Acta Mechanica Solida Sinica

, Volume 24, Issue 2, pp 117–124 | Cite as

Heat transfer characteristics of conductive material under inner non-uniform electromagnetic fields

  • Huijuan Bai
  • Xiaojing Zheng


Electronic transport properties can be influenced by the applied electromagnetic fields in conductive materials. The change of the electron distribution function evoked by outfields obeys the Boltzmann equation. In this paper, a general law of heat conduction considering the non-uniform electromagnetic effect is developed from the Boltzmann equation. An analysis of the equation leads to the result that the electric field gradient and the magnetic gradient in the conductive material are responsible for the influences of electromagnetic fields on the heat conduction process. A physical model is established and finite element numerical simulation reveals that heat conduction can be increased or delayed by the different directions of the electric field gradient, and the existence of the magnetic gradient always hinders heat conduction.

Key words

heat conduction non-uniform electromagnetic field Boltzmann equation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Friedberg, J.P., Mitchell, R.W., Morse, R.L. and Rudsinski, L.I., Resonant absorption of laser light by plasma targets. Physics Review Letters, 1972, 28(13): 795–798.CrossRefGoogle Scholar
  2. [2]
    Muhammad, S.A., Latif, A. and Iqbal, M., Theoretial model for heat conduction in metals during interaction with ultra short laser pulse. Laser and Particle Beams, 2006, 24(3): 347–353.Google Scholar
  3. [3]
    Liu, F., Shi, Y. and Lei, X., Numerical investigation of the temperature field of a metal plate during high-frequency induction heat forming. Journal of Mechanical Engineering Science, 2009, 223(4): 979–986.CrossRefGoogle Scholar
  4. [4]
    Thomson, G. and Mark, S.P., Controlled laser forming for rapid prototyping. Rapid Prototyping Journal, 1997, 3(4): 137–143.CrossRefGoogle Scholar
  5. [5]
    Shi, Y.J., Yao, Z.Q., Shen, H. and Hu, J., Research on the mechanisms of laser forming for the metal plate. International Journal of Machine Tools & Manufacture, 2006, 46(12–13): 1689–1697.CrossRefGoogle Scholar
  6. [6]
    Adrian, L., Andreas, C. and Eckhard, B., Thermoelectric currents in laser induced melts pools. Journal of Laser Applications, 2009, 21(2): 82–87.CrossRefGoogle Scholar
  7. [7]
    Wang, X.Z. and Zheng, X.J., Analyses on nonlinear coupling of magneto-thermo-elasticity of ferromagnetic thin shell—II: Finite element modeling and application. Acta Mechanica Solida Sinica, 2009, 22(3): 197–205.CrossRefGoogle Scholar
  8. [8]
    Tian, X.G. and Shen, Y.P., Study on generalized magneto-thermoelastic problems by FEM in time domain. Acta Mechanica Sinica, 2005, 21(4): 380–387.CrossRefGoogle Scholar
  9. [9]
    Asakawa, Y., Promotion and retardation of heat transfer by electric fields. Nature, 1976, 261(5557): 220–221.CrossRefGoogle Scholar
  10. [10]
    Ryde, T., Arajs, S. and Nunge, R.J., Heat transfer from a wire to hexane in a nonuniform electric field. Journal of Applied Physics, 1991, 69(2): 606–609.CrossRefGoogle Scholar
  11. [11]
    Srivastava, J.P., Elements of Solid State Physics. New Dehil: Prentice-Hall of India Pvt. Ltd, 2003.Google Scholar
  12. [12]
    Ziman, J.M., Electrons and Phonons. Landon: Oxford University Press, 1960.zbMATHGoogle Scholar
  13. [13]
    Guan, Y.H., Fan, G., Zhang, J.T. and Wang, H.G., A study of heat conduction equation under electromagnetic field condition during laser heat treatment. In: Laser Processing of Materials and Industrial Applications II, Proceedings SPIE, 1998, 3550: 372–377.Google Scholar
  14. [14]
    Kalkan, A.K. and Talmage, G., Heat transfer in liquid metals with electric currents and magnetic fields: the conduction case. International Journal of Heat and Mass Transfer, 1994, 37(3): 511–521.CrossRefGoogle Scholar
  15. [15]
    Zhu, L.L. and Zheng, X.J., A theory for electromagnetic heat conduction and a numerical model based on Boltzmann equation. International Journal of Nonlinear Sciences and Numerical Simulation, 2006, 7(3): 339–344.CrossRefGoogle Scholar
  16. [16]
    Chapman, S. and Cowling, T.G., The Mathematical Theory of Non-Uniform Gases. Great Britain: Cambridge University Press, 1970.zbMATHGoogle Scholar
  17. [17]
    Tien, C.L., Majumdar, A. and Gerner, F.M., Microscale energy transport. Washington DC: Taylor & Francis, 1998.Google Scholar
  18. [18]
    Yan, S.S., Fundamentals of Solid State Physics. Beijing: Peking University Press, 2000.Google Scholar
  19. [19]
    Hashizume, H., Kurusu, T. and Toda, S., Numerical analysis of current distribution in type-II superconductors based on T-method. International Journal of Applied Electromagnetics in Materials, 1992, 3(3): 205–213.Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2011

Authors and Affiliations

  1. 1.Key Laboratory of Mechanics on Western Disaster and Environment, Ministry of Education, PRC, Department of Mechanics and Engineering Science, College of Civil Engineering and MechanicsLanzhou UniversityLanzhouChina

Personalised recommendations