A simple time domain calculation method for transient heat transfer models

This paper presents a simple time domain calculation method to derive thermal response factors and conduction transfer conduction (CTF) coefficients of finite differential models for estimating transient heat transfer through building structures. It is developed on the basis of converting the matrix exponential function, which is a part of the solution of the state equation established from the finite differential equations of building finite differential models, to matrix polynomial. The thermal response factors and CTF coefficients can be easily derived from the matrix polynomial with simple arithmetic and integral in time domain. This method avoids the time-consuming root-finding process of conventional methods and the computation of all the internal temperature of the finite differential model, while utilizing the advantage of the thermal response factors/CTF coefficients which relate the desired outputs at a moment to the previous inputs through a set of coefficients. Various case studies were conducted to validate the performance of this time domain calculation method in calculating the thermal response factors and CTF coefficients of various order finite differential models.