### Thermotechnical analysis of the structuresby using numerical methods

Pages 91-99

In the paper the features of a structural thermotechnical analysis with the use of numerical methods are considered. Characteristics of heat transfer processes can be obtained using experimental or theoretical analysis. A theoretical investigation works with mathematical model, not with real physical phenomenon. The mathematical model for heat transfer processes consists of a set of differential equations. If the methods of classical mathematics are used for solving these equations, many phenomena of practical interest will be predicted. That’s why in order to solve these problems it is advisable to apply numerical methods. In this paper an algorithm of numerical calculation of threedimensional temperature fields is considered.The numerical algorithm for solving the differential equation of steady three-dimensional thermal conductivity is represented. Discretization of this equation was performed by control-volume method. A solution of a set of discretized equations can be obtained by using a convenient combination of the direct method TDMA (Tri-diagonal matrix algorithm) for one-dimensional situation and the Gauss-Seidel method. The described approach allows us taking into consideration thermal inhomogeneity, such as thermal bridges, and the features of the geometry of the structure. The computing program TEPL was developed on the basis of the described algorithms. As a result of the calculation made by TEPL three-dimensional temperature field was obtained. On the basis of this field thermal resistance and temperature distribution in the structure were calculated.The examples of using the program for solving real practical problems are shown in the paper. Roofing consisted of sandwich panels supported by purlins with the use of screws in one case and rivets as fasteners in the other. The main difference between these two structures is that screws are installed through the insulation layer of a panel and violate its integrity, while rivets are connected to the lowest sheet of a panel and purlin flange and do not make any changes in insulation. The results of the numerical analysis in TEPL show that screws are thermal bridges and must be taken into account in the process of calculating thermal resistance of roofs.

DOI: 10.22227/1997-0935.2013.11.91-99

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