Unsteady heat transfer from a sphere in a uniform cross-flow

Abstract

Three different types of unsteady heat transfer problems are considered: the first considers the free thermal evolution of a spherical particle subjected to a uniform isothermal ambient flow, where the particle temperature evolves toward the ambient flow temperature; the second considers the unsteady heat transfer problem in response to a sudden jump in the particle temperature; and the third considers oscillatory heat transfer due to oscillatory particle temperature in an isothermal ambient flow. In each case a range of Reynolds or Peclet number is considered. The first set of simulations show that unsteady heat transfer from a spherical particle under free thermal evolution can be described by an effective Nusselt number, at least over the range of parameters considered in this study. The effective Nusselt number under unsteady free thermal evolution deviates from the steady-state counterpart and the difference depends on the heat capacity ratio between the surrounding fluid to the particle. The existence of an effective Nusselt number indicates a faster decay of the thermal history kernel, which is confirmed with response to a step change in particle temperature in the second set of simulations. The final set of simulations considers the behavior of the thermal history kernel in the frequency space. We observe the low frequency response, or correspondingly the long time behavior, of the thermal history kernel at finite Peclet number to deviate significantly from the classical one over square root decay obtained for zero Peclet number limit.