Визначення температурного поля в системі тіл циліндр – півпростір при неідеальному тепловому контакті через проміжковий шар

Abstract

Побудовано розв’язок осесиметричної температурної задачі для системи тіл циліндр – півпростір при неідеальному тепловому контакті з урахуванням тонкого проміжкового шару у випадку ізотропних матеріалів. Отримано формули для визначення температури при різних варіантах температурних умов на бічних поверхнях циліндра і півпростору. Досліджено вплив контактної провідності й коефіцієнтів теплопровідності проміжкового шару на розподіл температурних полів у зоні контакту двох тіл.

Solution of the axes-symmetric temperature task for the body system cylinder-semispase under non-ideal heat contact taking into account thin intermediate layer in the case of isotropic materials has been built. Circular cylinder of the finite hight with the flat basis, which is in the non-ideal heat contact through the intermediate layer with the semispase, is being analysed. On the free end of the cylinder the temperature is constant and its side surface is head-insulated. Free surface of the semispase is kept under zero temperature. Heat exchange with the outside environment occurs from the side surface of the thin intermediate layer according to the Newton’s law. The temperature in the cylinder area is found by the Furier’s method, and in the semispase with the help of the Hanckel’s transformation to the Laplace’s equation, written in the cylinder coordenates system. Providing the boundary conditions for the temperature on the side surfases and in the contact area body system cylinder-semispase, the task is reduced to the system of integral equations relatively unknown function, due to which the temperature in the semispase is found. Taking advantage of the Hanckel’s transformation and the Bessel’s function we obtain non-finite system of the linear algebraic equations relatively constants, through which the temperature fields in the system of two bodies are expressed. While solving the system of the linear algebraic equations the reduction method was used. The graphs of the temperature distribution for the cylinder and semispase in the contact area have been built. The effect of the contact conductivity and heat exchange coefficient of the thin intermediate layer on the temperature distribution in the contact area have been investigated. It was shown, that these coefficients affect sufficiently the temperature field in the semispase. Decrease of the temperature in the contact area in the case of the intermediate layer as compared with the ideal heat contact is caused by the fact, that the heat exchange occurs throug the side surface of the intermediate layer.