The Effect of the Wall Heat Capacity on the Unsteady Temperature Distribution Inside Buildings: a Simple Analytical Approach

The best way to keep the required format of the manuscript is to overwrite these instructions with its text. Papers Heating buildings is important in everyday life. Especially today, every saving of thermal energy is important to stop the global warming of our planet. In this context, the influence of the thermal capacity of walls on the time-dependent temperature change inside buildings is most often ignored in the literature. Therefore, this work aims to investigate the influence of the thermal capacity of the wall on the time-dependent change of the internal temperature in a building room by developing a simple theoretical model enabling the calculation of unsteady heat transfer through the building wall, taking into account the role of the thermal capacity of the external wall. The theoretical analysis also takes into account the heat capacity of the air occurring in a limited cubic space, which has not been taken into account in other studies on this topic. Two cases of time-dependent changes in outdoor temperature are considered here: a constant outdoor temperature and a periodically changing ambient temperature. After applying a few simplifying assumptions, the problem can be reduced to a system of ordinary differential equations, which can then be solved analytically. Thus, the developed methodology can be used to design partitions in energy-efficient buildings.