Numerical simulations on laminar natural convection in a square cavity with a conducting circular block

Numerical simulation on steady-state two-dimensional laminar natural convection in a square cavity with a conducting circular block will be reported in this paper. The cavity was inclined at an angle F to the horizontal. Simulations were carried out with F varying from 15° to 90° on increments of 15°. Three values of Rayleigh number of 104, 105and 106were used. Thermal conductivity ratios k* for block to fluid were 0.2 and 5. Results indicated that the flow fields would be very complicated when the Rayleigh number increased. This is more obvious at smaller angles of F. For certain values of k and F, the average Nusselt number of the hot wall would increase with the Rayleigh number. When the angle F increased to exceed a critical value, the average Nusselt number for k* of 0.2 is larger than that for k* of 5. The critical value F decreases as the Rayleigh number increases.