Harmonic analysis of building thermal response applied to the optimal location of insulation within the walls

Abstract

The analysis of heat transfer through building walls using Fourier transforms and the matric method are briefly reviewed. The formalism is applied to a simple one-room building. By making a few simplifying assumptions and by considering only one- or two-layer walls and roofs, the equations are kept sufficiently short to preserve the insight of the reader into the effects of a few construction features upon the building's thermal response. Such construction features, mainly the placement of insulation inside or outside the main wall mass, are extensively discussed, with an eye on their potential energy savings. The results are: (1) the placement of insulation outside the wall masonry reduces the amplitude of the internal temperature swing caused by weather conditions and by internal heat gains. If the inside temperature is left free to oscillate within a few degrees, the amplitude of the heating or cooling load is greatly reduced, allowing for substantial energy savings. However, the building is thermally sluggish and inefficient durign thermostat setbacks because of its large wall heat storage. (2) Inside placement of insulation increases the room temperature response to weather conditions and to internal heat gains. Thus, heating or cooling is needed for temperature peak-shaving. In return the building's response to a thermostat setting change is quick and the heat stored in the walls, lost during a setback, is relatively small.