On the Transient Convective Transport from a Body of Arbitrary Shape

Abstract

The net rate of transient convective heat transfer from a body at uniform temperature in steady flow is shown to be invariant to pointwise reversal of the flow. Such reversal is physically possible in both creeping and potential flows. Creeping flow and the unseparated potential flow of a low Prandtl number fluid yield physically important transfer problems. Additionally, the theorem is applicable to problems for which flow reversal has no physical significance; numerical reversal of any incompressible streaming flow will leave the net transfer rate unchanged. The proof is not based on symmetry and places no restriction on the shape of the body. It remains valid over the entire range of Reynolds and Peclet numbers even though local transfer rates may differ significantly in the two directions of flow. The theorem applies to the analogous mass transport and is generalized to include a homogeneous first order reaction decreasing the concentration.