate Heat Transfer by Natural Convection and Surface Radiation in a Square Enclosure With Thick Adiabatic Walls

A numerical solution of heat transfer by combined natural convection and surface radiation in a square enclosure with thick adiabatic top and bottom walls and isothermal vertical walls is presented. The present model was used to obtain new results with the addition of thermal conduction at the thick top and bottom walls for a thermal conductivity ratio, K = k_solid/k_fluid, that ranges from 0 to 10, emissivity of the adiabatic walls that ranges from 0 to 1, and the Rayleigh Number that ranges from 10³ to 10⁶. The model was validated by comparing the results to a benchmark solution and other solutions found in the literature. The results showed that with an increase in thermal conductivity ratio, the flow circulation decreases while the average Nusselt Number increases indicating increased heat transfer across the thick walls and the fluid in the corners. The results indicate that while past studies have shown negligible impact of the emissivity of the adiabatic walls on characteristics of the flow and heat transfer within the cavity, when a wall with moderate heat capacity and conductivity is considered, the resulting flow velocity and temperature distribution within the cavity are found to be significantly influenced by the thick wall emissivity. As the conductivity ratio increases this discrepancy between thin and thick walls becomes greater, there is further need for a more complex and accurate model including the thick walls. The results also showed that an increase in the emissivity of the adiabatic walls results in a slight decrease in the average Nusselt Number.