Numerical analysis of conjugate natural convection and surface radiation in an enclosure with local heat source

Mathematical simulation of natural convection and surface radiation in a square cavity having heat-conducting walls of finite thickness with a heat source located at the bottom of the cavity in convective heat exchange with an environment has been carried out. Numerical analysis has been based on a solution of the two-dimensional Boussinesq equations in the dimensionless variables such as stream function, vorticity, and temperature. Main attention was paid to the effects of Rayleigh number 10⁴ ≤ Ra ≤ 10⁶, an emissivity of internal surfaces of walls 0 ≤ ε < 1, a thermal conductivity ratio 1 ≤ k1,2 ≤ 15, a thickness of walls 0.1 ≤ l/L ≤ 0.3, and a dimensionless time 0 ≤ τ ≤ 100 on the velocity and temperature fields. The effect scales of the key parameters on the average Nusselt numbers have been determined.