building heat transfer; computational optimization; Fourier analysis
New materials, structures and technologies used in civil engineering impeach traditional evaluations of the annual thermal consumption of buildings, based on the quasi-stationary estimate of the thermal resistance of the building envelope, or some operational parts of such building with the guaranteed temperature. The complete proper physical analysis, applying the principles of thermodynamics and appropriate constitutive relations for particular material layers and air in rooms, is not realistic because of the stochastic character of physical processes, of the need of identification of a lot of material characteristics, of the barely predictable behaviour of users, as well as of the limited financial budgets of investors. From the soliciting compromise solutions, this paper pays attention to the simplified formulation of dynamic behaviour of a building as a nonlinear thermal system, referring to certain analogy with the analysis of electrical circuits. Numerical solution applies the finite element technique, the method of lines and the spectral analysis of differential operators. The practical implementation is performed in MATLAB.