DETERMINING NON-STATIONARY TEMPERATURE FIELD OF PRE-HEATED INHOMOGENEOUS ISOTROPIC CYLINDRICAL COVER
DOI:
https://doi.org/10.32782/KNTU2618-0340/2020.3.2-2.20Keywords:
inhomogeneous isotropic shell, thermal action, cylindrical shell, isotropic metal ceramics, temperature regimeAbstract
The method of reduction of the three-dimensional thermal conductivity problem for an inhomogeneous isotropic shell of arbitrary geometric configuration to two-dimensional one has been provided. The shell is referred to a mixed curvilinear orthogonal coordinate system. The method is based on the use of a linear law of temperature distribution over the thickness of the shell, which is applicable for thin shells and has been experimentally confirmed. Using the averaging of the temperature over the thickness of the shell, a system of initial equations for the integral characteristics of the temperature for the shell of arbitrary configuration has been obtained. A system of two-dimensional equations for the integral temperature characteristics of a cylindrical inhomogeneous isotropic shell has been written as a partial case. The initial and boundary conditions for the integral characteristics of a finite-length cylindrical shell have been formulated. Using the double-finite integral Fourier transform in spatial coordinates and the Laplace time transform, the general solution of the obtained system of two-dimensional equations on the integral characteristics of temperature has been recorded. For the case of a cylindrical shell of this type preheated to a given temperature from an inhomogeneous isotropic material under conditions of convective heat exchange with the environment, the expression of the temperature field has been found. The temperature field of a cylindrical shell made of isotropic inhomogeneous cermets on its outer surface has been numerically analyzed depending on the values of axial and circular coordinates at different values of dimensionless time and a given coefficient of inhomogeneity. The analysis for the case of the power law of change of the coefficient of inhomogeneity in the radial variable has been performed. The dependence of the temperature field in the center of the heating region on the dimensionless time for different values of the heat transfer coefficient has been discovered. It has been established that with a decrease in the proportion of ceramics, the temperature on the outer surface of the shell decreases. It has been found that the temperature is constant in the heating area, and when moving to the unheated area, it decreases sharply to ambient temperature.
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