LAMINAR FREE CONVECTION IN VERTICAL AIR-FILLED CAVITIES WITH MIXED BOUNDARY CONDITIONS

A numerical investigation was conducted on the two-dimensional laminar free convection within rectangular cavities having mixed boundary conditions on the vertical surfaces and adiabatic top and bottom walls. The time-dependent governing energy, vorticity and stream function equations were solved using a modified ADI method and Gauss-Seidel SOR. Steady state solutions for air (Pr ≈ 0.7) were obtained for cavity aspect ratios of 0.5 to 15 over a modified Rayleigh number range of 690 to 1.3 × 10₅. For a given heat flux, it was found that the average Nusselt number peaked at an aspect ratio of about 1.5. The boundary between the asymptotic and laminar boundary layer regimes also showed a reversing behaviour in this region. In general, the reported results are compatible with and form an extension to the limited numerical and experimental results of previous investigators.