A Short Method to Compute Nusselt Numbers in Rectangular and Annular Channels With Any Ratio of Constant Heat Rate

Abstract

An analytic investigation of the thermal exchanges in channels is conducted with the prospect of building a simple method to determine the Nusselt number in steady, laminar or turbulent and monodimensional flow through rectangular and annular spaces with any ratio of constant and uniform heat rate. The study of the laminar case leads to explicit laws for the Nusselt number, while the turbulent case is solved using a Reichardt turbulent viscosity model resulting in an easy to solve one-dimensional ordinary differential equation system. This differential equation system is solved using a matlab based boundary value problems solver (bvp4c). A wide range of Reynolds, Prandtl, and radius ratios is explored with the prospect of building correlation laws allowing the computing of Nusselt numbers for any radius ratio. Those correlations are in good agreement with the literature. The correlations are also compared with a CFD analysis made on a case extracted from the Réacteur Jules Horowitz.