Phenomena of Hyperbolic Heat Conduction in the Hot Mold with an Inner Defect

내부결함이 있는 고온 금형에서의 쌍곡선형 열전도 현상

  • Published : 2001.07.01


In the glass forming process, the phenomena of hyperbolic heat conduction in the hot mold with an inner defect are studied analytically. It is shown that the temperature predicted by the parabolic model is underestimated compared to the one by the hyperbolic model. As the rmal wave is reflected from the area with defects and then arrives at the surface supplied by the heat flux, it is expected that there exists thermal shock in the materials. The area with defects is assumed to be adiabatic since its thermal conductivity is much lower compared to the one of the material. The results also indicate that the sudden temperature -jump in the mold surface can cause diverse problems such as glass defect (embryo mark, etc), oxidation of mold and coating, and change of material properties.


Defect;Hyperbolic Heat Conduction;Hot Mold;Parabolic Heat Conduction;Thermal Wave


  1. IMSL On-Line pdf Documentation, 1997, Visual Numerics, Inc
  2. Hector, L. G., Kim, W. S., And Ozisik, M. N., 1992, 'Propagation and Reflection of Thermal Waves in a Finite Medium Due to Axisymmetric Surface Sources,' Int. J. Heat Mass Transfer, Vol. 35 No. 4, pp. 897-912
  3. Lam, T. T. and Yeung, W. K., 1997, 'Thermal Wave in the Substrate of Integrated Circuit Chips,' Advances in Electronic Packaging, ASME, Vol. 19-2, pp. 2037-2044
  4. Li, J., Gu, Y., Guo, Z., 1998, 'Analysis of the Phenomena of Non-Fourier Heat Conduction in Switch-Q Laser Process for Reducing the Core Loss of Grain-Oriented Silicon Steel,' J. Of Material Processing Technology, Vol. 74, pp. 292-297
  5. Cattaneo, C., 1958, 'Sur une Forme de L'equation de la Chaleur le Paradoxe D'une Propagation Instantance,' C. R. Acad. Sci. 247, pp. 431-432
  6. Vernotte, P., 1958, 'Les Paradoxes de la Theorie Continue de L'equation de la Chaleur,' C. R. Acad. Sci. 246, pp. 3154-3155