Numerical simulation for non-linear thermal wave

Applied Mathematics and Computation

Volumn 175, Issue 2, 2006, Pages 1385-1399

  Liu, Kuo Chi ^a  

^a FAR EAST UNIVERSITY   (Taiwan)

Author keywords

Control volume; Laplace transform method; Modified discretization scheme; Nonlinear

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; LAPLACE TRANSFORMS; NUMERICAL METHODS; THERMAL CONDUCTIVITY;

CONTROL VOLUME; HYPERBOLIC HEAT CONDUCTION; MODIFIED DISCRETIZATION SCHEME; NON-LINEAR THERMAL WAVE; NONLINEAR;

HEAT CONDUCTION;

EID: 33646488017     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.08.033     Document Type: Article

References (21)

1. Kelly D.C. Diffusion: a relativistic appraisal. Am. J. Phys. 36 (1968) 585-591
2. Vedavarz A., Mitra K., and Kumar S. Hyperbolic temperature profile for laser surface interactions. J. Appl. Phys. 76 (1994) 5014-5021
3. Vedavarz A., Kumar S., and Moallemi M.K. Significance of non-Fourier heat waves in conduction. J. Heat Transfer 116 (1994) 221-223
4. Baumeister K.J., and Hamill T.D. Hyperbolic heat-conduction equation-a solution for the semi-infinite body problem. ASME J. Heat Transfer 93 (1971) 126-127
5. Mourer M.J., and Thompson H.A. Non-Fourier effects at high heat flux. ASME J. Heat Transfer 95 (1973) 284-286
6. Wiggert D.C. Analysis of early-time heat conduction by method of characteristics. J. Heat Transfer 99 (1977) 35-40
7. Carey G.F., and Tsai M. Hyperbolic heat transfer with reflection. Numer. Heat Transfer 5 (1982) 309-327
8. Bai C., and Lavine A.S. Hyperbolic heat conduction in a superconducting film. ASME. Thermal Eng. Proc. 49 (1991) 87-92
9. Chen H.T., and Lin J.Y. Numerical analysis for hyperbolic heat conduction. Int. J. Heat Mass Transfer 36 (1993) 2891-2898
10. Lin J.Y., and Chen H.T. Numerical solution of hyperbolic heat conduction in cylindrical and spherical systems. Appl. Math. Model. 18 (1994) 384-390
11. Tang D.W., and Araki N. Wavy, wavelike, diffusive thermal responses of finite rigid slabs to high-speed heating of laser-pulses. Int. J. Heat Mass Transfer 42 (1999) 855-860
12. Chen H.T., and Liu K.C. Study of hyperbolic heat conduction problem in the film and substrate composite with the interface resistance. Jan. J. Appl. Phys. 41 (2002) 6267-6275
13. Liu K.C., and Chen H.T. Numerical analysis for the hyperbolic heat conduction problem under a pulsed surface disturbance. J. Appl. Math. Comput. 159 (2004) 887-901
14. Glass D.E., Özisik M.N., and McRae D.S. Hyperbolic heat conduction with temperature-dependent thermal conductivity. J. Appl. Phys. 59 (1986) 1861-1865
15. Kar A., Chan C.L., and Mazumder J. Comparative studies on nonlinear hyperbolic and parabolic heat conduction for various boundary conditions: analytic and numerical solutions. J. Heat Transfer 114 (1992) 14-20
16. Lin J.Y., and Chen H.T. Study of hyperbolic heat conduction with temperature-dependent thermal properties. J. Heat Transfer 116 (1994) 750-753
17. Pulvirenti B., Barletta A., and Zanchini E. Finite-difference solution of hyperbolic conduction with temperature-dependent properties. Numer. Heat Transfer A 34 (1998) 169-183
18. Cattaneo C. A form of heat conduction equation which eliminates the paradox of instantaneous propagation. Comptes Rendus 247 (1958) 431-433
19. Vernotte P. Les paradoxes de la théorie continue de l'equation de la chaleur. Comptes Rendus 246 (1958) 3154-3155
20. Honig G., and Hirdes U. A method for the numerical inversion of Laplace transforms. J. Comp. Appl. Math. 10 (1984) 113-132
21. Méndez V. Nonlinear hyperbolic heat conduction. J. Non-equilibrium Thermodyn. 22 (1997) 217-232