FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
The stability of steady-state solutions of the diffusion complex heat transfer model |
Grenkin G. V., Chebotarev A.Yu. |
2014, issue 1, P. 18-32 |
Abstract |
| The nonstationary model of radiative-convective-conductive heat transfer in a three-dimensional domain within the diffusion P1 approximation of radiative transfer is considered. The sufficient conditions of asymptotic stability of steady states are established. |
Keywords: radiative heat transfer equations, diffusion approximation, nonlocal solvability, asymptotic stability |
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References |
| [1] D. A. Boas, Diffuse photon probes of structural and dynamical properties of turbid media: theory and biomedical applications, A Ph.D. Dissertation in Physics, University of Pennsylvania, 1996. [2] M. F. Modest, Radiative Heat Transfer, Academic Press, 2003. [3] S. E. Siewert, “An improved iterative method for solving a class of coupled conductiveradiative heat-transfer problems”, J. Quant. Spectrosc. Radiat. Transfer., 54:4 (1995), 599–605. [4] 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. [5] A. Klar, N. Siedow, “Boundary layers and domain decomposition for radiative heat transfer and diffusion equations: applications to glass manufacturing process”, Eur. J. Appl. Math., 9:4 (1998), 351–372. [6] G. Th?omes, R. Pinnau, M. Sea?id, T. G?otz, A. Klar, “Numerical methods and optimal control for glass cooling processes”, Trans. Theory Stat. Phys., 31:4-6 (2002), 513–529. [7] R. Pinnau, M. Seaid, “Simplified PN Models and Natural Convection–Radiation”, Math. in Industry, V. 12 (2008), 397–401. [8] 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. [9] A. E. Kovtaniuk, “Algoritmy parallel'nykh vychislenii dlia zadach radiatsionno-konduktivnogo teploobmena”, Komp'iuternye issledovaniia i modelirovanie, 4:3 (2012), 543–552. [10] A. E. Kovtanyuk, A.Yu. Chebotarev, “An iterative method for solving a complex heat transfer problem”, Appl. Math. Comput., 219 (2013), 956–9362. [11] A. A. Amosov, “Global'naia razreshimost' odnoi nelineinoi nestatsionarnoi zadachi s nelokal'nym kraevym usloviem tipa teploobmena izlucheniem”, Differentsial'nye uravneniia, 41:1 (2005), 93–104. [12] R. Pinnau, “Analysis of Optimal Boundary Control for Radiative Heat Transfer Modelled by the SP1-System”, Comm. Math. Sci., 5:4 (2007), 951–969. [13] P.-E. Druet, “Existence of weak solutions to the time-dependent MHD-equations coupled to heat transfer with nonlocal radiation boundary conditions”, Nonlinear Anal. Real World Appl., 10:5 (2009), 2914–2936. [14] B. Ducomet, S. Necasova, “Global Weak Solutions to the 1D Compressible Navier-Stokes Equations with Radiation”, Commun. Math. Anal., 8:3 (2010), 23–65. [15] O. Tse, R. Pinnau, N. Siedow, “Identification of temperature dependent parameters in laser–interstitial thermo therapy”, Math. Models Methods Appl. Sci., 22:9 (2012), 1–29. [16] C. T. Kelley, “Existence and uniqueness of solutions of nonlinear systems of conductiveradiative heat transfer equations”, Transport Theory Statist. Phys., 25:2 (1996), 249–260. [17] 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., 409:2 (2014), 808–815. [18] 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. Math. Anal. Appl., 412:1 (2014), 520–528. [19] A. E. Kovtaniuk, A.Iu. Chebotarev, “Statsionarnaia zadacha slozhnogo teploobmena”, Zh. vychisl. matem. fiz., 54:4 (2014), 191-199. [20] A. A. Amosov, “O razreshimosti odnoi zadachi teploobmena izlucheniem”, Dokl. AN SSSR, 245:6 (1979), 1341–1344. [21] M. T. Laitinen, T. Tiihonen, “Heat transfer in conducting, radiating and semitransparent materials”, Math. Meth. Appl. Sci., 21 (1998), 375–392. [22] M. Laitinen, “Asymptotic analysis of conductive-radiative heat transfer”, Asymptotic Analysis, 29:3-4 (2002), 323–342. [23] A. A. Amosov, “Stationary nonlinear nonlocal problem of radiative-conductive heat transfer in a system of opaque bodies with properties depending on the radiation frequency”, Journal of Mathematical Sciences, 164:3 (2010), 309–344. [24] A. A. Amosov, “Nonstationary nonlinear nonlocal problem of radiative-conductive heat transfer in a system of opaque bodies with properties depending on the radiation frequency”, Journal of Mathematical Sciences, 165:1 (2010), 1–41. [25] Partial Differential Equations — MATLAB & Simulink. http://www.mathworks.com/help/matlab/math/partial-differential-equations.html. |