Addressing Mismatch Between the Peripheral and Local Nusselt Number for Non-Axisymmetric Flow Conditions: Redefining the Mean Temperature

Abstract

For non-axisymmetric conditions, the traditional fluid mean (bulk) temperature at a tube cross section, subjected to constant heat flux, can be higher than the temperature of a point on the wall. This results in a mismatch between the direction of applied heat flux and the temperature difference resulting in (misleading) negative peripheral heat transfer coefficient and Nusselt number (Nu). The resulting cross-sectional Nu (average of peripheral Nu values) differs from that calculated from average surface temperature and mean temperature. To address this gap in the literature, a detailed procedure is investigated based on a radial mean temperature of individual lines calculated from the lowest temperature spot in the cross-section to wall points, physically satisfying the mechanism of actual heat transfer from hot to cold spots. Each radial line’s mean temperature is used to calculate a peripheral Nu. These peripheral and average Nu are always positive and matches with the cross-sectional Nu that is calculated using the traditional method – single average cross-sectional temperature. This method is verified for different duct geometries including circular, square, and rectangular. The method also succeeds in the estimation of the peripheral and cross-sectional Nu values for eccentric annular ducts that are inherently non-axisymmetric and have negative Nu values according to the published literature.