Cattaneo-Vernotte equation : identification of relaxation time using evolutionary algorithms

• Autorzy: Mochnacki B. , Paruch M.
• Języki publikacji: EN

Abstrakty

EN

The Cattaneo-Vernotte equation describing the heat conduction process in domain of solid body results from the generalization of the well - known Fourier law, in which the delay time’ (relaxation time τq) is introduced. The Cattaneo-Vernotte equation should be, among others, used in a case of microscale heat transfer analysis when the thermal processes are characterized by the extremely short duration (e.g. ultrafast laser pulse), the considerable temperature gradients and the very small dimensions (e.g. thin metal film). In the paper the problem of relaxation time identification is considered. In particular, the heat conduction process proceeding in domain of thin metal film subjected to a laser pulse is analyzed. The inverse problem solution is obtained using the evolutionary algorithms. The information concerning the time-dependent temperature distribution on the surface of metal film is assumed to be known. At the stage of numerical computations the finite difference method (FDM) is applied. In the final part of the paper the example of computations is shown.

Słowa kluczowe

EN

Cattaneo-Vernotte equation; evolutionary algorithms

PL

równanie Cattaneo-Vernotte; algorytmy ewolucyjne

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2013
• Tom: Vol. 12, nr 4
• Strony: 97--102
• Opis fizyczny: Bibliogr. 7 poz., rys., tab.

Twórcy

autor

Mochnacki B.

• Institute of Mathematics, Czestochowa University of Technology, Częstochowa, Poland Higher School of Labour Safety Management in Katowice, Katowice, Poland

autor

Paruch M.

• Institute of Computational Mechanics and Engineering, Silesian University of Technology, Gliwice, Poland

Bibliografia

• [1] Chen J.K., Beraun J.E., Numerical study of ultrashort laser pulse interactions with metal films, Numerical Heat Transfer 2001, Part A, 40, 1-20.
• [2] Kaba I.K., Dai W., A stable three - level finite difference scheme for solving the parabolic two-step model in a 3D micro sphere heated by ultrashort-pulsed lasers, Journal of Computational and Applied Mathematics 2005, 181, 125-147.
• [3] Majchrzak E., Mochnacki B., Greer A.L., Suchy J.S., Numerical modeling of short pulse laser interactions with multi-layered thin metal films, Computer Modeling in Engineering and Sciences 2009, 41, 2, 131-146.
• [4] Majchrzak E., Mochnacki B., Suchy J.S., Finite difference model of short-pulse laser interactions with thin metal film, Computer Methods in Materials Science 2009, 9, 2, 316-322.
• [5] Mochnacki B., Majchrzak E., Modeling of microscale heat transfer in cylindrical domains, Computer Methods in Materials Science 2011, 11, 2, 337-342.
• [6] Mochnacki B., Majchrzak E., Identification of macro and micro parameters in the solidification model, Bulletin of the Polish Academy of Sciences - Technical Sciences 2007, 55, 1, 107-113.
• [7] Michalewicz Z., Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag, Berlin 1996.