An unconditionally stable three level finite difference scheme for solving parabolic two-step micro heat transport equations in a three-dimensional double-layered thin film

International Journal for Numerical Methods in Engineering

Volumn 59, Issue 4, 2004, Pages 493-509

  Dai, Weizhong ^a   Li, Quang ^a   Nassar, Raja ^a   Shen, Lixin ^a  

^a LOUISIANA TECH UNIVERSITY   (United States)

Author keywords

Finite difference; Micro heat transport equations; Stability; Thin film

Indexed keywords

CHROMIUM; FINITE DIFFERENCE METHOD; HEAT TRANSFER; THERMOANALYSIS;

CHROMIUM PADDING; HEAT DIFFUSION EQUATIONS; HEAT TRANSPORT EQUATIONS;

THIN FILMS;

FINITE DIFFERENCE TECHNIQUE; HEAT TRANSFER; MATHEMATICAL METHOD;

EID: 0442296780     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.887     Document Type: Article

References (25)

1. Joseph DD, Preziosi L. Heat waves. Reviews of Modern Physics 1989; 61:41-73.
2. Joshi AA, Majumdar A. Transient ballistic and diffusive phonon heat transport in thin films. Journal of Applied Physics 1993; 74:31-39.
3. Qiu TQ, Tien CL. Heat transfer mechanisms during short-pulse laser heating of metals. Journal of Heat Transfer (ASME) 1993; 115:835-841.
4. Qiu TQ, Tien CL. Short-pulse laser heating on metals. International Journal of Heat and Mass Transfer 1992; 35:719-726.
5. Anisimov SI, Kapeliovich BL, Perel'man TL. Electron emission from metal surfaces exposed to ultrashort laser pulses. Soviet Physics JETP 1974; 39:375-377.
6. Qui TQ, Tien CL. Femtosecond laser heating of multi-layer metals-I. Analysis. International Journal of Heat and Mass Transfer 1994; 37:2789-2797.
7. Qiu TQ, Juhasz T, Suarez C, Bron WE, Tien CL. Femtosecond laser heating of multi-layer metals-II. Experiments. International Journal of Heat and Mass Transfer 1994; 37:2799-2808.
8. Tzou DY. Macro To Micro Heat Transfer. Taylor & Francis:Washington, DC, 1996.
9. Özisik MN, Tzou DY. On the wave theory in heat conduction. ASME Journal of Heat Transfer 1994; 116: 526-536.
10. Chen JK, Beraun JE. Numerical study of ultrashort laser pulse interactions with metal films. Numerical Heat Transfer, Part A 2001; 40:1-20.
11. Tzou DY, Zhang YS. An analytic study on the fast-transient process in small scales. International Journal of Engineering Science 1995; 33:1449-1463.
12. Chiffell RJ. On the wave behaviour and rate effect of thermal and thermomechanical waves. M.S. Thesis, University of New Mexico, Albuquerque, NM, 1994.
13. Tzou DY, Chiu KS. Temperature-dependent thermal lagging in ultrafast laser heating. International Journal of Heat and Mass Transfer 2001; 44:1725-1734.
14. Wang L, Xu M, Zhou X. Well-posedness and solution structure of dual-phase-lagging heat conduction. International Journal of Heat and Mass Transfer 2001; 44:1659-1669.
15. Wang L, Zhou X. Dual-Phase-Lagging Heat Conduction. Shandong University Press: Jinan, 2000.
16. Antaki P. Solution for non-Fourier dual phase lag heat conduction in a semi-infinite slab with surface heat flux. International Journal of Heat and Mass Transfer 1998; 41:2253-2258.
17. Tang DW, Araki N. Wavy, wavelike, diffusive thermal responses of finite rigid slabs to high-speed heating of laser-pulses. International Journal of Heat and Mass Transfer 1999; 42:855-860.
18. Lin CK, Hwang CC, Chang YP. The unsteady solution of a unified heat conduction equation. International Journal of Heat and Mass Transfer 1997; 40:1716-1719.
19. Al-Nimr MK, Arpaci VS. The thermal behaviour of thin metal films in the hyperbolic two-step model. International Journal of Heat and Mass Transfer 2000; 43:2021-2028.
20. Dai W, Nassar R. A finite difference scheme for solving the heat transport equation at the microscale. Numerical Methods for Partial Differential Equations 1999; 15:697-708.
21. Dai W, Nassar R. A finite difference scheme for solving a three-dimensional heat transport equation in a thin film with microscale thickness. International Journal for Numerical Methods in Engineering 2001; 50: 1865-1880.
22. Dai W, Nassar R. A compact finite difference scheme for solving a one-dimensional heat transport equation at the microscale. Journal of Computational and Applied Mathematics 2001; 130:431-441.
23. Dai W, Nassar R. A compact finite difference scheme for solving a three-dimensional heat transport equation in a thin film. Numerical Methods for Partial Differential Equations 2000; 16:441-458.
24. Lees M. Alternating direction and semi-explicit difference methods for parabolic partial differential equations. Numerische Mathematik 1961; 3:398-412.
25. Incropera EP, Dewitt DP. Fundamentals of Heat and Mass Transfer (3rd edn). Wiley: New York, 1990.