Estimation of Thermal Conductivity in a Non-Linear Heat Conduction Medium Based on Integral Method

Sin Kim; Min Chan Kim; Kyung Youn Kim

Journal of Industrial and Engineering Chemistry, Vol.11, No.5, 749-755, September, 2005

Export Citation

Estimation of Thermal Conductivity in a Non-Linear Heat Conduction Medium Based on Integral Method

Sin Kim, Min Chan Kim^{1, †}, and Kyung Youn Kim²

Department of Nuclear and Energy Engineering, Korea
¹Department of Chemical Engineering, Korea
²Department of Electronic Engineering, Cheju Natiional University, Cheju 690-756, Korea

E-mail:

The paper presents an integration approach to estimate temperature-dependent thermal conductivity in a transient non-linear heat conduction medium using the integral approach. The unknown thermal conductivity is assumed to vary linearly with respect to temperature. For a one-dimensional heat conduction medium possessing a heated and an insulated wall, this study approximates the spatial temperature distribution, as a polynomial having unknown time-dependent coefficients that satisfy four known boundary data (two prescribed heat fluxes and two measured temperatures), and the energy conservation. The integral heat conduction equations are solved to determine the unknown coefficients. Some numerical examples are introduced to show the performance of the proposed approach.

Keywords:inverse heat conduction problem;thermal conductivity;integral method

[References]

Alifanov OM, Artyukhin EA, Rumyantsev SV, Extreme Methods for Solving Ill-Posed Problems with Applications to Inverse Heat Transfer Problems, p. 42~93, Bell House, Inc., New York (1995)
Huang CH, Ozisik MN, Int. J. Heat Fluid Flow, 11, 262 (1990)
Jurkowski T, Jarny Y, Delaunay D, Int. J. Heat Mass Transf., 40(17), 4169 (1997)
Huang CH, Ozisik MN, Numer. Heat Transf. A-Appl., 20, 95 (1991)
Huang CH, Yan JY, Chen HT, J. Thermophys. Heat Transf., 9, 667 (1995)
Chen HT, Lin JY, Wu CH, Huang CH, Numer. Heat Transf. B-Fundam., 29, 509 (1996)
Chen HT, Lin JY, Int. J. Heat Mass Transf., 41(14), 2237 (1998)
Yang CY, Appl. Math. Model., 23, 469 (1999)
Kim S, Kim MC, Kim KY, Int. Commun. Heat Mass Transf., 29, 107 (2002)
Kim S, Kim MC, Kim KY, Int. J. Heat Mass Transf., 46, 1801 (2203)
Kim S, Chung BJ, Kim MC, Kim KY, Numer. Heat Transf. A-Appl., 44, 521 (2003)

[Related Articles]

[1] Alifanov OM, Artyukhin EA, Rumyantsev SV, Extreme Methods for Solving Ill-Posed Problems with Applications to Inverse Heat Transfer Problems, p. 42~93, Bell House, Inc., New York (1995)

[2] Huang CH, Ozisik MN, Int. J. Heat Fluid Flow, 11, 262 (1990)

[3] Jurkowski T, Jarny Y, Delaunay D, Int. J. Heat Mass Transf., 40(17), 4169 (1997)

[4] Huang CH, Ozisik MN, Numer. Heat Transf. A-Appl., 20, 95 (1991)

[5] Huang CH, Yan JY, Chen HT, J. Thermophys. Heat Transf., 9, 667 (1995)

[6] Chen HT, Lin JY, Wu CH, Huang CH, Numer. Heat Transf. B-Fundam., 29, 509 (1996)

[7] Chen HT, Lin JY, Int. J. Heat Mass Transf., 41(14), 2237 (1998)

[8] Yang CY, Appl. Math. Model., 23, 469 (1999)

[9] Kim S, Kim MC, Kim KY, Int. Commun. Heat Mass Transf., 29, 107 (2002)

[10] Kim S, Kim MC, Kim KY, Int. J. Heat Mass Transf., 46, 1801 (2203)

[11] Kim S, Chung BJ, Kim MC, Kim KY, Numer. Heat Transf. A-Appl., 44, 521 (2003)