Numerical visualization of convective heat transfer from a sphere — with and without radial mass efflux

The conception of a heat function, just like the stream function used in a laminar two dimensional incompressible flow field visualization, has been introduced to visualize the convective heat transfer or the flow of energy around a sphere when the sphere is either being cooled or heated by a stream of fluid flowing around it. The heat function is developed in a spherical polar coordinate and is used to generate the heat lines around the sphere. The heat lines essentially show the magnitude and direction of energy transfer around the sphere with and without the existence of a finite radial velocity at the surface. The steady state hydrodynamic field around the sphere is numerically obtained up to a maximum Reynolds number of 100 and the corresponding thermal field has been obtained by solving the steady state energy equation. The field properties thus obtained are utilized to form the heat function, which becomes an effective tool for visualization of convective heat transfer.