The spread of eigen time-values to find the wall heat transfer coefficients dk

Abstract

It has long been recognised that in evaluation of wall heat transfer coefficients, a series of values with units of time, denoted here by zj (z1 is of order hours), has to be found by search, and that consecutive values are sometimes close and may be missed. This problem is investigated here through two approaches: (i) the zj-related properties are examined of various simplifications of a basic seven-parameter model, so having fewer parameters than those of multilayer building walls; (ii) the series of zj values, found from imposition of zero-temperature boundary conditions are placed in sequence with those found from the other three boundary conditions. Using an appropriate non-dimensional form for zj, the spread of these values has been examined for one of the sets of walls of widely varying construction listed by ASHRAE. The significance of this approach is that the transient thermal behaviour of walls can be visualised and interpreted in terms of the set of eigenfunction temperature profiles associated with its series of zj values. An appendix sketches the broader mathematical framework into which the study fits, and another outlines its use in the present context.