Half-Space Temperature Field with a Movable Thermally Thin-Coated Boundary Under External Heat Flux

• Main Authors: P. A. Vlasov, I. K. Volkov
• Format: Article
• Language: Russian
• Published: MGTU im. N.È. Baumana 2014-01-01
• Series: Nauka i Obrazovanie
• Subjects: temperature field; half-space; moving boundary
• Online Access: http://technomag.edu.ru/jour/article/view/734

<p>In engineering practice analytical methods of the mathematical theory of heat conduction hold a special place. This is due to many reasons, in particular, because of the fact that the solutions of the relevant problems represented in analytically closed form, can be used not only for a parametric analysis of the studied temperature field and to explore the specific features of its formation, but also to test the developed computational algorithms, which are aimed at solving real-world application heat and mass transfer problems. Difficulties arising when using the analytical mathematical theory methods of heat conduction in practice are well known. Also they are significantly exacerbated if the boundaries of the system under study are movable, even in the simplest case, when the law of motion is known.</p><p>The main goal of the conducted research is to have an analytically closed-form problem solution for finding the orthotropic half-space temperature field, a boundary of which has thermally thin coating exposed to extremely concentrated stationary external heat flux and uniformly moves parallel to itself.</p><p>The assumption that the covering of the boundary is thermally thin, allowed to realize the idea of \concentrated capacity", that is to accept the hypothesis that the mean-thickness coating temperature is equal to the temperature of its boundaries. This assumption allowed us to reduce the problem under consideration to a mixed problem for a parabolic equation with a specific boundary condition.</p><p>The Hankel integral transform of zero order with respect to the radial variable and the Laplace transform with respect to the temporal variable were used to solve the reduced problem. These techniques have allowed us to submit the required solution as an iterated integral.</p>