Mixed convection from an isolated spherical particle

A numerical study on mixed convection around a hot spherical particle moving vertically downwards in a still fluid medium has been made. The flow field is considered to be axisymmetric for the range of Reynolds number (based on the diameter and the settling velocity of the particle) considered. A third-order accurate upwind scheme is employed to compute the flow field and the temperature distribution. The form of the wake and the thermal field is analyzed for several values of Grashof number and the Reynolds number. The influence of buoyancy on drag and the rate of heat transfer are studied. At moderate Reynolds number, recirculating eddy develops in the downstream of the sphere. With the rise of surface temperature this eddy collapses and the fluid adjacent to the heated surface develops into a buoyant plume above the sphere. The increase in surface temperature of the sphere delays the flow separation. Our results show that the drag force and the rate of heat transfer strongly depend on Grashof number for the moderate values of Reynolds number. The conjugate heat transfer from the moving sphere is also addressed in the present paper. We have compared our computed solution with several empirical and asymptotic expressions available in the literature and found them in good agreement.