Numerical simulation of non-Fourier effects in combined heat transfer

Abstract

The non-Fourier effects on transient and steady temperature distribution in combined heat transfer are studied. The processes of coupled conduction and radiation heat transfer in grey, absorbing, emitting, scattering, one-dimensional medium with black boundary surfaces are analysed numerically. The hyperbolic heat conduction equation is solved by flux splitting method, and the radiative transfer equation is solved by P1 approximate method. The transient thermal responses obtained from non-Fourier heat conduction equation are compared with those obtained from the Fourier heat conduction equation. The results show that the non-Fourier effect can be important when the conduction to radiation parameter and the thermal relaxation time are larger. Further, the radiation effect is more pronounced at small values of single scattering albedo and conduction to radiation parameters. Analysis results indicate that the internal radiation in the medium significantly influences the wave nature.

Keywords

non-Fourier conduction single-scattering albedo absorbing emitting relaxation time transient and steady heat transfer

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References

Viskanta

, ‘Radiation transfer: interaction with conduction and convection and approximate methods in radiation’ In Proceedings of the 7th International Heat Transfer Conference, Munich, 1982, vol. 1, pp. 103–121.

Siegel

, ‘Transient thermal effects of radiant energy in translucent materials’ ASME J. Heat Transf. 120 (1991): 4–23.

Fernandes

Francis

, ‘Combined conductive and radiative heat transfer in an absorbing, emitting, and scattering cylindrical medium’ ASME J Heat Transf. 104 (1981): 594–601.

Ratzel

A. C.

Howell

, ‘Heat transfer by conduction and radiation in one-dimensional planar media using the differential approximation’ ASME J Heat Transf. 104 (1981): 388–391.

Sakami

Charette

Le Dez

, ‘Application of the discrete ordinates method to combined conductive and radiative heat transfer in a two-dimensional complex geometry’ JQSRT 56 (1991): 517–533.

Yao

Chung

B. T. F.

, ‘Transient heat transfer in a scattering-radiating-conducting layer’ J. Thermophys. Heat Transf. 13 (1991): 18–24.

Lazard

Andre

Maillet

, ‘Transient coupled radiative-conductive heat transfer in a gray planar medium with anisotropic scattering’ JQSRT 69 (2002): 23–33.

Ozisik

M. N.

Tzou

D. Y.

, ‘On the wave theory in heat conduction’ ASME J. Heat Transf. 116 (1991): 526–535.

Tzou

D. Y.

, Macro- to micro-scale heat transfer: the lagging behavior (Washington, DC: Taylor & Francis 1997).

10.

J. P.

Chu

H. S.

, ‘Propagation and reflection of thermal waves in a rectangular plate. J‘ Numer. Heat Transf. Part A 36 (1991): 51–74.

11.

Lor

W. B.

Chu

H. S.

, ‘Hyperbolic heat conduction in thin-film high T _c superconductors with interface thermal resistance’ Cryogenics 39 (1991): 739–750.

12.

Lor

W. B.

Chu

H. S.

, ‘Effect of interface thermal resistance on heat transfer in a composite medium using the thermal wave model’ Int. J. Heat Mass Transf. 43 (2002): 653–663.

13.

Tzou

D. Y.

Chiu

K. S.

, ‘Temperature-dependent thermal lagging in ultrafast laser heating’ Int. J. Heat Mass Transf. 44 (2002): 1725–1734.

14.

Naji

Al-Nimr

M. A.

Hader

, ‘The validity of using the microscopic hyperbolic heat conduction model under a harmonic fluctuating boundary heating source’ Int. J. Thermophys. 24 (2) (2003): 545–557.

15.

Yang

C. Y.

, ‘Estimation of the periodic thermal conditions on the non-Fourier fin problem’ Int. J. Heat Mass Transf. 48 (2002): 3506–3515.

16.

Zhang

Cheng

, ‘Theoretical study of transient thermal conduction and temperature distribution generated by pulsed laser’ J. Appl. Phys. B Lasers Opt. 70 (2002): 85–90.

17.

Glass

D. E.

Ozisik

M. N.

McRae

D. S.

, ‘Hyperbolic heat conduction with radiation in an absorbing and emitting medium’ J. Numer. Heat Transf., Part B: Fundam. 12 (1981): 321–333.

18.

Cattaneo

, ‘A form of heat conduction equation which eliminates the paradox of instantaneous propagation’ Comput. Rendus 247 (1951): 431–433.

19.

Vernotte

, ‘Les paradoxes de la theorie continue de l'equation de la chaleur’ Comput. Rendus 246 (1951): 3154–3155.

20.

Tannehill

J. C.

Anderson

D. A.

Pletcher

R. H.

, Computational fluid mechanics and heat transfer 2nd edition, (Washington, DC: Taylor and Francis 1997): pp. 375–386.

21.

Modest

M. F.

, Radiative heat transfer (New York: McGraw-Hill 1993).

22.

Hsin-Sen

Senpuu

Chia-Hui

, ‘Non-Fourier heat conduction with radiation in an absorbing, emitting and isotropically scattering medium’ J. Quant. Spectros. Radiat. Transf. 73 (2002): 571–582.