Solving Complex Thermal and Mass Transport Problems with the Lattice Monte Carlo Method

Abstract:

The Lattice Monte Carlo (LMC) method recently developed by the authors is an unusually powerful and flexible method in which a given phenomenological thermal or mass transport problem is mapped onto a fine-grained lattice which is then analyzed with discrete random walk methods. We provide an overview of the LMC method. For mass diffusion we highlight the addressing of diffusion with reversible reaction. For thermal transport we highlight a calculation of the effective thermal conductivity of sintered hollow sphere structures making use of CT scans of actual material as well as the determination of temperature profiles in phase-change composites.

• Periodical: Materials Science Forum (Volumes 654-656)
• Pages: 1476-1481
• DOI: https://doi.org/10.4028/www.scientific.net/MSF.654-656.1476
• Online since: June 2010
• Authors: Thomas Fiedler, Graeme E. Murch, Irina V. Belova
• Keywords: Effective Properties, Mass Diffusion, Numerical Method, Thermal Conduction

References

[1] G.E. Murch, in Diffusion in Crystalline Solids, edited by G.E. Murch and A.S. Nowick, Chapter 7, Academic Press, Orlando, FL (1984).

[2] Y. Mishin, I.V. Belova and G.E. Murch: Def. Diff. Forum Vols. 237-240 (2005), p.271.

[3] A. Haji-Sheikh and E.M. Sparrow: J. Heat Transfer, (Trans ASME) Vol. 89 (1967), p.121.

[4] T. Fiedler, A. Öchsner, N. Muthubandara, I.V. Belova, G.E. Murch: Mater. Sci. Forum Vol. 553 (2007), p.51.

[5] I.V. Belova, G.E. Murch, in Cellular and Porous Materials. Thermal Properties, Simulation and Prediction, ed. A. Öchsner, G.E. Murch, J.S. de Lemos, Ch. 3, Wiley-VCH, Weinheim (2008).

DOI: 10.1002/9783527621408

[6] I.V. Belova, G.E. Murch, T. Fiedler and A. Öchsner: Diffus. Fundamentals Vol. 4 (2007), p.15. 1.

[7] L.G. Harrison: Trans. Farad. Soc. Vol. 57 (1961), p.1191.

[8] E.W. Hart: Acta Metall. Vol. 5 (1957), p.597.

[9] I. Kaur, Y. Mishin and W. Gust: Fundamentals of Grain and Interphase Boundary Diffusion, Wiley, Chichester (1995).

[10] I.V. Belova and G.E. Murch: Phil. Mag. A Vol. 81 (2001), p.2447.

[11] P. Murray and G.F. Carey: J. Comp. Phys. Vol. 74 (1988), p.440.

[12] Z. Koza: Physica A Vol. 300 (2003), p.160.

[13] J. Crank: The Mathematics of Diffusion, 2nd Edition, Oxford, Oxford University Press, (1979).

[14] T. Fiedler, A. Öchsner, I.V. Belova, G.E. Murch: Def. Diff. Forum Vol. 273/276 (2008), p.222.

[15] T. Fiedler, A. Öchsner, I.V. Belova, G.E. Murch: Def. Diff. Forum Vol. 273/276 (2008), p.216.

[16] T. Fiedler, R. Löffler, T. Bernthaler, R. Winkler, I.V. Belova, G.E. Murch and A. Öchsner: Mater. Lett. Vol. 63 (2009), p.1125.

DOI: 10.1016/j.matlet.2008.10.030

[17] T. Fiedler, E. Solórzano, F. Garcia-Moreno, A. Öchsner, I.V. Belova and G.E. Murch: Adv. Eng. Mater. Vol. 11 (2009), p.843.

DOI: 10.1002/adem.200900132

[18] T. Fiedler, A. Öchsner, I.V. Belova and G.E. Murch: Adv. Eng. Mater. Vol. 10 (2008), p.361.

[19] E. B. S. Mettawee and G. M. R. Assassa: Solar Energy Vol. 81 (2007), p.839.

[20] M. Kenisarin and K. Mahkamov: Renew. Sustain. Energy Rev. Vol. 11 (2007), p. (1913).