On transient natural convection heat transfer in the annulus between concentric, horizontal cylinders with isothermal surfaces

Abstract

The transient natural convection heat transfer problem between two horizontal isothermal cylinders is formed within the Boussinesq approximation and solved numerically through the vorticity-stream function approach. Specifically, we discretize both the vorticity and energy equations via the alternating direction implicit (ADI) method and the stream function equation by the successive over relaxation (SOR) method. Within our range of interest, the transient time from the transient state to the steady state is found to be very small in comparison with a typical operation time. Under such circumstances, the steady-state Nusselt number can be used in lieu of the transient Nusselt number. Our numerical results are summarized by three Nusselt number vs Grashof number curves with the diameter ratio as a parameter, which serve as a guide to natural convective heat transfer calculations for an annulus.