Heat transfer from a moving fluid sphere with internal heat generation

Abstract

In this work, we solve numerically the unsteady conduction-convection equation including heat generation inside a fluid sphere. The results of a numerical study in which the Nusselt numbers from a spherical fluid volume were computed for different ranges of Reynolds number (0<Re<100), Peclet number (0<Pe<10000) and viscosity ratio (0<k<10), are presented. For a circulating drop with Re?0, steady creeping flow is assumed around and inside the sphere. In this case, the average temperatures computed from our numerical analysis are compared with those from literature and a very good agreement is found. For higher Reynolds number (0<Re<100), the Navier-Stokes equations are solved inside and outside the fluid sphere as well as the unsteady conduction-convection equation including heat generation inside the fluid sphere. It is proved that the viscosity ratio k (k = ?d/?c) influences significantly the heat transfer from the sphere. The average Nusselt number decreases with increasing k for a fixed Peclet number and a given Reynolds number. It is also observed that the average Nusselt number is increasing as Peclet number increases for a fixed Re and a fixed k.