Calculating Building Heating and Cooling Loads Using the Frequency Response of Multilayered Slabs

摘要

This thesis describes the development of a method for calculating room heating and cooling loads using frequency response methods to calculate heat flow through multi-layered room walls and roofs. Existing methods for calculating room loads are discussed and the need to consider the effects of thermal mass are emphasized. A detailed derivation of the solution of the transient one-dimensional heat conduction equation for multi-layered slabe which leads to the calculation of response factors and conduction transfer functions is presented. Next, the special case of a fixed temperature on one side of a multi-layered slab and a sinusoidal temperature variation on the other side is examined and the simplifications which result are described. This frequency response method for calculating heat flow can be applied to buildings if the outdoor climate can be represented by a reasonably small number of sinusoidal components. To determine the extent of sinusoidal variation in climate, time series analysis techniques were applied to hourly measured weather data from four climatically different sites in order to separate the deterministic periodic behavior in the data from its stochastic behavior. A combined deterministic plus stochastic model was found to be adequate for the climate variables studied. This model included as its deterministic component sinusoids with frequencies corresponding to the annual cycle, the diurnal cycle, and the first harmonic of the diurnal cycle. The use of this method as part of a simplified room load-calculating procedure was compared to results from a more detailed approach, and again, very good agreement was found.