Applicability of calculation methods for conduction transfer function of building constructions

Conduction transfer function (CTF) is widely used to calculate conduction heat transfer in building cooling/heating loads and energy calculations. It can conveniently fit into any load and energy calculation techniques to perform conduction heat transfer calculations. There are three popular methods, direct root-finding (DRF) method, state-space (SS) method and frequency-domain regression (FDR) method to calculate CTF coefficients. The limitation of a methodology possibly results in imprecise or false CTF coefficients. This paper investigates the applicability of three methods as Fourier number and thermal structure factor are varied and in detail explains the sources that introduce error in the CTF solutions. The results show that the calculation error of SS and DRF methods becomes increasing as the reciprocal of the product of Fourier number and thermal structure factor becomes increasing. The maximal error even reaches almost 100%. However, the calculation error of FDR method always remains within 1% no matter how Fourier number and thermal structure factor are varied. Thus, FDR method is more robust and reliable than SS and DRF methods. And it is more practical to calculate CTF coefficients and may be a better choice to calculate the cooling/heating loads for building structures for the architect/designer.