Thermal Modeling of Walls, Foundations and Whole Buildings Using Dynamic Thermal Networks

Doctoral thesis, 2005

The modeling of the energy balance of buildings is a major task in building physics. A new theory called dynamic thermal networks is under development at the Building Physics Research Group at Chalmers. The calculations are based on step-response functions, and the problems are illustrated in so-called dynamic networks. Long time scales for heat flux through building foundations and the surrounding ground are handled by a special reduction procedure. The aim of this thesis is to apply the theory to increase knowledge of the factors that influence a dynamic heat loss calculation. The theory is used to illustrate the thermal behavior of different wall types, different foundations and whole buildings in three dimensions. The thermal behavior of a crawl space and an attic is studied as well, where the influence of long-wave radiation between internal surfaces is accounted for. A few applications of the theory on energy balances for two- and three-surface problems are presented, and an example of an application in a moisture problem is shown. The step-response functions for one-dimensional cases are calculated analytically by using a combination of Fourier and Laplace techniques. The response functions for two- and three-dimensional cases are calculated numerically. Analytical expressions are fitted to the numerical values for short and long time to give better precision and faster calculation time. The work reported in this thesis shows that it is fairly simple to apply the theory to whole heat balances. A building’s heat balance can be calculated in a few minutes only for a time step of one hour during a year with an ordinary desktop computer. The full accuracy of the calculations for the three-dimensional step-response heat flow process in the building’s envelope is essentially retained in the modeling during the annual cycle. The investigations of the thermal behavior of buildings and different building components show that a great deal of information can be gained from the response functions. However, it is also clear that there is much more to develop and learn about thermal behavior and step-responses.