A Differential Quadrature Solution of Natural Convection in an Enclosure with a Finite-Thickness Partition

Abstract

Natural convection in a rectangular enclosure divided by a partition with a finite thickness and conductivity is studied numerically. A temperature difference is imposed between the two isothermal vertical walls, and the other two walls are assumed adiabatic. Governing equations with the Boussinesq approximation are solved using the polynomial differential quadrature (PDQ) method. The results show that flow on either side of the enclosure is unicellular for low values of the aspect ratio. A multicellular flow forms the flow field in the bigger zone of the enclosure for higher aspect ratios. With increasing aspect ratio, heat transfer shows an increasing trend and reaches a maximum value. Beyond the maximum point, the foregoing trend reverses to decrease with further increase of the aspect ratio. The average Nusselt number decreases toward a constant value as the partition is distanced from the hot wall toward the middle of the enclosure. Decreasing the thermal conductivity ratio produces higher average Nusselt numbers. However, for higher aspect ratios, the increasing trend of the average Nusselt number with decreasing thermal conductivity ratio reverses to decrease as the thermal conductivity ratio is decreased further below a certain value.

Notes

¹A comparison of various numerical results for air-filled two-dimensional square enclosures with vertical walls at different isothermal temperatures was presented by de Vahl Davis and Jones [1] and de Vahl Davis [2].