NUMERICAL CALCULATION OF THERMALLY DRIVEN TWO-DIMENSIONAL UNSTEADY LAMINAR FLOW IN CAVITIES OF RECTANGULAR CROSS SECTION

Abstract

Numerical results are reported for thermally driven laminar flow in two-dimensional rectangular geometries with one plane, the aperture plane, removed. Finite-difference expressions are derived from a set of approximated transport equations in which large temperature and density variations are allowed but high-frequency pressure oscillations are not. The approach allows small time step limitations to be removed from the calculation procedure. A second-order accurate quadratic upstream interpolation technique is used for the finite differencing of convection terms in the transport equations, thus reducing numerical diffusion error. Parameters varied in the calculations were cavity aspect ratio and inclination angle with respect to gravity, inside wall temperature, and Grashof number. A value of Prandtl number corresponding to air was fixed (Pr = 0.73). For the conditions studied, flow and temperature fields within the cavity are determined mainly by local heat transfer events.