Transient heat flow calculation for multilayer constructions using a frequency-domain regression method

A frequency-domain regression method is developed for transient heat flow calculation of multilayer constructions, which estimates a simple polynomial s-transfer function of transient heat conduction in a building construction on the basis of its theoretical frequency characteristics. This simple polynomial s-transfer function is completely equivalent to the hyperbolic s-transfer function in terms of frequency characteristics. First, the frequency characteristics of the total transmission matrix are calculated within the frequency range concerned. Then, a set of linear equations is solved to yield a simple polynomial s-transfer function for internal, cross and external heat conduction, respectively. Finally, the response factors or CTFs are obtained simply by applying inverse Laplace transforms or Z-transforms on the polynomial s-transfer function. The validations and comparisons show that this method has high accuracy and efficiency and has no stability problem.