Modeling the Transient Response of Thermal Circuits

Abstract

Although stationary models for thermal circuits have been widely used, a direct analogy of transient responses of electric circuits to thermal systems is still difficult to establish. In this work, a thermal circuit model for transient responses is developed. The model states that each thermal object is a thermal resistance and a heat capacitor in parallel. The heat capacitor is the heat capacity of the overall material plus a correction term due to the thermal contacts of all thermal objects. The transient response of three basic thermal circuits is modeled, based on the proposed method, and validated, using the heatrapy Python package: single thermal resistance, two thermal resistances in series and two thermal resistances in parallel. A more complex model of a thermal circuit involving a heat source, a heat transfer medium and convection of heat to the surroundings is also developed and validated with data from literature of a thermal switch used in caloric cooling. The proposed method tackles computational issues introduced by the majority of numerical approaches.