Основы решения нелинейных нестационарных задач теплопроводности многослойных стенок - Демченко, В. Г.; Драганов, Б. Х. (Енергетика і автоматика, 2017)
FUNDAMENTALS SOLVING NONLINEAR NONSTATIONARY PROBLEMS THE HEAT MULTILAYER WALL V. G. Demchenko, B. H. Draganov Taking into account the actual values of thermophysical characteristics of materials as a function of temperature leads to the need to solve non-linear first-order non-stationary problems of heat transfer through a single-layered and multilayered wall of external fences of buildings. In this case, it is necessary to take into account the influence of the dependence of the thermophysical characteristics of materials on their temperature on heat transfer through the outer enclosing structures of buildings. The aim of the study is to develop a method for solving nonlinear nonstationary thermal conductivity problems of a multilayer wall. Among integral, the most convenient is the method of finite integral transformations, since it makes it possible to move from images to originals much easier than in cases of other integral transformations. The method of finite integral transformations leads to a nonhomogeneous boundary value problem of heat conduction in the image region in the case of single-walled walls to an ordinary differential equation of the first order, and in the case of multilayer walls to the (n - 1) dimensional vector system (2n + 1) of Volterra integral equations of the second kind, the solution Which are known. This is the manifestation of the new side of the method of finite integral transformations. The above method was used to solve a nonlinear nonstationary heat conduction problem for a multilayer wall. Effective methods were proposed for reducing non-stationary heat transfer problems through multilayer walls, taking into account the dependence of thermal characteristics on temperature to vector integral equations, and then to a system of algebraic equations. Problems of non-stationary heat transfer through single-layered and multi-layered enclosures with ideal and non-ideal thermal contacts between layers were set and solved for the conditions of sharp temperature difference between the external and internal air. The above theoretical studies allow us to explain the physical processes taking place in lightweight structures in summer and winter conditions. Thus, it is possible to indicate ways and means to improve the efficiency of the heat supply of a particular facility.