ANALYTICAL STUDY OF THE TEMPERATURE DISTRIBUTION IN SOLIDS SUBJECTED TO NONUNIFORM MOVING HEAT SOURCES

Abstract

We propose in this paper an analytical study of the temperature distribution in a solid subjected to moving heat sources. The power dissipated by the heat sources is considered nonuniform. The study was made in steady state. The model is three-dimensional. It is valid regardless of the relative velocity of the source. We have considered three cases of semi-elliptic distribution of the power with: (i) the maximum at the center of the source, (ii) the maximum at the inlet of the source, (iii) the maximum at the output of the source. These configurations simulate the conformity imperfection of contact due to wear and / or the non-uniformity of contact pressure in frictional devices. We compare the temperature change for these different scenarios and for different relative velocities, considering the same total power dissipation. The reference case is that of a uniform source dissipating the same power.

Keywords

Dates

  • Submission Date2012-08-26
  • Revision Date2013-05-25
  • Acceptance Date2013-05-25
  • Online Date2013-06-16

DOI Reference

10.2298/TSCI120826071H

References

  1. Boussinesq, J., Calcul des températures successives d'un milieu homogène et atherme indéfini que sillone une source de chaleur, Comptes Rendus, 110 (1890), pp. 1242-1244.
  2. Rosenthal, D., Etude théorique du régime thermique pendant la soudure à l'arc, Comptes Rendus, 2 (1935), pp.1277-1292.
  3. Blok, H., Les températures de surface dans des conditions de graissage sous extrême pression, Proc. Sd.World Petrol. Congr., 3 (1937), pp. 471-486.
  4. Jaeger, J.C., Moving sources of heat and the temperature at sliding contacts, Proc. Royal Soc. of New South Wales, 76 (1942), pp. 203-224.
  5. Archard, J.F., The temperature of rubbing surfaces,Wear, 2 (1958), pp. 438- 455.
  6. DesRuisseaux, N.R., Zerkle, R.D., Temperature in semi-infinite and cylindrical bodies subject to moving heat sources and surface cooling, ASME J. Heat Transfer, 92 (1970), 3, pp. 456-464.
  7. Ling, F.F., Simkins, T.E., Measurement of pointwise juncture condition of temperature at the interface of two bodies in sliding contact, ASME J. Basic Eng., 85 (1963), pp. 481-486.
  8. Gecim, B., Winer, W.O., Steady temperature in a rotating cylinder subject to surface heating and convective cooling, ASME J. Tribology, 106 (1984), 1, pp. 120-127.
  9. Patula, E.J., Steady-state temperature distribution in a rotating roll subject to surface heat fluxes and convective cooling, ASME J. Heat Transfer, 103 (1981), 1, pp. 36-41.
  10. Osman, T., Guenoun, S., Boucheffa, A., Temperature field in a rotating roller subjected to interface heating, EPJ Applied Physics, 50 (2010), 2, pp. 205041-205044.
  11. Hamraoui, M., Thermal behaviour of rollers during the rolling process, Applied Thermal Engineering, 29 (2009), 11, pp. 2386-2390.
  12. Hamraoui, M., Osman, T., Boucheffa, A., Rashidi, M.M., Analytical modelling of the three-dimensional steady-state temperature in a bearing ring, Mecanique & Industrie, 12 (2011), 1, pp. 1-4.
  13. Hamraoui, M., Zouaoui, Z., Modelling of heat transfer between two rollers in dry friction, International Journal of Thermal Sciences, 48, (2009), 6, pp. 1243-1246.
  14. Baïri, A., Garcia-de-Maria, J.M., Laraqi, N., Effect of thickness and thermal properties of film on the thermal behavior of moving rough interfaces, European Physical Journal - Applied Physics, 26, (2004), 1, pp. 29-34.
  15. Blok, H., Flash temperature concept, Wear, 6 (1963), pp. 483-493.
  16. Laraqi, N., An Exact Explicit Analytical Solution for Steady-State Temperature of a Half Space Subjected to a Circular Moving Heat Source, ASME J. Tribology, 125 (2003), 4, 859-862.
  17. Laraqi, N., Alilat, N., Garcia de Maria, J.M, Baïri, A., Temperature and division of heat in a pin-on-disc frictional device - Exact analytical solution, Wear, 266 (2009), 7-8, pp. 765-770.
  18. Baïri, A., Alilat, N., Bauzin, J.G., Laraqi, N., Three-dimensional stationary thermal behavior of a bearing ball, International Journal of Thermal Sciences, 43 (2004), 6, pp. 561-568.
  19. Belghazi, H, El Ganaoui, M., Labbe, J.C., 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, 49 (2010), 2, pp. 311-318.
  20. Laraqi, N., El Ganaoui, M., Analytical computation of transient heat transfer macro constriction resistance: application to thermal spraying processes, C. R. Mecanique, 340 (2012), 7, pp. 536-542.
Volume 17, Issue 3, Pages687 -694