Modelling of transient heat transport in two-layered crystalline solid films using the interval lattice Boltzmann method

• Autorzy: Belkhayat-Piasecka A. , Korczak A.

Identyfikatory

DOI

10.17512/jamcm.2017.4.06

• Języki publikacji: EN

Abstrakty

EN

In the paper, the numerical modelling of heat transfer in one-dimensional crystalline solid films is considered. A generalized two-layer problem is described by the Boltzmann transport equations transformed in the phonon energy density equations supplemented by the adequate boundary-initial conditions. Such an approach in which the parameters appearing in the problem analysed are treated as the constant values is widely used, but in this paper the interval values of relaxation time and the boundary condition for silicon and diamond are taken into account. The problem formulated has been solved by means of the interval lattice Boltzmann method using the rules of directed interval arithmetic. In the final part of the paper the results of numerical computations are presented.

Słowa kluczowe

EN

Boltzmann transport equation; interval lattice Boltzmann method; directed interval arithmetic

PL

równanie transportu Boltzmanna; interwałowa metoda siatek Boltzmanna; skierowana arytmetyka interwałowa

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2017
• Tom: Vol. 16, nr 4
• Strony: 57--65
• Opis fizyczny: Bibliogr. 13 poz., rys.

Twórcy

autor

Belkhayat-Piasecka A.

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

autor

Korczak A.

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

Bibliografia

• [1] Chen G., Borca-Tasciuc D., Yang R.G., Nanoscale heat transfer, [in:] Encycl. of Nanoscience and Nanotechnology, CA, American Scientific Publishers, Valencia, 7, 2004, 429-359.
• [2] Smith A.N., Norris P.M., in Heat Transfer Handbook, A. Bejan, D. Kraus, Eds. 2003, 1309.
• [3] Escobar R.A., Ghai S.S., Jhon M.S., Amon C.H., Multi-length and time scale thermal transport using the lattice Boltzmann method with application to electronics cooling, Journal of Heat and Mass Transfer 2006, 49, 97-107.
• [4] Joshi A.A., Majumdar A., Transient ballistic and diffusive phonon heat transport in thin films, Journal of Applied Physics 1993, 74(1), 31-39.
• [5] Narumanchi S., Murthy J.Y., Amon C.H., Simulation of unsteady small heat source effects in sub-micron heat conduction, Journal of Heat Transfer 2003, 123, 896-903.
• [6] Ghai S.S., Kim W.T., Amon C.H., Jhon M.S., Transient thermal modeling of a nanoscale hot spot in multilayered film, Journal of Applied Physics 2006, 99.
• [7] Majchrzak E., Mochnacki B., Suchy J.S., Numerical simulation of thermal processes proceeding in a multi-layered film subjected to ultrafast laser heating, Journal of Theoretical and Applied Mechanics 2009, 47, 2, 383-396.
• [8] Majchrzak E., Mochnacki B., Greer A.L., Suchy J.S., Numerical modeling of short pulse laser interactions with multi-layered thin metal films, CMES: Computer Modeling in Engineering and Sciences 2009, 41, 2, 131-146.
• [9] Pisipati S., Chen Ch., Geer J., Sammakia B., Murray B.T., Multiscale thermal device modeling using diffusion in the Boltzmann Transport Equation, International Journal of Heat and Mass Transfer 2013, 64, 286-303.
• [10] Markov S.M., On directed interval arithmetic and its applications, Journal of Universal Computer Science 1995, 1, 514-526.
• [11] Piasecka-Belkhayat A., Interval boundary element method for transient diffusion problem in two layered domain, Journal of Theoretical and Applied Mechanics 2011, 49, 1, 265-276.
• [12] Escobar R.A., Smith B., Amon C.H., Lattice Boltzmann modeling of subcontinuum energy transport in crystalline and amorphous microelectronic devices, Journal of Electronic Packaging 2006, 128(2).
• [13] Piasecka-Belkhayat A., Korczak A., Modelling of transient heat transport in one-dimensional crystalline solids using the interval lattice Boltzmann method, Recent Advances in Computational Mechanics, Taylor & Francis Group, A Balkema Book, London 2014, 363-368.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).