Analytical model, sensitivity analysis, and algorithm for temperature swings in direct gain rooms

Abstract

An analytical method is presented for determining the temperature swings in direct gain rooms for relatively clear days. Fundamental network concepts, such as the delta to star transformation and the Norton theorem, are used to obtain the solution for a representative room temperature and the storage mass front surface temperature, in the frequency domain. The storage mass is modelled as a two-port element, analogous to a transmission line, and thus no discretization is required. Heat sources representing the absorbed solar radiation and the ambient temperature source are modelled analytically by Fourier series. The results of a sensitivity analysis are given, illustrating the flexibility of the method in studying the effects of changing the values of room design variables and the daylength. The daylength is shown to determine the relative magnitude of the harmonics of the solar radiation absorbed in the room; the number of harmonics required in the analysis increases with decrease of the daylength and of the amount of storage mass. Comparison of results with a lumped parameter model shows a maximum difference of 12% in the storage mass surface temperature swings. It is useful to know how frequently the room is likely to overheat under real weather conditions. Thus, an algorithm implementing the method is also described, and it requires as input the daily clearness index and the daily ambient temperature range.