Correlation between the sum of the flux conduction transfer function coefficients and a dimensionless function of the thermal properties of building walls

Abstract

The estimation of the conduction transfer function (CTF) coefficients is the main step to obtain the transient heat flows on the inside and outside surfaces of a multilayer wall, and thus the heating and cooling loads in a building. Taking a wide variety of construction types, 76 walls from the ASHRAE Handbooks of Fundamentals, it is demonstrated that the aspects of wall transient thermal behaviour can be summarised by a non-dimensionalised function V of the thermal capacity and resistance of the layers of the wall. The sum of the flux CTFs, Σdk, is highly correlated with this measure and the correlation coefficient increases when the sampling time interval decreases. The current interest for nearly zero energy buildings demand management techniques requires the calculation of the CTFs for highly insulated walls and short sampling intervals. The study is extended to the possibility of the CTFs with shorter time steps but longer time steps are needed for thick walls. The theory of the plain slab runs as a thread through the study: the scatter of wall Σdk values cluster around the Σdk:V relation for a slab; the response factor function (exit flux following imposition of a temperature change at the other surface) follows readily from a classical expression in transient thermal response (and from which the slab CTF’s readily follow), and an appendix presents the slab’s recently discovered exact Σdk:V relation.