The harmonic method: A new procedure to obtain wall periodic cross response factors

Thermal accumulation phenomena are one of the hardest problems to solve in thermal load and energy calculations in buildings. The evolution in the mathematical modeling of building envelopes wants to provide a response to the growing need for accuracy in equipment dimensioning and energy certification calculation methods.Among all existing methods, the response factors method and the transfer function method, developed by Mitalas (1967) and Stephenson (1971), stand out due to their simplicity, accuracy and widespread use.After that, with the release of the RTS (Radiant Time Series) method, developed by J.D. Spitler, D.E. Fisher and C.O. Pedersen in 1997, the concept of periodic response factors is introduced, adding the hypothesis of 24-h periodicity of the input conditions.The main difficulty of the method lies in obtaining these so called response factors or weighting factors, which requires an approximate, complex, and high computing cost procedure.In this paper, a new method to obtain 24 h periodic wall response factors called the Harmonic Method is presented, which constitutes an improvement over usual methods used to obtain wall response factors. It will be shown that this method is able to reduce computational effort and increase accuracy compared to previous calculation algorithms.

► We have developed a new method of obtaining wall periodic response factors.
► This method is easier to implement and requires less computational effort.
► We avoid root finding procedures and calculates directly the periodic factors.
► The procedure calculates the analytical solution, without numerical approximations.