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ISSN Print: 1064-2285
ISSN Online: 2162-6561
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MATHEMATICAL MODELING OF HEAT TRANSFER PROBLEMS FOR THIN PLATES WITH TEMPERATURE-DEPENDENT CONDUCTIVITY
ABSTRACT
In this paper, the steady-state heat transfer phenomenon in a flat plate with temperature-dependent thermal conductivity is considered. The plate thickness is small enough in order to allow a two-dimensional description involving only the mean value of temperature over the plate thickness. A nonuniform, but known, internal heat supply and a convective heat exchange between the plate and the environment according to Newton's law of cooling are assumed. The resulting mathematical description consists of a nonlinear partial differential equation subjected to a Neumann boundary condition. The thermal conductivity is assumed to be a piecewise constant function of the temperature, and the Kirchhoff transformation is employed for constructing a new mathematical approach with an equivalent minimum principle. Proofs of existence and uniqueness of the solution are presented.
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Kolev Zhivko, Kadirova Seher, Negreanu G.P., Vlăduţ N.V., Tazerout M., Numerical modeling of the thermal conduction process in water-air convector’s fins, E3S Web of Conferences, 180, 2020. Crossref