Convective Motion and Heat Transfer in a Slowly Rotating Fluid Quasi-Sphere With Uniform Heat Source and Axial Gravity

Abstract

The laminar natural convection of a rotating fluid quasi-sphere in the presence of an axial gravity field and uniform heat source is presented. The influence of the Rayleigh number Ra and the Taylor number Ta on the flow pattern and heat transfer rate from the fluid quasi-sphere is discussed. The governing nonsteady, three-dimensional Navier–Stokes equations for an incompressible fluid, formulated in a Cartesian coordinate system, have been numerically solved by using the h/p spectral element method. It is shown that for a given Ta number, as the Ra number is increased, the heat transfer on the northern hemisphere is enhanced whereas the average Nusselt number on the southern hemisphere is reduced. On the other hand for a given Ra number, as the Ta number is increased, the heat transfer is a function of the convective motion intensity. It has been found that for low and high Ra numbers the heat transfer rate slightly depends on the rotation rate. However at intermediate Ra numbers, the net effect of an increased rotation rate is a reduction of the heat transfer through the wall, hence an increase of the maximum temperature of the fluid sphere is observed. We show that the net effect of the Coriolis force is to damp the convective motion and to allow a redistribution of the vorticity field.