An improved algorithm for thermal dynamic simulation of walls using Z-transform coefficients

The Transfer Function Method (TFM), recommended by American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE), is one of the most modern tools available to solve heat transfer problems in building envelopes and environments. TFM utilises Z-transform to solve the equations system that describes the heat transfer in a multi-layered wall. Due to an analogy with an electric circuit, it is possible to write the equations system in a matrix suitable to be solved by computer. Authors carried out an analysis on an historical building placed in the south of Italy to test the reliability and the quality of the thermal dynamic simulation using TFM. The analysis is performed using some control systems tools like Bode plots, step response, root and poles location. Results show clearly that, for very massive building, a simply application of TFM fails but if the poles and the residuals are re-ordered in a different position, it will be possible to solve the numerical problem. Furthermore, the analysis shows that the choice of the sampling period is a significant factor to obtain a reliable simulation.