Determination of the temperature field for the cylinder-layer system
Journal Title: Вісник Тернопільського національного технічного університету - Year 2015, Vol 77, Issue 1
Abstract
Solution of the axes-symmetric temperature task for the body system cylinder-layer 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 layer, is being analysed. On the free end of the cylinder the temperature is constant and its side surface is heat – insulated. Heat exchange with the outside environment occurs from the side surface of the thin intermediate layer and on the free surfaces of the layer according to the Newton’s law. The temperature in the cylinders is found by the Furier’s method, and in the layer with the help of the Hanckel’s transformation to the Laplace’s equation, written in the cylinder coordinates system. Providing the boundary conditions for the temperature on the side surfaces and in the contact area body system cylinder – layer, the task is reduced to the system of intergal equations relatively unknown functions, due to which the temperature in the layer 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 the layer 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 layer. 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 accurs through the side surface of the intermediate layer.
Authors and Affiliations
Bogdan Okrepkiy, Borys Shelestovskyi
Keywords
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