Optimal Control Problem of Complex Heat Transfer for SP1 Approximation

Andrey Sushchenko

doi:10.4028/www.scientific.net/KEM.685.99

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HomeKey Engineering MaterialsKey Engineering Materials Vol. 685Optimal Control Problem of Complex Heat Transfer...

Optimal Control Problem of Complex Heat Transfer for SP₁ Approximation

Abstract:

The optimal control problem for evolution radiative heat transfer in SP₁ approximation is considered. The problem is solved by weak form technique and Lagrange method. Numerical experiments for real materials are done.

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Key Engineering Materials (Volume 685)

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99-103

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https://doi.org/10.4028/www.scientific.net/KEM.685.99

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February 2016

Authors:

Andrey Sushchenko*

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Optimal Control, Radiative Heat Transfer, SP₁ Approximation

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References

[1] M.F. Modest, Radiative Heat Transfer, Academic Pres, (2003).

Google Scholar

[2] A.E. Kovtanyuk, K.V. Nefedev, I.V. Prokhorov, Advanced computing method for solving of the polarized-radiation transfer equation, Lecture Notes in Computer Science 6083 LNCS (2010) 268-276.

DOI: 10.1007/978-3-642-14822-4_30

Google Scholar

[3] I.V. Prokhorov, The Cauchy problem for the radiative transfer equation with generalized conjugation conditions, Comput. Math. Math. Phys. 53 (5) (2013) 588–600.

DOI: 10.1134/s0965542513050114

Google Scholar

[4] S. Andre, A. Degiovanni, A theoretical study of the transient coupled conduction and radiation heat transfer in glass: phonic diffusivity measurements by the flash technique, Int. J. Heat Mass Transfer, 38 (18) (1995) 3401-3412.

DOI: 10.1016/0017-9310(95)00075-k

Google Scholar

[5] C.T. Kelley, Existence and uniqueness of solutions of nonlinear systems of conductive-radiative heat transfer equations, Transport Theory Statist. Phys. 25 (2) (1996) 249-260.

DOI: 10.1080/00411459608204839

Google Scholar

[6] J.M. Banoczi, C.T. Kelley, A fast multilevel algorithm for the solution of nonlinear systems of conductive-radiative heat transfer equations, SIAM J. Sci. Comput. 19 (1) (1998) 266-279.

DOI: 10.1137/s1064827596302965

Google Scholar

[7] A.E. Kovtanyuk, N.D. Botkin, K. -H. Hoffmann, Numerical simulations of a coupled conductive-radiative heat transfer model using a modified Monte Carlo method, Int. J. Heat and Mass Transfer 55 (2012) 649-654.

DOI: 10.1016/j.ijheatmasstransfer.2011.10.045

Google Scholar

[8] A.E. Kovtanyuk, A. Yu. Chebotarev, An iterative method for solving a complex heat transfer problem, Applied Math. Comput. 219 (2013) 9356-9362.

DOI: 10.1016/j.amc.2013.03.091

Google Scholar

[9] A.E. Kovtanyuk, A. Yu. Chebotarev, N.D. Botkin, K. -H. Hoffmann, Solvability of P1 approximation of a conductive-radiative heat transfer problem, Applied Math. And Comput. 249 (2014) 247-252.

DOI: 10.1016/j.amc.2014.10.054

Google Scholar

[10] A.A. Amosov, On the solvability of a problem of radiative heat transfer, Soviet Physics Doklady 24 (1) (1979) 261-262.

Google Scholar

[11] A.A. Amosov, The limiting relation between two problems on radiative heat transfer, Soviet Physics Doklady 24 (11) (1979) 439-441.

Google Scholar

[12] A.E. Kovtanyuk, A. Yu. Chebotarev, N.D. Botkin, K. -H. Hoffmann, The unique solvability of a complex 3D heat transfer problem, J. Math. Anal. Appl. 409 (2014) 808-815.

DOI: 10.1016/j.jmaa.2013.07.054

Google Scholar

[13] A.E. Kovtanyuk, A. Yu. Chebotarev, Steady-state problem of complex heat transfer, Comput. Math. and Math. Phys. 54 (4) (2014) 719-726.

DOI: 10.1134/s0965542514040095

Google Scholar

[14] A.E. Kovtanyuk, A. Yu. Chebotarev, N.D. Botkin, K. -H. Hoffmann, Unique solvability of a steady-state complex heat transfer model, Communications in Nonlinear Science and Numerical Simulation 20 (2015) 776-784.

DOI: 10.1016/j.cnsns.2014.06.040

Google Scholar

[15] A.A. Astrakhantseva, A.E. Kovtanyuk, Numerical modeling the radiative-convective-conductive heat transfer, 2014 Int. Conf. on Computer Technologies in Physical and Engineering Applications, ICCTPEA 2014 - Proceedings 6893306 (2014) 106-107.

DOI: 10.1109/icctpea.2014.6893306

Google Scholar

[16] R. Pinnau, Analysis of optimal boundary control for radiative heat transfer modeled by the SPN system. Comm. Math. Sci., 5(4) (2007) 951-969.

DOI: 10.4310/cms.2007.v5.n4.a11

Google Scholar

[17] D. Clever, J. Lang, Optimal control of radiative heat transfer in glass cooling with restrictions on the temperature gradient, Optimal Control Appl. and Meth., 33(2) (2012) 157-175.

DOI: 10.1002/oca.984

Google Scholar

[18] O. Tse, R. Pinnau, Optimal control of a simplified natural convection-radiation model, Comm. Math. Sci., 11(3) (2013) 679-707.

DOI: 10.4310/cms.2013.v11.n3.a2

Google Scholar

[19] A.E. Kovtanyuk, A. Yu. Chebotarev, N.D. Botkin, K. -H. Hoffmann, Theoretical analysis of an optimal control problem of conductive-convective-radiative heat transfer, J. of Math. Analysis and Applications 412 (2014) 520-528.

DOI: 10.1016/j.jmaa.2013.11.003

Google Scholar

[20] A.E. Kovtanyuk, A. Yu. Chebotarev, Optimal control of complex heat transfer, 2014, Int. Conf. on Computer Technologies in Physical and Engineering Applications, ICCTPEA 2014 - Proceedings 6893370 (2014) 221-222.

DOI: 10.1109/icctpea.2014.6893370

Google Scholar

[21] G. V. Grenkin, A. Yu. Chebotarev, A nonstationary problem of complex heat transfer, Computational Mathematics and Mathematical Physics, 54 (11) (2014) 1737-1747.

DOI: 10.1134/s0965542514110062

Google Scholar