The transfer function method (TFM) is considered an effective tool for the prediction of transient heat transfer through building envelope components [ASHRAE Handbook --Fundamentals]. In fact, one of the main advantages of this procedure is the compact form of the solution and the accurate results obtained by means of a reduced computational effort. For this reason, conduction transfer function (CTF) coefficients are well established within the building thermal analysis field and have been extensively validated. Nevertheless, the algorithms for the generation of these coefficients are only available for one-dimensional building elements as multilayer walls, roofs, and floors. For multidimensional domains, mainly for mathematical difficulties, the CTF coefficients have been evaluated by means of appropriate input/output identification techniques applied to experimental or numerical responses. Because of the errors affecting the above data, the available sets of coefficients provide results of little practical usefulness.

This paper presents a general procedure of the calculation of heat flow through multidimensional building components, based on the finite element method (FEM) and on an original condensation technique. As a final result, the heat flow is obtained in the form of a simple recurrence scheme in which a set of coefficients is recognizable, which is very similar to the CTF coefficients. The validation of the suggested approach is made by comparing responses of typical typologies of floor radiant panels to numerical results carried out by a reliable computer code (ANSYS Revision 5.4).

In order to show a practical application of the procedure, a simple simulation model was used. Starting from the balance equations written for the thermal performance of a room (Kusuda 1976), a radiant floor panel was inserted as a heating element and certain simplifications, such as ignoring heat sources in the room space, were adopted. For three different panel constructions, the time evolutions of the indoor air temperature and the surface panel temperature have been calculated in the start-up period. The results show the combined influence of the panel structure and thermal mass of the building envelope on the performance of the room.

Units: SI