The heat [formula omitted] ratio for a building and its response time

Abstract

If a thermal system is in a steady state and at zero time a step change in excitation is applied, the time taken for the temperature at some node to change by 63 per cent of its ultimate change is defined as the response time, t r , there. If the temperature at the node concerned is fixed, the ratio of the heat, S, stored in the system relative to an ambient temperature of zero, to the heat, L, lost from the system, provides another time, t sl = S L . For many years, t sl , which is easy to calculate, has been assumed to be of order t r , which is easy to interpret. When this is so, the storate loss time provides a measure of the speed of the building's thermal response. Previous work has demonstrated that, in some circumstances, t sl may equal t r exactly, or almost exactly, but that, in other circumstances, the two times may differ considerably. This paper examines the relationship between the two for a number of elementary thermal systems whose response can be calculated using published solutions. The effects corresponding to changes in ambient temperature and to a change in heat input have been examined. It appears that, whilst t r t sl can vary over a wide range, for the most part the ratio lies fairly close to unity and it seems likely that this may be the case for a building enclosure with its complex pattern of heat exchange and storage. It is useful to introduce a third time, the fundamental decay time, t d . The value of t r is of the same order of magnitude as t d , or is less than it. A standing wave matrix, similar in structure to the transmission matrix for handling progressive waves in a slab, is used to find the system's eigenfunctions. A review is given of some previous work concerned with the relationship between building response time and the storage loss ratio.