Forced heat convection in laminar flow through rectangular ducts

Abstract

In this paper we consider the problem of finding the heat transfer to the wall of a duct which has a rectangular cross-section and through which a hot viscous fluid passes in steady established laminar motion. We shall make the usual simplifying assumptions that the thermal properties of the fluid are independent of temperature, that liquids are incompressible and that gases obey the perfect gas law. The first is strictly true only for small heat input and, of course, the assumption of established motion ignores the hydrodynamical boundary layer in the inlet. The problem is of engineering interest since, in many applications of gas-flow heat exchangers, flow passages are used which have small cross-section and a high ratio of surface area to core volume, so that the Reynolds number is often small enough for laminar flow to exist. Practical cross-sections can often be approximated by simple geometrical shapes and theoretical correlations of heat transfer with cross-section are of value in reducing the amount of practical test data required.