Rational Compact Modeling of Transient Forced Laminar

Although transient convection is ubiquitous in natural and manmade phenomena, few research works attempted to create a compact model for it, leading to models that often contradict the underlying physics. This study analytically deduces the correct modeling pattern for a simple geometry that can be applied to various systems, such as the transient heating of evacuated solar tubes due to temporary cloud shading or modeling of building wall heating in zero-energy buildings. Unlike detailed models, which require extensive numerical solutions of partial differential equations to determine temperature distributions over time and space, the proposed compact model relies on a few straightforward equations to establish a direct relationship between the heat flux and the resulting temperature difference for any boundary and initial conditions. This analysis reveals two primary advantages: firstly, it replaces conventional unphysical approaches based on time-variant thermal resistance by introducing physically meaningful time constants for the fluid bulk and near-wall temperatures; and secondly, this single model can adapt to different time-varying input heat flux functions. Validation against comprehensive CFD simulations confirms the effectiveness of the proposed model.