Rational Compact Modeling of Transient Forced Laminar Convection

Abstract

Although transient convection is ubiquitous in natural and manmade phenomena, few research works attempted to make a compact model for it, altogether, others attempted a compact model that contradicts problem physics. The correct modelling pattern is deduced here analytically for a simple geometry, but it can readily be used for many common applications such as the transient heating of an evacuated solar tube due to temporary cloud shading or for a more precise model of transient building wall heating in a zero-energy building approach. As opposed to detailed model, which is based on the governing PDE with a fixed and rigid boundary and initial conditions, usually solved numerically, aiming at obtaining temperatures everywhere and at any time for a prescribed boundary and initial conditions, the compact model on the contrary is based on a few simple equations, and aims at giving directly the relation between heat flux and the temperature difference producing it, for any boundary and initial conditions. For transient convection prevails as of today an unphysical approach consisting of modeling it by using a time variant thermal resistance. In this work, starting from the energy PDE, applied to a simple but typical transient forced convection problem, we will get analytically the correct modelling pattern. This has two main advantages: It replaces the classical unphysical approach, with a pair of time constants, one for each important temperature (the fluid bulk and that near the wall), which has an evident physical meaning and can be readily extended to more complex geometries. In contrast with the time varying resistance model, one and the same model as deduced here can be reused for any arbitrary time varying function of the input heat flux. Model validation was made by comparing with a fully blown CFD simulation.