On the lumped capacitance approximation accuracy in RC network building models

Thermal resistor-capacitor networks are a popular method for control-oriented building modeling. A basic assumption underlying this method is that the continuous temperature distribution in a wall or window is well-approximated by a small number of lumped capacitances. In this paper, we explore the accuracy of this approximation when a single capacitance is used. We derive conditions on the dimensionless parameters that characterize the problem, called Biot numbers, that lead to small errors in approximating a wall or window's surface heat fluxes and internal energy. The lumped capacitance approximation can be surprisingly accurate for Biot numbers much larger than the conventional upper bound of 0.1. In particular, the approximation is nearly exact for window panes, and is often acceptable for uniform walls. A large Biot number at an indoor wall surface, however, leads to large lumped capacitance approximation errors.