Analysis of Temperature Distribution in a Two-Layer Composite Cylindrical Shell Due to Convective Heat Exchange on its Outer Surface

A non-stationary thermal conductivity problem for a two-layer cylindrical shell is formulated. The materials of the constituent layers of the shell are assumed to be homogeneous and isotropic. This shell is convectively heated by the external environment. The system of linear two-dimensional equations for the integral temperature characteristics summed over the component layers of the shell was used as the initial system of equations of the problem under consideration. When obtaining this system, the hypothesis of a linear distribution of temperature along the thickness of the entire shell was applied. On the basis of the developed two-dimensional mathematical model of thermal conductivity for layered cylindrical shells, a general solution to the thermal conductivity problem for a two-layered cylindrical shell was obtained. A temperature distribution was found for such a shell, which is locally convectively heated by the external environment in a rectangular region on the outer surface. For the numerical analysis, a metal-ceramic cylindrical shell was considered, the inner layer of which is made of tungsten, and the outer layer is made of ceramics. Under such a structure and conditions of heat exchange with the external environment for the considered shell, the effect of its geometric parameters and thermophysical characteristics of the materials of its component layers on the temperature field on the outer surface of the shell was investigated. The revealed new qualitative and quantitative regularities can be used to estimate temperature fields in composite elements of layered structures and in structures with one-sided coatings. The dependences of temperature distributions on geometric parameters and thermophysical characteristics obtained in this work are the basis of the theoretical basis for the analysis of temperature regimes of metal-ceramic cylindrical shells. In particular, metal-ceramic dental crowns to predict their temperature regimes are modeled by the two-layer metal-ceramic cylindrical shells described above, which are locally convectively heated by the external environment