Heat Transfer from a Moving Fluid Sphere with Internal Heat Generation

ACL; International audience; 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 < \kappa < 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 \kappa (\kappa = = μd/μc) influences significantly the heat transfer from the sphere. The average Nusselt number decreases with increasing \kappa 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 \kappa.