Heat transport solutions in rectangular shields using harmonic polynomials.

Abstract

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.