Numerical study of transient laminar natural convection over an isothermal sphere

Abstract

The full Navier–Stokes equations and the energy equation for laminar natural convection heat transfer over an isothermal sphere have been discretized using the finite control volume formulation and solved by employing the SIMPLEC method. Transient and “steady-state” results have been obtained for a wide range of high Grashof numbers (10 5 ⩽ Gr ⩽ 10 9) and a wide range of Prandtl numbers ( Pr = 0.02, 0.7, 7 and 100). Main results are listed below. A plume with a mushroom-shaped cap forms above the sphere and drifts upward continuously with time. The upward movement of the plume cap is slowed as the Prandtl number increases. The size and the level of temperature of the transient cap and plume stem decrease with increasing Gr and Pr. The time at which the “steady-state” is reached, increases with the Prandtl number. The presence of a vortex in the wake of the sphere has been predicted and has been clearly delineated as a function of both Grashof and Prandtl numbers. The overall Nusselt numbers and total drag coefficients for the range of Grashof and Prandtl numbers investigated are presented and they are in very good agreement with studies available in the literature.