DETERMINATION AND ANALYSIS OF THE TEMPERATURE FIELD IN INHOMOGENEOUS ANISOTROPIC COVER UNDER LOCAL HEATING
DOI:
https://doi.org/10.32782/KNTU2618-0340/2%20021.4.2.2.14Keywords:
nonstationary thermal conductivity, anisotropic shell, stratification, local heatingAbstract
A nonstationary thermal conductivity problem is formulated for an inhomogeneous anisotropic shell, which exchanges heat with the environment according to Newton's law and is heated by nonstationary heat sources. The shell material is inhomogeneous in thickness and anisotropic with one plane of thermal symmetry. By analogy with the theory of elasticity for shells, the spatial problem of thermal conductivity is reduced to a mathematically simpler two-dimensional problem. This simplification corresponds to the first Liav approximation and occurs for thin-walled structures. Two-dimensional equations of thermal conductivity of inhomogeneous anisotropic shells are recorded for two frequently used laws of temperature distribution over shell thickness: cubic and linear distributions. For a shell composed of a package of rigidly interconnected homogeneous anisotropic layers of different thickness, it is assumed that the hypothesis about the nature of the temperature distribution over the thickness holds for the whole package. The thermophysical characteristics of the layered shell as a whole are given by asymmetric unit functions. For the case of such piecewise continuous inhomogeneity, the expressions of the integral characteristics of thermophysical parameters due to the physical properties of the layers are obtained. For an inhomogeneous circular closed orthotropic cylindrical shell of finite length and constant thickness using the double-finite coordinate Fourier transform and the Laplace integral over time, the general solution of the nonstationary thermal conductivity problem is written. The temperature field of a layered cylindrical shell of antisymmetric regular structure, the orthotropy axes of each layer of which are alternately oriented parallel and perpendicular to the coordinate axes, is investigated. The temperature distribution in the two-layer graphite-epoxy composite shell under local heating at the initial moment of time by a given temperature field and environment by convective heat exchange is numerically analyzed. The dependence of the integral characteristics of the temperature on the physical and geometrical parameters of the shell is investigated.
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