Simple Models for Laminar Thermally Developing Slug Flow in Noncircular Ducts and Channels

Abstract

Solutions to the classical Graetz slug flow problem (uniform velocity distribution) in noncircular ducts are examined. These solutions have applications where a constant uniform velocity distribution exists across a channel or duct. These are most often realized in the laminar flow of low Prandtl number liquids, such as liquid metals, and low Reynolds number flows through porous media. Expressions are developed for a number of applications using the asymptotic correlation method of Churchill and Usagi. These expressions vary depending on the definition used for the dimensionless heat transfer coefficient, in the case of constant wall temperature boundary condition (T), and the dimensionless wall temperature for the constant flux boundary conditions (H) and (H1). Finally, simple expressions are developed for predicting the thermal entrance length and fully developed flow Nu values for noncircular ducts.