Predictions of buoyancy-induced flow in various across-shape concave enclosures

The present study was conducted to numerically investigate the steady laminar buoyancy-driven and convection heat transfer characteristics within three different across-shape concave enclosures for the Prandtl number of 0.71 and 4, the Grashof number range 104 ≤ Gr ≤ 2 × 105, and the gap range 0 ≤ H1/H2 ≤ 0.25. The steady Navier–Stokes equations, governing the flow under Boussinesq approximation, are solved with the dimensionless stream function-vorticity formulation in terms of curvilinear coordinates using the finite difference method. The results show that the effects of various shapes, the strength of the vortex is relatively bigger in the rectangular–rectangular concave enclosure than in the rectangular–circular concave enclosure at the same Grashof number. Heat transfer from the different across-shape concave enclosures is evaluated, and flow and heat transfer characteristics are discussed.