IJPAM: Volume 115, No. 3 (2017)

Title

ОN NON-STATIONARY HEAT TRANSFER IN ANISOTROPIC
BODIES WITH GENERAL ANISOTROPY AND
GIVEN DISTRIBUTED HEAT SOURCES

Authors

Vladimir F. Formalev$^{1}$, Ekaterina L. Kuznetsova$^2$,
Sergey A. Kolesnik$^{3}$, Elena A. Pegachkova$^{4}$
$^{1,3,4}$Department of Applied Mathematics and Physics
Moscow Aviation Institute (National Research University)
Volokolamskoe shosse 4, Moscow, 125993, RUSSIA
$^{2}$Department of Applied Mechanics
Moscow Aviation Institute (National Research University)
4 Volokolamskoe Shosse, Moscow, 125993, RUSSIA

Abstract

A new analytical solution is obtained for the first initial-boundary problem of heat transfer in an anisotropic plate with general anisotropy (non-zero off-diagonal components of thermal conductivity tensor) and given heat sources distributed over space and time. The tensorial character of heat transfer results in presence of mixed derivatives in the differential equation of thermal conductivity. The solution is obtained by constructing a source function and further use of the basic integral Green's function. Convergence of the functional series of improper integrals is investigated. We analyze numerical results on the effect of principal components and orientation angles of principal axes of thermal conductivity tensor on non-stationary temperature fields.

History

Received: May 29, 2017
Revised: July 2, 2017
Published: July 27, 2017

AMS Classification, Key Words

AMS Subject Classification: 80A20, 74E10, 74F05
Key Words and Phrases: heat transfer, green's function, anisotropy, thermal conductivity, temperature fields

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How to Cite?

DOI: 10.12732/ijpam.v115i3.12 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 115
Issue: 3
Pages: 585 - 597


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