Transient Internal Forced Convection Under Step Wall Heat Flux Condition

A new closed-form analytical model is developed to predict transient laminar forced convection inside a circular tube following a time-wise step change in the wall heat flux. The proposed all-time model is based on a blending of two asymptotes; i) short-time asymptote: transient pure conduction in an infinite cylinder and ii) long-time asymptote: steady-state convective heat transfer inside a circular duct. Different fluid velocity profiles are taken into consideration and the model covers: i) Slug Flow (SF); ii) Hydrodynamically Fully Developed Flow (HFDF); and iii) Simultaneously Developing Flow (SDF) conditions. The present model is developed for the entire range of the Fourier and Prandtl numbers. As such, short- and long-time asymptotes for the fluid bulk temperature are obtained. The Nusselt number is defined based on the local temperature difference between the tube wall temperature and the fluid bulk temperature. It is shown that irrespective of the velocity profile, at the initial times the Nusselt number is only a function of time. However, at the steady state condition it depends solely upon the axial location. In addition, during the transient period, the Nusselt number is much higher than that of the long-time response. We also performed an independent numerical simulation using COMSOL Multiphysics to validate the present analytical model. The comparison between the numerical and the present analytical model shows good agreement; a maximum relative difference less than 9.1%.