Some analytical solutions in problems of optimization of variable thermal conductivity coefficient

Автор: Vatulyan A.O., Nesterov S.A.

Журнал: Владикавказский математический журнал @vmj-ru

Статья в выпуске: 3 т.26, 2024 года.

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New formulations and solutions to problems of optimization of a variable thermal conductivity coefficient for an inhomogeneous pipe and a flat wall with mixed boundary conditions are presented. The quality functionals are either the average temperature or the maximum temperature, and as a limitation - either the condition of constancy of the integral thermal conductivity coefficient, or a priori information about the change in the thermal conductivity coefficient in a known range. To solve problems for a pipe, two optimization methods are used: 1) a variational approach based on the introduction of conjugate functions and the construction of an extended Lagrange functional; 2) Pontryagin’s maximum principle. To solve the optimization problem for a flat wall under the assumption of weak material inhomogeneity, the expansion method in terms of a small physical parameter is used. As the fourth problem, optimization of the variable thermal conductivity coefficient of a non-uniform flat wall with boundary conditions of the first kind is considered. The solution to a singular optimization problem is found among broken extremals. Using specific examples, a comparison was made of the values of minimized functionals for bodies with a constant thermal conductivity coefficient and an optimal variable coefficient. The gain from optimization is estimated.

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Optimization, thermal conductivity coefficient, functionally graded material, flat wall, pipe, lagrange variational method, pontryagin's maximum principle, small parameter expansion method, singular problem

Короткий адрес: https://sciup.org/143183198

IDR: 143183198   |   DOI: 10.46698/v9056-4395-2233-f

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