AN ANALYTICAL SUPERPOSITION APPROACH TO WALL HEAT-CONDUCTION UNDER ARBITRARY TEMPERATURE PERTURBATIONS FOR AIR-CONDITIONING APPLICATIONS

An analytical solution is derived for the transient wall heat conducti on problem under arbitrary outdoor air temperature perturbations. This is obtained by expanding the arbitrary perturbation in a Fourier seri es, consisting of a step function and an infinite sum of cosine and si ne functions. The analytical solutions in the cases of step, cosine an d sine temperature perturbations are derived separately from each othe r and are then superimposed to produce the resultant solution. Simple linear expressions are derived, which express the maximum indoor heat flow provoked by the arbitrary temperature perturbation in terms of pa rameters characterizing the perturbation. Such simple expressions are very useful in air-conditioning calculations for predicting peak loads and sizing heating or cooling equipment.