Розрахунок впливу подвійної нелінійності і анізотропії матеріалу на розподіл температур в циліндрі при високотемпературному теплообміні

Abstract

На основі розробленого методу розв’язання крайових задач двічі нелінійної нестаціонарної теплопровідності, розглянуто вплив термочутливості матеріалу, зонального конвективно-променевого теплообміну і анізотропії на розподіл температурних полів по довжині, в центрі і поверхні напівнескінченного суцільного циліндра. Встановлено, що при зростанні критерію Фур’є якісно змінюється характер нагріву від осі до поверхні циліндра, як за нелінійностями, так і анізотропії. Для випадку подвійної нелінійності, графічно показано розподіл температурних полів при різних анізотропіях в порівнянні з ізотропним матеріалом.

At the present stage of the development of technology, it is necessary to ensure the strength, reliability and durability of the structure that successfully functions under conditions of high-temperature heat exchange as maximum as possible. In this regard, graphite structural elements are widely used, and they are also applied for parts of space and aircraft, jet and rocket engines. The transversely isotropic graphite cylinder used in this work has a unique set of qualities that make it indispensable for problems in nuclear physics and power engineering; however, in the calculation of thermal engineering practice, it has not been studied enough, since it contains a large scatter of thermophysical characteristics for various grades of graphite. The aim of the study, including the basis of the developed method for solving boundary value problems of doubly nonlinear unsteady thermal conductivity, is to consider the effect of temperature dependences of the thermophysical characteristics of the material on temperature, zonal radiative-convective heat transfer and anisotropy on the distribution of temperature fields along the length, at the center and surface of a semi-infinite solid cylinder. The essence of this method is that the Goodman’s and Kirchhoff’s transformations are applied to the problem posed converted to a dimensionless form, then the relative temperature and functions from it, are expanded in the series of sines on the a priori interval, then the superposition principle is applied, after which the original setting is converted to a set of linearized problems with reduced thermophysical characteristics. Linear problems are solved by the method of integral transformations, which are summed up. The upper limit of the priori interval is determined from the condition that the relative temperature obtained from the solution of the problem Fo → ∞ takes the value of the upper limit of the a priori interval. A large number of numerical calculations in the Matlab environment graphically show changes in the relative temperature on the axis and surface of the cylinder in a wide range of Fourier criteria. It is found that with an increase in the Fourier criterion, the character of heating changes qualitatively from the axis to the surface of the cylinder, both in terms of nonlinearities and anisotropy. For the case of double nonlinearity, the location of the temperature fields at different anisotropies in comparison with an isotropic material is shown graphically.