ABSTRACT
In this chapter, we review different mathematical methods to analyze transient heat flows in the building fabric, i.e., elements such as walls and roofs. How these methods are combined to determine building peak or design loads of an entire building or zone is addressed in the next chapter. We start by examining the limitations of a steady-state analysis and the need for dynamic models. Methods for analyzing transient heat conduction through building elements can be classified into continuous and distributed according to how the elements are treated. The partial differential heat equation is an example of the former type of formulation, which can be solved when the initial and boundary conditions are specified. The equations that define the dynamic response of each surface to changes in temperature are then solved incrementally as external temperature conditions change. The distributed methods arrive at a solution by proceeding to discretize the building element into discrete layers. The well-known finite difference approach is one such approach, and this is also described. The time-series formulation is another approach that is more prevalent in building science literature. Both the conduction transfer function (CTF) model and the conduction time-series (CTS) model, fall under this category, and are described. Furthermore, we treat, at some length, the thermal network model, which is a third solution approach. The 1R1C thermal network is presented and solved as the simplest possible dynamic model. It serves to explain the important concept of the time constant and to estimate the warm-up and cooldown times of a building. We also discuss extensions to more complicated networks. The connection between thermal networks and transfer function models is pointed out, and a solved example illustrates the close agreement in their transient solutions. Finally, the frequency-domain response function method is briefly described.
