Derivation of equivalent continuous dilution for cyclic, unsteady driving forces

This article uses an analytical approach to determine the dilution of an unsteadily-generated solute in an unsteady solvent stream, under cyclic temporal boundary conditions. The goal is to find a simplified way of showing equivalence of such a process to a reference case where equivalent dilution is defined as a weighted average concentration. This derivation has direct applications to the ventilation of indoor spaces where indoor air quality and energy consumption cannot in general be simultaneously optimized. By solving the equation we can specify how much air we need to use in one ventilation pattern compared to another to obtain same indoor air quality. Because energy consumption is related to the amount of air exchanged by a ventilation system, the equation can be used as a first step to evaluate different ventilation patterns effect on the energy consumption. The use of the derived equation is demonstrated by representative cases of interest in both residential and non-residential buildings.