Dynamics of Air and Wall Temperatures in Multiroom Buildings

Abstract

Temperatures have been recorded every five minutes in a number of rooms in a student dormitory. The experimental data are presented as an example of room temperature dynamics in a large multi-room building. Statistical analyses of the data have been carried out to provide auto-correlations of individual room temperatures, its power spectral density, histogram, and the cross-correlations between the temperatures in neighboring rooms. A fairly complicated behavior is observed. A parallel, simplified mathematical model is set up for air and wall temperatures in multiple rooms to explain the temperature dynamics. Each room has an independent heater that switches on and off at certain lower and upper limits, respectively. The governing equations are based on energy balances with heat exchanges occurring between the air in a room and the walls surrounding it, and with the exterior. The instants at which heaters switch on or off are determined by the temperatures, leading thus to a non-linear set of equations. The governing equations are non-dimensionalized to provide the significant non-dimensional groups of the system: there are two which characterize the problem. Limiting solutions for large and small values of these groups provide physical explanation for the effect of the walls. Numerical solutions of this set of first-order ordinary differential equations are easily obtained, and examples of this are shown. The results show that there are still other physical effects to be considered before theory and experiments can be reasonably compared.