Integral conditions in the inverse problems of heat conduction

: pp. 219–227
Received: May 13, 2020
Accepted: June 16, 2020
Kremenchuk Mykhailo Ostrohradskyi National University
Kremenchuk Mykhailo Ostrohradskyi National University
Kremenchuk Mykhailo Ostrohradskyi National University

Thermal processes of new technological methods of heat treatment (thermocyclic, electropulse) of metals and alloys are considered in the paper.  Mathematical models of the temperature field in a moving tape and a wire with cyclically acting pulsed heat sources are considered.  Based on these models, the formulation of inverse problems for homogeneous and inhomogeneous thermal conductivity equations is proposed.  For each case (internal, external heat source or a combination), the appropriate method for solving the inverse problem is proposed.  The integral condition of heat balance is used to construct the solutions of the inverse problems.  An integral condition of energy balance is used to construct a quadratic residual functional in an extreme problem.  The inverse problem in the case when we have a combination of internal and external periodic heat sources is solved using the search method, where the integral condition was used to find the deviations and further refinements of the desired function of the source.

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Mathematical Modeling and Computing, Vol. 7, No. 2, pp. 219–227 (2020)