Bulk Temperature, Heat-Transfer Coefficient, and Nusselt Number-Revisited

Abstract

Convective heat transfer on surfaces is often presented in the form of the heat-transfer coefficient (h) or nondimensionally in the form of the Nusselt number (Nu). For internal flows, h and Nu depend on the bulk temperature in addition to the geometry and the nature of the flow. However, the bulk temperature is clearly defined only for a simple duct without flow separation. Also, even when it is well defined, it is hard to measure experimentally so that it is often approximated when experimentalists measure h. In this study, computational fluid dynamics (CFD) is used to examine several approximations of the bulk temperature that are commonly used in experimental measurements and how these approximations affect the measured heat-transfer coefficient and Nusselt number. The effects of compressibility and temperature-dependent properties on heat-transfer and Nusselt are also examined. The test problem used is flow and heat transfer in a straight duct with a circular cross section under laminar and turbulent conditions and under compressible and incompressible flow conditions with constant and temperature-dependent properties. This test problem was selected because exact solutions and well-established correlations exist for the incompressible-flow cases to validate the CFD and to assess the errors created by the approximations to the bulk temperature. Nomenclature