Numerical Analysis for Dual-Phase-Lag Heat Conduction in Layered Films

REFERENCES

• C. Cattaneo , A Form of Heat Conduction Equation which Eliminates the Paradox of Instantaneous Propagation , Compte Rendus , vol. 247 , pp. 431 – 433 , 1958 . [CSA]
   Google Scholar
• P. Vernotte , Les paradoxes de la théorie continue de l'equation de la Chaleur , Compte Rendus , vol. 246 , pp. 3154 – 3155 , 1958 . [CSA]
   Google Scholar
• Y. Taitel , On the Parabolic, Hyperbolic and Discrete Formulation of the Heat Conduction Equation , Int. J. Heat Mass Transfer , vol. 15 , pp. 369 – 371 , 1971 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• C. Körner and H. W. Bergman , The Physical Defects of the Hyperbolic Heat Conduction Equation , Appl. Phys. A , vol. 67 , pp. 397 – 401 , 1998 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• S. Godoy and L. S. García-Colín , Nonvalidity of the Telegrapher's Diffusion Equation in Two and Three Dimensions for Crystalline Solids , Phys. Rev. E , vol. 55 , pp. 2127 – 2131 , 1997 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• D. Y. Tzou , The Generalized Lagging Response in Small-Scale and High-Rate Heating , Int. J. Heat Mass Transfer , vol. 38 , pp. 3231 – 3240 , 1995 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• S. D. Brorson , J. G. Fujimoto , and E. P. Ippen , Femtosecond Electron Heat-Transport Dynamics in Thin Gold Film , Phys. Rev. Lett. , vol. 59 , pp. 1962 – 1965 , 1987 . [CSA] [CROSSREF]
   PubMed Web of Science ®Google Scholar
• H. E. Elsayed-Ali , Femtosecond Thermoreflectivity and Thermotransmissivity of Polycrystalline and Single-Crystalline Gold Films , Phys. Rev. B , vol. 43 , pp. 4488 – 4491 , 1991 . [CSA] [CROSSREF]
   PubMed Web of Science ®Google Scholar
• D. Y. Tzou , Macro- to Microscale Heat Transfer: The Lagging Behavior , pp. 25 – 56 , Taylor & Francis , Washington , DC , 1996 .
   Google Scholar
• D. Y. Tzou , Experimental Support for the Lagging Response in Heat Propagation , J. Thermophys. Heat Transfer , vol. 9 , pp. 686 – 693 , 1995 . [CSA]
   Web of Science ®Google Scholar
• P. J. Antaki , Solution for Non-Fourier Dual Phase Lag Heat Conduction in a Semi-infinite Slab with Surface Heat Flux , Int. J. Heat Mass Transfer , vol. 41 , pp. 2253 – 2258 , 1998 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• D. W. Tang and N. Araki , Non-Fourier Heat Conduction Behavior in Finite Mediums under Pulse Surface Heating , Mater. Sci. Eng. A , vol. 292 , pp. 173 – 178 , 2000 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• M. A. Al-Nimr and N. S. Al-Hunti , Transient Thermal Stresses in a Thin Elastic Plate due to a Rapid Dual-Phase-Lag Heat Conduction Model , ASME J. Heat Transfer , vol. 122 , pp. 731 – 746 , 2000 . [CSA]
   Google Scholar
• W. Dai and R. Nassar , A Domain Decomposition Method for Solving Three-Dimensional Heat Transport Equations in Double Layered Thin Films with Micro-scale Thickness , Numer. Heat Transfer A , vol. 38 , pp. 243 – 256 , 2000 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• W. Dai and R. Nassar , A Hybrid Finite Element-Finite Difference Method for Solving Three-Dimensional Heat Transport Equations in Double Layered Thin Films with Micro-scale Thickness , Numer. Heat Transfer A , vol. 38 , pp. 573 – 588 , 2000 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• W. Dai and R. Nassar , A Finite Difference Method for Solving 3-D Heat Transport Equations in Double Layered Thin Film with Micro-scale Thickness and Nonlinear Interfacial Conditions, Numer. Heat Transfer A , vol. 39, pp. 21–33, 2001. [CSA]
   Web of Science ®Google Scholar
• W. Dai , L. Shen , and T. Zhu , A Stable Three-Level Finite-Difference Scheme for Solving a Three-Dimensional Dual-Phase-Lagging Heat Transport Equation in Spherical Coordinates , Numer. Heat Transfer B , vol. 46 , pp. 121 – 139 , 2004 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• J. I. Frankel , B. Vick , and M. N. Özisik , General Formulation and Analysis of Hyperbolic Heat Conduction in Composite Media , Int. J. Heat Mass Transfer , vol. 30 , pp. 1293 – 1305 , 1987 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• M. S. Kazimi and C. A. Erdman , On the Interface Temperature of Two Suddenly Contacting Materials , ASME J. Heat Transfer , vol. 97 , pp. 615 – 617 , 1975 . [CSA]
   Web of Science ®Google Scholar
• W. B. Lor and H. S. Chu , Hyperbolic Heat Conduction in Thin-Film High T c Superconductors with Interface Thermal Resistance , Cryogenics , vol. 39 , pp. 739 – 750 , 1999 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• W. B. Lor and H. S. Chu , Effect of Interface Thermal Resistance on Heat Transfer in a Composite Medium Using the Thermal Wave Model , Int. J. Heat Mass Transfer , vol. 43 , pp. 653 – 663 , 2000 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• H. T. Chen and K. C. Liu , Study of Hyperbolic Heat Conduction Problem in the Film and Substrate Composite with the Interface Resistance , Jpn. J. Appl. Phys. , vol. 41 , pp. 6267 – 6275 , 2002 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• K. C. Liu , C. N. Lin , and J. S. Wang , Numerical Solutions for the Hyperbolic Heat Conduction Problems in a Layered Solid Cylinder with Radiation Surface , J. Appl. Math. Comput. , vol. 164 , pp. 805 – 820 , 2005 . [CSA] [CROSSREF]
   Google Scholar
• J. R. Ho , C. P. Kuo , and W. S. Jiaung , Study of Heat Transfer in Multilayered Structure within the Framework of Dual-Phase-Lag Heat Conduction Model Using Lattice Boltzmann Method , Int. J. Heat Mass Transfer , vol. 46 , pp. 55 – 69 , 2003 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar