An unconventional free boundary problem of heat conduction is formulated and the theorems of the existence and uniqueness of a classical local solution are proved. The problem models the process of melting (dissolution) of paraffin sediments in a thin porous layer, where a nonisothermal motion of an incompressible liquid is accompanied by the heat exchange with an unbounded impermeable thermally anisotropic medium, and the absorption of a latent heat of fusion (dissolution) occurs at a constant temperature.
A model problem for heat conduction with a free boundary in a concentrated capacity / A. FASANO; M. PRIMICERIO; L. RUBINSTEIN. - In: JOURNAL OF THE INSTITUTE OF MATHEMATICS AND ITS APPLICATIONS. - ISSN 0020-2932. - STAMPA. - 26:(1980), pp. 327-347. [10.1093/imamat/26.4.327]
A model problem for heat conduction with a free boundary in a concentrated capacity
FASANO, ANTONIO;PRIMICERIO, MARIO;
1980
Abstract
An unconventional free boundary problem of heat conduction is formulated and the theorems of the existence and uniqueness of a classical local solution are proved. The problem models the process of melting (dissolution) of paraffin sediments in a thin porous layer, where a nonisothermal motion of an incompressible liquid is accompanied by the heat exchange with an unbounded impermeable thermally anisotropic medium, and the absorption of a latent heat of fusion (dissolution) occurs at a constant temperature.
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