{"title":"Lattice Monte Carlo Analyses of Thermal Diffusion in Laminar Flow","authors":"Thomas Fiedler, Irina V. Belova, Graeme E. Murch","volume":39,"journal":"International Journal of Physical and Mathematical Sciences","pagesStart":356,"pagesEnd":361,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/11969","abstract":"Lattice Monte Carlo methods are an excellent\r\nchoice for the simulation of non-linear thermal diffusion\r\nproblems. In this paper, and for the first time, Lattice Monte\r\nCarlo analysis is performed on thermal diffusion combined\r\nwith convective heat transfer. Laminar flow of water modeled\r\nas an incompressible fluid inside a copper pipe with a constant\r\nsurface temperature is considered. For the simulation of\r\nthermal conduction, the temperature dependence of the\r\nthermal conductivity of the water is accounted for. Using the\r\nnovel Lattice Monte Carlo approach, temperature distributions\r\nand energy fluxes are obtained.","references":"[1] G. E. Murch, \"Simulation of Diffusion Kinetics with the Monte Carlo\r\nMethod\" in Diffusion in Crystalline Solids, G. E. Murch, A.S. Nowick,\r\nEds, Orlando: Academic Press, 1984, pp. 379 - 427.\r\n[2] Y. Mishin, I. V. Belova, and G. E. Murch, \"Atomistic Modelling of\r\nDiffusion in the TiAl Compound\" Defect Diffus. Forum, vol. 237-240,\r\npp. 271 - 276, 2005.\r\n[3] I. V. Belova and G. E. Murch, \"Bridging Different Length and Time\r\nScales in Diffusion Problems Using a Lattice Monte Carlo Methods\"\r\nSol. St. Phen., vol. 129, pp. 1 - 10, 2007.\r\n[4] I. V. Belova, G. E. Murch, N. Muthubandara, and A. \u251c\u00fbchsner, \"Analysis\r\nof Oxygen Segregation at Metal-Oxide Interfaces Using a New Lattice\r\nMonte Carlo Method\" Sol. St. Phen., vol. 129, pp. 111 - 118, 2007.\r\n[5] I. V. Belova, G. E. Murch, T. Fiedler, and A. \u251c\u00fbchsner, \"Lattice-based\r\nwalks and the Monte Carlo method for addressing mass, thermal and\r\nelasticity problems\" Defect Diffus. Forum, vol. 283-286, pp. 13 - 23,\r\n2009.\r\n[6] I. V. Belova, G. E. Murch, T. Fiedler, and A. \u251c\u00fbchsner, Diffusion\r\nFundamentals, vol. 4, pp. 15.1-15.23, 2007. On-line.\r\n[7] T. Fiedler, A. \u251c\u00fbchsner, N. Muthubandara, I. V. Belova, G. E. Murch,\r\n\"Calculation of the Effective Thermal Conductivity in Composites Using\r\nFinite Element and Monte Carlo Methods\" Mater. Sci. Forum, vol. 553,\r\npp. 51 - 56, 2007.\r\n[8] T. Fiedler, A. \u251c\u00fbchsner, I. V. Belova, and G. E. Murch, \"Calculations of\r\nthe effective thermal conductivity in a model of syntactic metallic\r\nhollow sphere structures using a Lattice Monte Carlo method\" Defect\r\nDiffus. Forum, vol. 273-276, pp. 216 - 221, 2008.\r\n[9] I. V. Belova and G. E. Murch, \"Thermal Properties of Composite\r\nmaterials and Porous Media: Lattice-Based Monte Carlo Approaches\"\r\nin Cellular and Porous Materials. Thermal Properties, Simulation and\r\nPrediction, A. \u251c\u00fbchsner, G. E. Murch, J. S. de Lemos, Eds Weinheim:\r\nWiley VCH, 2008, pp. 73 - 95.\r\n[10] T. Fiedler, I. V. Belova, A. \u251c\u00fbchsner, and G. E. Murch, \"Non-linear\r\ncalculations of transient thermal conduction in composite materials\"\r\nComp. Mater. Sci., vol. 45, pp. 434 - 438, 2009.\r\n[11] T. Fiedler, I. V. Belova, G. E. Murch, \"A Lattice Monte Carlo analysis\r\non coupled reaction and mass diffusion\" Comp. Mater. Sci., accepted for\r\npublication.\r\n[12] C. O. Bennett and J. E. Myers, Momentum, Heat, and Mass Transfer,\r\nNew York: McGraw-Hill Book Company, 1982.\r\n[13] C. Y. Ho, R. W. Powell, and P. E. Liley, \"Thermal Conductivity of the\r\nElements\" J. Phys. Chem. Ref. Data, vol. 1, pp. 279-442, 1972.\r\n[14] G. K. White and S.J. Collocott, \"Heat Capacity of Reference Materials\"\r\nJ. Phys. Chem. Ref. Data, vol. 13, no 4, pp. 1251-1257, 1984.\r\n[15] F. L. Levy, \"The thermal conductivity of commercial brines and\r\nseawater in the freezing range\", Int. J. Refrig., vol. 5, pp. 155-159, 1982.\r\n[16] D. R. Lide, CRC Handbook of Chemistry and Physics. Boca Raton:\r\nCRC Press, 1998.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 39, 2010"}