Comptes Rendus
Analytical solution for the 3D steady state conduction in a solid subjected to a moving rectangular heat source and surface cooling
[Solution analytique pour la conduction en régime permanent 3D dans un solide soumis à une source de chaleur rectangulaire mobile et à un refroidissement surfacique]
Comptes Rendus. Mécanique, Volume 337 (2009) no. 2, pp. 107-111.

L'échauffement des solides sous l'action du frottement ou du soudage par exemple joue un rôle important dans le comportement thermomécanique des matériaux. Nous proposons dans cet article un modèle analytique pour le calcul de la répartition tridimensionnelle de la température dans un solide soumis à une source de chaleur rectangulaire mobile et à un refroidissement surfacique. On utilise une transformée intégrale fréquentielle et une transformée intégrale de Fourier cosinus finie pour résoudre l'équation d'advection–diffusion associée à ce problème. La solution obtenue est explicite et n'impose aucune restriction en termes de vitesse, de dimensions et de coefficient d'échange. Elle se présente sous la forme de séries qui convergent rapidement.

Heating of solids, e.g. by friction or welding, plays an important role in the thermomechanical behaviour of materials. An analytical model to compute the three-dimensional temperature distribution in a solid, subjected to a moving rectangular heat source with surface cooling is proposed in this article. A frequential integral transform and a finite cosine Fourier integral transform are used to solve the advection–diffusion equation related to this problem. The obtained solution is explicit and does not impose any restriction on the speed, the dimensions and the heat convection coefficient. It is presented in series form which converges rapidly.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2009.02.003
Keywords: Heat transfer, Moving heat sources, Advection–diffusion problem, Analytical solution
Mots-clés : Transferts thermiques, Sources de chaleur mobiles, Problème d'advection–diffusion, Solution analytique

Talaat Osman 1 ; Abderrahmane Boucheffa 1

1 Université Paris 11, IUT d'Orsay, Département mesures physiques, plateau du Moulon, 91400 Orsay, France
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Talaat Osman; Abderrahmane Boucheffa. Analytical solution for the 3D steady state conduction in a solid subjected to a moving rectangular heat source and surface cooling. Comptes Rendus. Mécanique, Volume 337 (2009) no. 2, pp. 107-111. doi : 10.1016/j.crme.2009.02.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.02.003/

[1] N. Laraqi An exact explicit analytical solution for steady-state temperature of a half space subjected to a circular moving heat source, ASME Journal of Tribology, Volume 125 (2003), pp. 859-862

[2] J.C. Jaeger Moving sources of heat and the temperature at sliding contacts, Proc. Royal Soc. NSW, Volume 76 (1942), pp. 203-224

[3] N. Alilat; A. Baïri; N. Laraqi Three-dimensional calculation of temperature in a rotating disk subjected to an eccentric circular heat source and surface cooling, Numerical Heat Transfer, Volume 46 (2004) no. 2, pp. 167-180

[4] H.A. Francis Interfacial temperature distribution within a sliding Hertzian contact, ASLE Trans., Volume 14 (1970), pp. 41-54

[5] N. Laraqi; N. Alilat; J.M. Garcia-de-Maria; A. Baïri Temperature and division of heat in a pin-on-disc frictional device – Exact analytical solution, Wear, Volume 266 (2009), pp. 765-770

[6] N.R. DesRuisseaux; R.D. Zerkle Temperature in semi-infinite and cylindrical bodies subject to moving heat sources and surface cooling, ASME J. Heat Transfer (1970), pp. 456-464

[7] N. Laraqi; A. Baïri; L. Ségui Temperature and thermal resistance in frictional devices, Applied Thermal Engineering, Volume 24 (2004) no. 17, pp. 2567-2581

[8] A. Baïri; N. Laraqi Diagrams for fast transient conduction in sphere and long cylinder subject to sudden and violent thermal effects on its surface, Applied Thermal Engineering, Volume 23 (2003), pp. 1373-1390

[9] A. Baïri; N. Laraqi; N. Alilat; Z. Zouaoui Fast transient conduction in infinite plate subject to violent thermal effects, Applied Thermal Engineering, Volume 24 (2004) no. 1, pp. 1-15

[10] F.F. Ling; T.E. Simkins Measurement of point-wise juncture condition of temperature at the interface of two bodies in sliding contact, ASME Journal of Basic Engineering, Volume 85 (1963), pp. 481-486

[11] N. Laraqi; A. Baïri Theory of thermal resistance between solids with randomly sized and located contacts, Int. J. Heat Mass Transfer, Volume 45 (2002) no. 20, pp. 4175-4180

[12] J.P. Bardon Bases physiques des conditions de contact thermique imparfait entre milieux en glissement relatif, Revue Générale de Thermique Fr., Volume 386 (1994), pp. 86-91

[13] B. Salti; N. Laraqi 3-D numerical modelling of heat transfer between two sliding bodies. Temperature and thermal contact resistance, Int. J. Heat Mass Transfer, Volume 42 (1999) no. 13, pp. 2363-2374

[14] A. Baïri; J.M. Garcia-de-Maria; N. Laraqi Effect of thickness and thermal properties of film on the thermal behaviour of moving rough interfaces, European Physical Journal – Applied Physics, Volume 26 (2004) no. 1, pp. 29-34

[15] J.G. Bauzin; N. Laraqi Simultaneous estimation of frictional heat flux and two thermal contact parameters for sliding solids, Numerical Heat Transfer, Volume 45 (2004) no. 4, pp. 313-328

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