Admittance/Fourier Series Revisited: Understanding Periodic Heat Flows

Thermal modelling of buildings typically involves the use of software programs that are highly accurate but complex. As such many users do not have a good “feel” for how heat flows in and out of a building. The simplest type of manual calculation method is a steady state model which allows some insight into the flow of heat in a building. However modelling of thermal storage in building elements with mass is seen to be too difficult to be solved readily and as such complex thermal software programs are utilised. In the late 1960s and early 1970s the admittance method was developed which calculated quite accurately the thermal response of building elements with mass. Typically the thermal response of a building to 24 hour cyclic inputs - temperatures and solar radiation - was calculated. When extended to higher frequencies utilising a Fourier series representation of temperatures and solar radiation, accuracy improves further. However this approach was soon overtaken by more complex computer based models which delivered greater modelling complexity and accuracy but tended to obscure the underlying physical processes. This paper re-examines the admittance/Fourier method as a pathway to enhancing understanding of the response of buildings to fluctuating temperatures and solar radiation. A simplified representation of yearly ambient temperature in terms of only three terms: a constant, a yearly and daily frequency - allows a very simple model of a building to be developed. This approach can allow building designers rapid insight into the performance of various materials and designs and in addition enhance their understanding of the fundamental physical processes involved.