## 4 Validation of the Model  
The mathematical model was validated by comparing its results to experimental data, available in two experimental literature, as described below. [PERSON], [PERSON], and [PERSON] [39] developed an experimental set-up, designed to measure the periodic heat flow through the external walls of a room. The experimental equipment is shown schematically in Figure 3: The thermal source (S) consists of a steel prismatic container, inside of which water circulates. The temperature can be controlled, in time, according to a pre-established law, by means of the regulation system (B). The latter is made up of a boiler (A), in which the water is heated by an electrical resistance unit, the feeding of which is controlled by a transformer (T) through a regulation system (G), fed-back by the actual water temperature value at the entrance of the source (S). The temperature, measured at (S), is compared with the programmed value in (F) and adjusted by the regulator (E). The source (S) consists of a central zone, which is dedicated to the actual thermal transmission, and a guard ring, which prevents lateral leakages. On both opposite sides of the source, the wall (P) being tested was fixed by means of appropriate fixing rods, in such a way as to achieve a symmetrical distribution of the thermal flux emitted from (S). The thermal capacity of the internal environment of the testing room was adjusted by means of 20 tubes of thin glass placed vertically, which contained water in different quantities according to the internal thermal capacity that one wishes to achieve. Ventilation was provided feeding air into the two symmetric, insulated rooms (whose internal dimensions were 1.4 \(\times\) 1.4 \(\times\) 1.0 m, each). Air was extracted by a fan (W) from an external environment whose temperature was constant, in practice. In fact, the tests were carried out in a semi-basement laboratory with a volume of about 2,000 m\({}^{3}\). The volumetric flow of the ventilated air was measured by rotameters (R), whose calibration was controlled periodically by inserting a Venturi meter (V) into the circuit. During the tests, measuring of the temperature was carried out by resistance thermometers, on the surface of the walls being tested, in contact with the source (S), and on the internal one facing of the environment delimited by the rooms (1 and 2), as well as on the inside of the rooms themselves. The test panel was made of three layers and the specification of each one is shown in Table 1.  
The experimental tests were carried out realizing 30 determinations, each one lasting 5 days, imposing a sinusoidal thermal wave on the external face of the panel being tested and recording the form of the wave transmitted into the two rooms (1 and 2). During the tests, the amplitude of the sinusoidal wave imposed by the source S was equal to 16 \(\pm\) 1 \({}^{\circ}\)C. The average temperature of the lab, in which the test section was placed, experienced a seasonal temperature excursion of about 10 \({}^{\circ}\)C and consequently, during the 150 days of tests, varied between 65 and 75 \({}^{\circ}\)C.  
The various series of tests differed, one from another, for the different internal thermal capacity referred to the unit area of the walls being tested, named M, equal to 2, 15, and 25 [k]/(m\({}^{2}\)K), respectively. Finally, the air changes were made to vary from zero to 25 times the volume of the room, per hour. The second validation was based on the experiments by [PERSON] and [PERSON] [PERSON] and [PERSON] (2010), in both steady-state and dynamic conditions, of six masonry walls, in order to investigate their heat transfer characteristics. The apparatus consisted of a calibrated hot box facility made up of two highly insulated chambers. This system was designed to accommodate walls with thermal resistances varying from 0.26 to 3.52 [K/(m\({}^{2}\)W)]. The outdoor chamber was maintained at a constant temperature or oscillating between