Numerical study of natural convection in fully open tilted cavities

A numerical simulation of two-dimensional laminar natural convection in a f ully open tilted square cavity with an isothermally heated back wall is con ducted. The remaining two walls of the cavity are adiabatic. Steady-state s olutions are presented for Grashof numbers between 10(2) and 10(5) and for tilt angles ranging from -60 degrees to 90 degrees (where 90 degrees repres ents a cavity with the opening facing down). The fluid properties are assum ed to be constant except for the density variation with temperature that gi ves rise to the buoyancy forces, which is treated by the Boussinesq approxi mation. The fluid concerned is air with Prandtl number fixed at 0.71. The g overning equations are expressed in a normalized primitive variables formul ation Numerical predictions of the the velocity and temperature fields are obtained using the finite-volume-based power law (SIMPLER: Semi-implicit Me thod for Pressure-Linked Equations Revised) algorithm. For a vertical open cavity (alpha = 0 degrees), the algorithm generated results that were in go od agreement with those previously published. Flow patterns and isotherms a re shown in order to give a better understanding of the heat transfer an fl ow mechanisms inside the cavity. Effects of the controlling parameters-Gras hof number and tilt angle-on the heat transfer (average Nusselt number) are presented and analyzed. The results also revealed that the open-cavity Nus selt number approaches the flat-plate solution when either Grashof number o r tilt angle increases. In addition, a correlation of the Nusselt number in terms of the Grashof number and tilt angle is developed and presented; a c omparison is made with available data from other literature.