Analytical solution of unsteady heat conduction in a two-layered material in imperfect contact subjected to a moving heat source

International Journal of Thermal Sciences

Volumn 49, Issue 2, 2010, Pages 311-318

  Belghazi, H ^a   El Ganaoui, M ^a   Labbe, J C ^a  

^a UNIVERSITY OF LIMOGES   (France)

Author keywords

Analytical; Contact; Heat conduction; Two layered material; Unsteady

Indexed keywords

ALUMINA SUBSTRATES; ANALYTICAL; ANALYTICAL APPROACH; ANALYTICAL CONTACT; ANALYTICAL MODEL; ANALYTICAL SOLUTIONS; COATING LAYER; COPPER TRACKS; FINITE DEPTH; GAUSSIAN LASER BEAM; HEAT EQUATION; IMPERFECT CONTACT; LAYERED MATERIAL; MOVING HEAT SOURCES; PRACTICAL SYSTEMS; SEPARATION OF VARIABLES METHOD; SOURCE TERMS; THERMAL CONTACT; THERMAL CONTACT RESISTANCE; TRANSIENT HEAT CONDUCTION; UNSTEADY HEAT CONDUCTION;

LASER CLADDING; SUBSTRATES;

HEAT CONDUCTION;

EID: 71649100856     PISSN: 12900729     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijthermalsci.2009.06.006     Document Type: Article

References (49)

1. Rosenthal D. The theory of moving sources of heat and its application to metal treatments. Transaction of the ASME 68 (1946) 849-866
2. Lankalapalli K.N., Tu J.F., and Gartner M. A model for estimating penetration depth of laser welding processes. Journal of Physics D: Applied Physics 29 (1996) 1831-1841
3. Majumdar P., and Xia H. A Green's function model for the analysis of laser heating of materials. Applied Mathematical Modelling 31 (2007) 1186-1200
4. Brockmann R., Dickmann K., Geshev P., and Matthes K.J. Calculation of temperature field in a thin moving sheet heated with laser beam. R. International Journal of Heat and Mass Transfer 46 (2003) 717-723
5. Cheng P.J., and Lin S.C. An analytical model for the temperature field in the laser forming of sheet metal. Journal of Materials Processing Technology 101 (2000) 260-267
6. Laraqi N. An exact explicit analytical solution of steady-state temperature in a half space submitted to a circular moving heat source. ASME Journal of Tribology 125 4 (2003) 859-862
7. Kang S.H., and Cho H.S. Analytical solution for transient temperature distribution in gas tungsten arc, welding with consideration of filler wire. Proceeding - Institution of Mechanical Engineers 213 Part B (1999) 799-811
8. Zubair S.M., and Chaudhry M.A. Heat conduction in a semi-infinite solid due to a time-dependent laser source. International Journal of Heat and Mass Transfer 39 (1996) 3067-3074
9. Yilbas B.S. 3-dimensional laser heating model including a moving heat source consideration and phase change process. Heat and Mass Transfer 33 (1998) 495
10. El-Adawi M.K., Abdel-Naby M.A., and Shalaby S.A. Laser heating of two - layer system with constant surface absorption an exact solution. International Journal of Heat and Mass Transfer 38 5 (1995) 947-952
11. Haji-Sheikh A., and Beck J.V. Temperature solution in multi-dimensional multi-layer bodies. International Journal of Heat and Mass Transfer 45 (2002) 1865-1877
12. Baïri A., Garcia-de-Maria J.M., and Laraqi N. Effect of thickness and thermal properties of film on the thermal behavior of moving rough interfaces. European Physical Journal - Applied Physics 26 1 (2004) 29-34
13. Salti B., and Laraqi N. 3-D numerical modeling of heat transfer between two sliding bodies: temperature and thermal contact resistance. International Journal of Heat and Mass Transfer 42 13 (1999) 2363-2374
14. Bauzin J.G., and Laraqi N. Simultaneous estimation of frictional heat flux and two thermal contact parameters for sliding solids. Numerical Heat Transfer 45 4 (2004) 313-328
15. Couëdel D., Rogeon P., Lemasson P., Varin M., Parpillon J.C., and Berthet R. 2D-heat transfer modelling within limited regions using moving sources: application to electron beam welding. International Journal of Heat and Mass Transfer 46 23 (2003) 4553-4559
16. Baïri A., and Laraqi N. Diagrams for fast transient conduction in sphere and long cylinder subject to sudden and violent thermal effects on its surface. Applied Thermal Engineering 23 (2003) 1373-1390
17. El Ganaoui M., and Bennacer R. On some latent heat effects on the floating zone growth. Advances in Space Research 36 1 (2005) 96-98
18. Bennacer R., El Ganaoui M., and Semma E. Quelques paramètres de contrôle de la convection thermocapillaire en croissance par fusion de zone. Comptes Rendus de Mécanique 332 5-6 (May-June 2004) 447-456
19. Séfiane K., Bennacer R., and El Ganaoui M. Numerical investigation of the role of thermal evaporation profile initiating Marangoni convection in capillary tubes. Mécanique et Industrie 5 (2004) 575-581
20. de Monte F. Transient heat conduction in one- dimensional composite slab. A natural analytic approach. International Journal of Heat and Mass Transfer 43 19 (2000) 3607-3619
21. de Monte F. Unsteady heat conduction in two-dimensional two slab-shaped regions. Exact closed-form solution and results. International Journal of Heat and Mass Transfer 46 8 (2003) 1455-1469
22. de Monte F. Transverse eigenproblem of steady-state heat conduction for multi-dimensional two-layered slabs with automatic computation of eigenvalues. International Journal of Heat and Mass Transfer 47 (2004) 191-201
23. Salt H. Transient conduction in a two-dimensional composite slab-1. International Journal of Heat and Mass Transfer 26 11 (1983) 1611-1616
24. Özisik M.N., and Mikhailov M.D. Unified Analysis and Solutions of Heat and Mass Diffusion. second ed. (1994), A Wiley-Interscience
25. Özisik M.N. Boundary Value Problem (1989), Dover Publications, INC., New York
26. Carslaw H.S., and Jaeger J.C. Conduction of Heat in Solids. second ed. (1993), Clarendon Press, Oxford pp. 87-89
27. Dai K., Li X.X., and Shaw L.L. Comparisons between thermal modeling and experiments: effects of substrate preheating. Rapid Prototyping Journal 10 1 (2004) 24-34
28. Kulasiri D., and Woodhead I. On modelling the drying of porous materials: analytical solutions to coupled partial differential equations governing heat and moisture transfer. Mathematical Problems in Engineering 3 (2005) 275-291
29. J.P. Kruth, X. Wang, T. Laoui, L. Froyen, Lasers and materials in selective laser sintering, 23(4) (2003) 357-371.
30. Chen T., and Zhang Y. Numerical simulation of two-dimensional melting and resolidification of a two-component metal powder layer in selective laser sintering, process. Numerical Heat Transfer, Part A 46 (2004) 633-649
31. Vafai K. Handbook of Porous Media. second ed. (2005), Taylor & Francis Group
32. Kanan Bala, Pradeep R., Pradhan N.S., and Saxena M.P. Effective thermal conductivity of copper powders. Journal of Physics D: Applied Physics 22 (1989) 1068-1072
33. Hmina N., and Scudeller Y. Détermination expérimentale de la résistance thermique d'interface d'un dépôt Métallique submicronique sur un substrat. Journal de Physique III 5 (1995) 881-901
34. Nield D.A., and Bejan A. Convection in Porous MEDIA. second ed. (1992), Springer-Verlag, New York
35. Addakiri S., semma E., El Ganaoui M., and Pateyron B. Defect and Diffusion Forum. Numerical Study of Melting/Solidification by a Hybrid Method Coupling a Lattice Boltzmann and a Finites Volumes Approaches vols. 283-286 (2009), Trans Tech Publications, Switzerland pp. 477-482
36. El Ganaoui M., Bontoux P., Lamazouade A., Leonardi E., and de Vahl Davis G. Computational model for solutal convection during directional solidification. Numerical Heat Transfer, Part B 41 (2001) 325-338
37. Bala K., Pradhan P.R., Saxena N.S., and Saksena M.P. Effective thermal conductivity of copper powders. Journal of Physics D: Applied Physics 22 (1989) 1068-1072
38. Wimmer J.M., Graham H.C., and Tallan N.M. In: Tallan N.M. (Ed). Electrical Conductivity in Ceramics and Glasspart B (1974), Marcel Dekker, New York 619
39. H. Belghazi, M. El Ganaoui, J.C. Labbe, Analytical solution of the unsteady heat conduction in two layered material within imperfect thermal contact. In: Y. Haik, Z. Saghir, M. Chacha, M. Younes, A. Al Amiri, F. Al Omari, S. Almuhtseb, A. Kazim (Eds.), Proceedings of the 2nd International Conference on Thermal Engineering Theory and Applications, (2006) 49-55.
40. Ben Naoua S., El Ganaoui M., Sammouda H., and Fauchais P. A Model for Rapid Solidification for Plasma Spraying vol. 553 (2007), Materials Science Forum (MSF) by Trans Tech Publications (TTP), Switzerland pp. 223-230
41. Laraqi N., and Bairi A. Theory of thermal resistance between solids with randomly sized and located contacts. International Journal of Heat and Mass Transfer 45 20 (2002) 4175-4180
42. Amara M., Timchenko V., El Ganaoui M., Leonardi E., and de Vahl Davis G. A 3D computational model of heat transfer coupled to phase change in multilayer materials with random thermal contact resistance. International Journal of Thermal Sciences 48 2 (2009) 421-427
43. Bouneder M., El Ganaoui M., Pateyron B., and Fauchais P. Relevance of a thermal contact resistance depending on the solid/liquid phase change transition for sprayed composite metal/ceramic powder by direct current plasma jets. Comptes Rendus Mécanique 336 7 (July 2008) 592-599
44. Grimaud A., Bouneder M., Menecier S., and El Ganaoui M. Faisabilité d'une méthode d'évaluation de la résistance thermique de contact entre une lamelle céramique écrasée sur un substrat métallique. Mécanique & Industries 8 (2007) 71-75
45. Bouvet A., and Bennacer R. Effect of heating rate on Arrhenius law: thermodamageable material. Journal of the Energy Institute 79 4 (2006) 228-231
46. Poirier D.R., and Geiger G.H. Transport Phenomena in Materials Processing (February, 1998), The Minerals, Metals and Materials Society, Warrendale, PA
47. Schlunder E.U. Heat Exchanger Design Handbook (1983), Hemisphere Publishing Corporation, New York, NY
48. Kaplan A.F.H. Model of the absorption variation during pulsed laser heating applied to welding of electronic Au/Ni-coated Cu-lead frames. Applied Surface Science 241 (2005) 362-370
49. Tolochko N.K., Khlopkov Y.V., Mozzharov S.E., Ignatiev M.B., Laoui T., and Titov V.I. Absorptance of powder materials suitable for laser sintering. Rapid Prototyping Journal 6 3 (2000) 155-160