Using the Lattice Boltzmann Method for the numerical study of non-fourier conduction with variable thermal conductivity

Document Type : Full Lenght Research Article

Authors

University of Kashan

Abstract

The lattice Boltzmann method (LBM) was used to analyze two-dimensional (2D)
non-Fourier heat conduction with temperature-dependent thermal conductivity. To this end, the evolution of wave-like temperature distributions in a 2D plate was obtained. The temperature distributions along certain parts of the plate, which was subjected to heat generation and constant thermal conductivity conditions, were also derived and compared. The LBM results are in good agreement with those reported in other works. Additionally, the temperature contours at four different times in which steady state conditions can be achieved were analyzed. The results showed that thermal conductivity increased with rising temperature. Given the material’s considerable effectiveness in transferring heat energy under heat generation conditions, the temperature gradient of the plate decreased to a level lower than that observed under constant thermal conductivity.

Keywords: Non-Fourier conduction, lattice Boltzmann method, variable thermal conductivity, constant thermal conductivity, heat generation

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References

[1] J. Zhou, Y. Zhang, J.K. Chen, Non-Fourier heat conduction effect on laser induced thermal damage in biological tissues,  Heat Transfer, A 54 (1), 65-70, (2008).        
[2] J.Y. Lin, The non-Fourier effect on the fin performance under periodic thermal conditions, Appl. Math, Model. 22, 629–640, (1998).
[3] D.W. Tang, N. Araki, Non-Fourier heat conduction behavior in finite mediums under pulse surface heating, Mater. Sci. Eng, A 292, 173–178, (2000).
[4] J.R. Ho, C.P. Kuo, W.S. Jiaung, C.J. Twu, Lattice Boltzmann scheme for hyperbolic heat conduction, Numer. Heat Transfer, B 41, 591–607, (2002).
[5] S.C. Mishra, A. Lankadasu, K. Beronov, Application of the lattice Boltzmann method for solving the energy equation of a 2-D transient conduction radiation problem, Int. J. Heat Mass Transfer, 48, 3648–3659, (2005).
[6] S.C. Mishra, H.K. Roy, Solving transient conduction-radiation problems using the lattice Boltzmann method and the finite volume method, J. Compute. Phys. 233, 89–107, (2007).
[7] M. H. Rahimian, I. Rahbari, F. Mortazavi, High order numerical simulation of non-Fourier heat conduction: An application of numerical Laplace transform inversion, International Journal of Heat and Mass Transfer, vol. 51, 51–58, (2014).
[8] W. Dreyer, S. Qamar, Kinetic flux-vector splitting schemes for the hyperbolic heat conduction, J. Comput. Phys. 198 (2), (2004).
[9] H. Chen, J. Lin, Numerical analysis for hyperbolic heat conduction, Int. J. Heat Mass Transfer 36 (11), 2891–2898, (1993).
[10] J.I. Frankel, B. Vick, M.N. Özisik, General formulation and analysis of hyperbolic heat conduction in composite media, Int. J. Heat Mass Transfer 30, 1293–1305, (1987).
[11] B. Abdel-Hamid, Modelling non-Fourier heat conduction with periodic thermal oscillation using the finite integral transform, Appl. Math, Model 23, 899–914, (1999).
[12] T.M. Chen, C.C. Chen, Numerical solution for the hyperbolic heat conduction problems in the radial–spherical coordinate system using a hybrid Green’s function method, Int. J. Therm. Sci. 49, 1193–1196, (2010).
[13] X. Lu, P. Tervola, M. Viljanen, Transient analytical solution to heat conduction in composite circular cylinder, Int. J. Heat Mass Transfer, 49, 341–348, (2006).
[14] G.E. Cossali, Periodic heat conduction in a solid homogeneous finite cylinder, Int. J. Therm. Sci. 48, 722–732, (2009).
[15] A. Moosaie, Axsymmetric non-Fourier temperature field in a hollow sphere, Arch. Appl. Mech. 79, 679–694, (2009).
[16] H. Ahmadikia and M. Rismanian, Analytical solution of non-Fourier heat conduction problem on a fin under periodic boundary conditions, Journal of Mechanical Science and Technology, vol. 25 (11) 2919-2926, (2011).
[17] R. Siegel, J. Howell, Thermal Radiation heat Transfer, Taylor & Francis: New York, (2002).
[18] C. Mishra, H. Sahai, Analyses of non-Fourier heat conduction in 1-D cylindrical ans spherical geometry- An application of the lattice Boltzmann method, International Journal of Heat and Mass Transfer, 55, 7015-7023, (2012).
[19] Q. Zou, S. Hou, G. D. Doolen, Analytical solutions of the lattice Boltzmann BGK model, Journal of Statistical Physics, vol(81), 319–334, (1995).
 
[20] P. Lallemand, L. S. Luo, heory of the lattice Boltzmann method-acoustic and thermal properties in two and three dimensions, Physical Review, E68, (036706), 1–25, (2003).
[21] T. M. Chen, C. C. Chen, Numerical solution for the hyperbolic heat conduction problems in the radial-spherical coordinate system using a hybrid Green’s function method, International Journal of Thermal Sciences, (2010).
[22] C. C. Wang, Direct and inverse solutions with non-Fourier effect on the irregular shape, International Journal of Heat and Mass Transfer, vol (53), (13-14), 2685–2693, (2010).
[23] C. Mishra, B. Mondal, T. Kush, B. Sima Rama Krishna, Solving transient heat conduction problems on uniform and non-uniform lattices using the lattice Boltzmann method, International Communications in Heat and Mass Transfer, vol(36), 322–328, (2009).

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History

  • Receive Date: 26 October 2016
  • Revise Date: 04 September 2017
  • Accept Date: 04 October 2017

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