Issue |
MATEC Web Conf.
Volume 282, 2019
4th Central European Symposium on Building Physics (CESBP 2019)
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Article Number | 02064 | |
Number of page(s) | 13 | |
Section | Regular Papers | |
DOI | https://doi.org/10.1051/matecconf/201928202064 | |
Published online | 06 September 2019 |
Heat transport solutions in rectangular shields using harmonic polynomials.
Military University of Technology, Faculty of Civil Engineering and Geodesy, gen W. Urbanowicza 2, 00-980 Warszawa, Poland
* Corresponding author: mariusz.owczarek@wat.edu.pl
The search for the temperature field in a two-dimensional problem is common in building physics and heat exchange in general. Both numerical and analytical methods can be used to obtain a solution. Here a method of initial functions, the basics of which were given by W.Z. Vlasov i A.Y. Lur’e were adopted. Originally MIF was used for analysis of the loads of a flat elastic medium. Since then it was used for solving concrete beams, plates and composite materials problems. Polynomial half-reverse solutions are used in the theory of a continuous medium. Here solutions were obtained by direct method. As a result, polynomial forms of the considered temperature field were obtained. The Cartesian coordinate system and rectangular shape of the plate were assumed. The governing are the Fourier equation in steady state . Boundary conditions in the form of temperature (τ(x),t(y)) or/and flux (p(x), q(y)) can be provided. The solution T(x, y) were assumed in the form of an infinite power series developed in relation to the variable y with coefficients Cn depending on x. The assumed solution were substituted into Fourier equation and after expanding into Taylor series the boundary condition for y = 0 and y=h were taken into account. Form this condition a coefficients Cn can be calculated and therefore a closed solution for temperature field in plate.
© The Authors, published by EDP Sciences, 2019
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