Temperature Field of Anisotropic Half-Space at its Local Heating under Conditions of Heat Exchange with External Environment

Authors: Attetkov A.V., Volkov I.K. Published: 08.06.2018
Published in issue: #3(78)/2018  
DOI: 10.18698/1812-3368-2018-3-4-12

Category: Mathematics | Chapter: Mathematical Physics  
Keywords: anisotropic half-space, heat exchange with external environment, local-heating, temperature field, integral transformations

The paper introduces a mathematical model of the process of generating the temperature field of an anisotropic half-space, whose boundary is subjected to a stationary heat flow with Gaussian-type intensity and to the external impact at a constant temperature. The study shows that the temperature field is the sum of two additive components. The first component is due to the external impact, the heat exchange with the environment being realized according to Newton's law. Using the composition of a two-dimensional exponential integral Fourier transformation and an integral Laplace transformation in an analytically closed form, we found a solution for the second additive component of the temperature field of the object under study. Consequently, we formulated sufficient conditions, whose implementation allows us to generalize the result obtained in the case of unsteady heat flows of an arbitrary structure under conditions of heat exchange with the external environment according to Newton's law


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