Heat and Mass Transfer

, Volume 39, Issue 5–6, pp 499–507 | Cite as

A numerical solution of two-dimensional hyperbolic heat conduction with non-linear boundary conditions

  • W. Shen
  • S. HanEmail author


An explicit TVD scheme is used for two-dimensional non-Fourier heat conduction problems in the general coordinate system with both convection and radiation boundary conditions. The hyperbolic heat flux model is used to simulate the non-Fourier heat conduction. Because of the wave nature of hyperbolic equations, characteristics are used to find the unknown value (either heat flux or temperature) on the boundaries. For convective boundary the unknown temperature is calculated explicitly; for radiation boundary Newton's iteration method is applied to find the boundary temperature. Results of numerical examples agree with the physical expectations indicating that the present approach can be used for modeling non-Fourier heat conduction with complex boundary conditions.


Heat Flux Thermal Wave Left Boundary Surface Radiation Transient Heat Conduction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Peshkov V (1944) Second sound in helium II. J Physics USSR 8: 381Google Scholar
  2. 2.
    Goodson KE; Flik MI (1993) Electron and phonon thermal conduction in epitaxial high-Tc superconducting films. ASME J Heat Transfer 115: 526–532Google Scholar
  3. 3.
    Xu X; Grigoropoulos CP; Russo E (1995) Transient temperature during pulsed excimer laser heating of thin polysilicon films obtained by optical reflectivity measurement. ASME J Heat Transfer 117: 17–24Google Scholar
  4. 4.
    Mitra K; Kumar S; Vedavarz A; Moallemi MK (1995) Experimental evidence of hyperbolic heat conduction in processed meat. ASME J Heat Transfer 117: 569–573Google Scholar
  5. 5.
    Qiu TQ; Tien CL (1993) Heat transfer mechanisms during short-pulse laser heating of metals. ASME J Heat Transfer 115: 835–841Google Scholar
  6. 6.
    Majumdar A (1993) Microscale heat conduction in dielectric thin film. ASME J Heat Transfer 115: 7–16Google Scholar
  7. 7.
    Tzou DY (1995) A unified fied approach for heat conduction from macro- to micro-scales. ASME J Heat Transfer 117: 8–16Google Scholar
  8. 8.
    Vernotte MP (1958) Les paradoxes de la theorie continue de l'Equation de la chyaleur. Computer Rendus 246: 3154–3155Google Scholar
  9. 9.
    Cattaneo C (1958) Sur une forme de l'Equation de la chaleur eliminant le paradoxe d'Une propagation instantenee. C R Acad Sci 247: 431–433Google Scholar
  10. 10.
    Sieniutycz S (1977) The variational principle of classical type of non-coupled non-stationary irreversible transport processes with convective motion and relaxation. Int J Heat Mass Transfer 20: 1221–1231Google Scholar
  11. 11.
    Luikov AV (1966) Application of irreversible thermo dynamics methods to investigation of heat and mass transfer. Int J Heat Mass Transfer 9: 139–152Google Scholar
  12. 12.
    Glass DE; Ozisik MN; Vick B (1985) Hyperbolic heat conduction with surface radiation. Int . Heat Mass Transfer 28: 1823–1830Google Scholar
  13. 13.
    Yang HQ (1990) Characteristic-based, high order accurate and non-oscillatory numerical method for hyperbolic heat conduction. Numer Heat Transfer B18: 221–241Google Scholar
  14. 14.
    Yeung WK; Tung TL (1998) A numerical scheme for non-fourier heat conduction, Part I: one-dimensional problem formulation and applications. Numer Heat Transfer B33: 215–233Google Scholar
  15. 15.
    Baumeister KJ; Hamill TD (1969) Hyperbolic heat conduction equation – a solution for the semi-infinite body problem. ASME J Heat Transfer 91: 543–548Google Scholar
  16. 16.
    Chen HT; Lin JY (1994) Numerical solution of two-dimensional nonlinear hyperbolic heat conduction problems. Numer Heat Transfer B25: 287–307Google Scholar
  17. 17.
    Yang HQ (1992) Solution of two-dimensional hyperbolic heat conduction by high-resolution numerical methods: AIAA 27th Thermophysics Conference, July 6–8, Nashville, TN, (AIAA 92-2937)Google Scholar
  18. 18.
    Tannehill JC; Anderson DA; Pletcher RH (1997) Computational fluid mechanics and heat transfer. Wanshington: Taylor & FrancisGoogle Scholar

Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Tennessee Technological University, Cookeville, TN 38505, USA

Personalised recommendations