Numerical Investigation of Non Fourier Heat Conduction in a Semi-infinite Body due to a Moving Concentrated Heat Source Composed with Radiational Boundary Condition

Authors: M. Akbari, S. Sadodin

Abstract:

In this paper, the melting of a semi-infinite body as a result of a moving laser beam has been studied. Because the Fourier heat transfer equation at short times and large dimensions does not have sufficient accuracy; a non-Fourier form of heat transfer equation has been used. Due to the fact that the beam is moving in x direction, the temperature distribution and the melting pool shape are not asymmetric. As a result, the problem is a transient threedimensional problem. Therefore, thermophysical properties such as heat conductivity coefficient, density and heat capacity are functions of temperature and material states. The enthalpy technique, used for the solution of phase change problems, has been used in an explicit finite volume form for the hyperbolic heat transfer equation. This technique has been used to calculate the transient temperature distribution in the semi-infinite body and the growth rate of the melt pool. In order to validate the numerical results, comparisons were made with experimental data. Finally, the results of this paper were compared with similar problem that has used the Fourier theory. The comparison shows the influence of infinite speed of heat propagation in Fourier theory on the temperature distribution and the melt pool size.

Keywords: Non-Fourier, Enthalpy technique, Melt pool, Radiational boundary condition

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1080464

References:

[1] A.A. Rostami, R. Greif,and E.R.Russo, "Modified Enthalpy Method Applied to Rapid melting and solidification", Int. J. Heat Mass Transfer, vol. 35, no. 9, pp. 2161-2172, 1992
[2] A.A. Rostami, and A.Raisi, "Temperature distribution and melt pool size in a semi-infinite body due to a moving laser heat source", Numerical Heat transfer, Part A. 31: 783-796, 1997.
[3] M. H. Sadd, and J. E. Didlake, "Non- Fourier Melting of a same infinite solid", J. Heat Transfer 2 vol 81, PP: 25-28, 2001.
[4] C. Cattaneo, "A Form of conduction Equation Which Eliminates the Paradox of Instantaneous Propagation"Compt.Rend.,vol.247,PP 431- 442,1986.
[5] P.Vernotte, "Paradox in the Continuous Theory of Heat Equation" Compt.Rend., vol.246,PP 3154-3159,1986.
[6] Fangming Jiang, "Non- Fourier heat conduction phenomena in porous material heated by microsecond laser pulse", Taylor & Francis, vol 6, PP: 331-346, 2002.
[7] N.M. abdel- Jabbar, and M. A. Ali. Nimr, "The Dual phase- lag heat conduction model in thin slab under fluctuating thermal disturbance" , Taylor & Francis, vol. 24, PP: 47-54, 2003.
[8] A.A. Rostami, R. Greif,and E.R.Russo, "Unsteady two dimensional heat transfer in laser heated materials", processing, in Transport phenomena in Material, ASME Publication HID, vol. 146, 1990.
[9] A. Raisi, "Calculation of the temperature field and the melt pool shape due to laser heating" (in Farsi), M.S. thesis, Isfahan University of technology, Isfahan, Iran, 1995.
[10] Y.S. Touloukian, and C.Y.Ho, "Eds, Thermophysical properties of Matters", plenum press, New York, vols. 1 and 4, 1972.
[11] W.M. Rohsenow, and J.P. Hartnett, "(Eds), Handbook of heat transfer fundamentals", chap3, Mc Graw Hill, New York, 1985.
[12] R. Mehrabian, Hsu, S. S.C.Kou, and A. Munitz, "Laser surface melting and solidification moving heat flux", metallurgical Trans, vol. 14B, PP: 213-227, 1982.
[13] Neilw. Ashcroft, and N. David. Mermin, "Solid State Physics", PP: 10,1975.