A frequency domain estimation of wall conduction transfer function coefficients

This article describes a novel method to evaluate the series of wall thermal response factors for multi-layer walls, values which give the surface heat flows at hourly intervals due to a triangular pulse of external temperature (base 2 h, height 1 K). Here, the pulse is resolved into its Fourier components, each component is linked with the sinusoidal response of the wall at the corresponding frequency and the sums of the products provide the response factors. The approach is conceptually and computationally simple; for high accuracy it entails summation of a large number n of products but when n is large they can be handled in blocks of 200, then 1000,… Response factors can readily be transformed to wall conduction transfer coefficients (TCs) and the method is illustrated through analysis of one of the 41 walls whose transfer coefficients are listed in various editions of the ASHRAE Handbook of Fundamentals. It extends the ASHRAE values (a) by providing more terms and to higher accuracy, so as to remove an anomaly in their presentation, (b) it provides TCs for same-side excitation (additional to the current cross-excitation values), and (c) it demonstrates that such values are appropriate for use with a heat source in the room.

► We describe a novel method to evaluate wall response factors and transfer coefficients. ► The method is conceptually simpler than the time domain approach and the Laplace transform method of earlier workers. ► It is illustrated through analysis of one of the 41 walls whose transfer coefficients are listed in ASHRAE Handbooks. ► It extends ASHRAE values by providing more terms and to higher accuracy. ► It provides transfer coefficients for same-side excitation and values for use with an internal heat source.