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S.I. Kuznetsov, A.V. Manzhirov, and I. Fedotov, "Heat Conduction Problem for a Growing Ball," Mech. Solids. 46 (6), 929-936 (2011)
Year 2011 Volume 46 Number 6 Pages 929-936
DOI 10.3103/S0025654411060124
Title Heat Conduction Problem for a Growing Ball
Author(s) S.I. Kuznetsov (Bauman Moscow State Technical University, 2-ya Baumanskaya 5, Moscow, 105005 Russia, k_s_i@bk.ru)
A.V. Manzhirov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, manzh@ipmnet.ru, manzh@inbox.ru)
I. Fedotov (Tshwane University of Technology, P.B. X680, Pretoria, 0001 FIN-40014 South African Republic, fedotovi@tut.ac.za)
Abstract The present paper studies unsteady temperature fields in growing bodies of spherical shape. The growth occurs due to constant accretion of layers of constant thickness on the surface of the main body. In the general case, the temperature of the accreted material is different from that of the main body, which causes a heat flow on the accretion surface. The solution of the initial boundary-value problem of heat conduction is sought as an expansion in the complete system of eigenfunctions of the differential operator generated by the problem.
Keywords growing body, heat conduction, ball, eigenfunctions, expansion, closed solution
References
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Received 18 August 2011
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