Refinement of the Generalized Graetz Problem Correlation With New Benchmark Calculations

Abstract

A recently proposed generalized correlation for the Graetz problem in heat transfer has two fitted constants that can be related back to two fundamental constants of fully developed transport. A new set of benchmark solutions for convection in annular tubes is used to assess the best linear relationship between fitted and fundamental constants used in this correlation for conditions spanning from circular tubes to parallel plate ducts. This work also improves the Leveque limit of the general correlation by considering peripheral variation in flow friction. The refined Graetz problem correlation for fully developed flow is able to predict exact thermal entry region solutions to within +/- 1.2% for all annular tube geometries having either constant temperature (T) or constant heat flux (H1) wall condition.