Thermal-electrical analogy and inertia for thermal performance of building envelops

¹ Quartz (EA 7393), LR2E-Lab, ECAM-EPMI, 13, Boulevard de l'Hautil, 95092, Cergy-Pontoise, France
² EBI, EBInnov-Lab, 49 Avenue des Genottes CS90009 95895, Cergy-Pontoise, France
³ LMT, ENS Paris-Saclay, CNRS, Université Paris-Saclay, 94235 Cachan, France

^* Corresponding author: r.absi@ecam-epmi.com

Abstract

For transient thermal performance of building envelops adequate parameters are needed to capture the time lag and decrement factor. It is surprising that, in the formal electrical analogy, "inertia" is not represented by same components in fluid mechanics and heat transfer. In Windkessel model for fluid flow in elastic tubes, the fluid inertia is represented by an electrical inductance while in thermal-electric analogy, thermal inertia is given by a capacitance. Some authors argued that the terminology of ''thermal inertia'' is used incorrectly in the literature. The aim of our communication is to provide some clarification about this controversy. We will show that the thermal effusivity which is the geometric mean of thermal conductivity and volumetric heat capacity plays the role of a "thermal mass". The revisited notion of inertia in mechanics will allow to show the analogy between: mechanical inertia (mass), thermal effusivity and electrical inductance. The three parameters show a tendency to keep invariant a certain physical quantity: velocity, temperature and current intensity respectively. However, the analogy is not complete, the capacitance used in the heat transfer seems to be similar to the one used in the Windkessel model which accounts for tube compliance and therefore to a local storage.