Numerical Simulation of Melting Problems Using the Lattice Boltzmann Method with the Interfacial Tracking Method

REFERENCES

• N. Hannoun, V. Alexiades, and T. Mai Resolving the Controversy Over Tin and Gallium Melting in a Rectangular Cavity Heated from the Side, Numer. Heat Transfer, Part B: Fundam., vol. 44, no. 3, pp. 253–275, 2003.
   Web of Science ®Google Scholar
• H. Hu and S. Argyopoilos Mathematical Modelling of Solidification and Melting: A Review, Modell. Simul. Mater. Sci. Eng., vol. 4, no. 4, pp. 371–396, 1996.
   Web of Science ®Google Scholar
• T. Goodman and J. Shea The Melting of Finite Slabs, J. Appl. Mech., vol. 27, no. 1, pp. 16–27, 1960.
   Google Scholar
• G. E. Bell A refinement of the Heat Balance Integral Method Applied to a Melting Problem, Int. J. Heat Mass Transfer, vol. 21, no. 11, pp. 1357–1362, 1978.
   Web of Science ®Google Scholar
• M. Okada Analysis of Heat Transfer During Melting from a Vertical wall, Inter. J. Heat Mass Transfer, vol. 27, no. 11, pp. 2057–2066, 1984.
   Web of Science ®Google Scholar
• Z. Zhang and A. Bejan Melting in an Enclosure Heated at Constant Rate, Int. J. Heat Mass Transfer, vol. 32, no. 6, pp. 1063–1076, 1989.
   Web of Science ®Google Scholar
• Y. Zhang, Z. Chen, Q. Wang, and Q. Wu Melting in an Enclosure with Discrete Heating at a Constant Rate, Exp. Therm Fluid Sci., vol. 6, no. 2, pp. 196–201, 1993.
   Web of Science ®Google Scholar
• O. Bertrand, B. Binet, H. Combeau, S. Couturier, Y. Delannoy, D. Gobin, M. Lacroix, P. Quere, M. Medale, J. Mencinger, H. Sadat, and G. Vieira Melting Driven by Natural Convection a Comparison Exercise: First Results, Int. J. Therm. Sci., vol. 38, no. 1, pp. 5–26, 1999.
   Web of Science ®Google Scholar
• A. Faghri and Y. Zhang Transport Phenomena in Multiphase System, Elsevier, Burlington, MA, 2006.
   Google Scholar
• N. Shamsundar and E. Sparrow Analysis of Multidimensional Conduction Phase Change via The Enthalpy Model, J. Heat Transfer, vol. 97, pp. 333–340, 1975.
   Web of Science ®Google Scholar
• V. Voller and C. Prakash A Fixed Grid Numerical Modeling Methodology for Convection-Diffusion Mushy Region Phase-Change Problems, Int. J. Heat Mass Transfer, vol. 30, pp. 1709–1719, 1987.
   Web of Science ®Google Scholar
• K. Morgan A Numerical Analysis of Freezing and Melting with Convection, Comput. Methods Appl. Mech. Eng., vol. 28, pp. 275–284, 1981.
   Web of Science ®Google Scholar
• J. Hsiao Analyses of Heat Transfer with Melting and Solidification, Numer. Heat Transfer, vol. 8, pp. 653–666, 1985.
   Web of Science ®Google Scholar
• Y. Zhang and J. Chen An Interfacial Tracking Method for Ultrashort Pulse Laser Melting and Resolidification of a Thin Metal Film, J. Heat Transfer, vol. 130, pp. 0624011–06240110, 2008.
   Google Scholar
• Q. Chen, Y. Zhang, and M. Yang An Interfacial Tracking Model for Convection-Controlled Melting Problem, Numer. Heat Transfer, Part B: Fundam., vol. 59, no. 3, pp. 209–225, 2011.
   Web of Science ®Google Scholar
• Z. Li, M. Yang, Q. Chen, and Y. Zhang Numerical Solution of Melting in a Discretely Heated Enclosure using an Interfacial Tracking Method, Numer. Heat Transfer, Part A: Appl., vol. 64, no. 11, pp. 841–857, 2013.
   Web of Science ®Google Scholar
• W. Tao Numerical Heat Transfer, Xi'an Jiaotong University Press, Xi'an, 2001.
   Google Scholar
• G. Kefayati Simulation of Ferrofluid Heat Dissipation Effect on Natural Convection at an Inclined Cavity Filled with Kerosene/Cobalt Utilizing the Lattice Boltzmann Method, Numer. Heat Transfer, Part A: Appl., vol. 65, no. 6, pp. 509–530, 2014.
   Web of Science ®Google Scholar
• S. Chen and G. Doolen Lattice Boltzmann Method for Fluid Flows, Annu. Rev. Fluid Mech., vol. 30, pp. 329–364, 1998.
   Web of Science ®Google Scholar
• T. Zhang and D. Che Lattice Boltzmann Simulation of Natural Convection in an Inclined Square Cavity with Spatial Temperature Variation, Numer. Heat Transfer, Part A: Appl., vol. 66, no. 6, pp. 712–732, 2014.
   Web of Science ®Google Scholar
• V. Novozhilov and C. Byrne Lattice Boltzmann Modeling of Thermal Explosion in Natural Convection Conditions, Numer. Heat Transfer, Part A: Appl., vol. 63, no. 11, pp. 824–839, 2013.
   Web of Science ®Google Scholar
• S. Choi, S. Kim, T. Lee, Y. Kim, and D. Hahn Computation of Turbulent Natural Convection in a Rectangular Cavity with the Lattice Boltzmann Method, Numer. Heat Transfer, Part B: Fundam., vol. 61, no. 6, pp. 492–504, 2012.
   Web of Science ®Google Scholar
• Z. Li, M. Yang, and Y. Zhang Hybrid lattice Boltzmann and Finite Volume Methods for Fluid Flow Problems, Int. J. Multiscale Comput. Eng., vol. 28, no. 2, pp. 279–286, 2014.
   Google Scholar
• Z. Li, M. Yang, and Y. Zhang A Coupled Lattice Boltzmann and Finite Volume Method for Natural Convection Simulation, Int. J. Heat Mass Transfer, vol. 70, pp. 864–874, 2014.
   Web of Science ®Google Scholar
• Z. Li, M. Yang, and Y. Zhang Hybrid lattice Boltzmann and Finite Volume Method for Natural Convection, J. Thermophys. Heat Transfer, vol. 28, no. 1, pp. 68–77, 2014.
   Web of Science ®Google Scholar
• Y. Peng, C. Shu, and Y. Chew Simplified Thermal Lattice Boltzmann Model for Incompressible Thermal Flows, Phys. Rev. E, vol. 68, no. 026701, 2003.
   Google Scholar
• Z. Guo, B. Shi, and C. Zheng A Coupled Lattice BGK Model for the Boussinesq Equations, Int. J. Numer. Methods Fluids, vol. 39, no. 4, pp. 325–342, 2002.
   Web of Science ®Google Scholar
• E. Semma, M. Gananoui, R. Bennacer, and A. Mohamad Investigation of Flows in Solidification by Using the Lattice Boltzmann Method, Int. J. Therm. Sci., vol. 47, pp. 201–208, 2008.
   Web of Science ®Google Scholar
• M. Jourabian, M. Faehadi, K. Sedighi, A. Darzi, and Y. Vazifeshenas Melting of NEPCM within a Cylindrical Tube: Numerical Study Using the Lattice Boltzmann Method, Numer. Heat Transfer, Part A: Appl., vol. 61, no. 12, pp. 929–948, 2012.
   Web of Science ®Google Scholar
• L. Chen, Y. He, Q. Kang, and W. Tao Coupled Numerical Approach Combining Finite Volume and Lattice Boltzmann Methods for Multi-Scale Multi-Physicochemical, J. Comput. Phys., vol. 255, no. 15, pp. 83–105, 2013.
   Web of Science ®Google Scholar
• W. Miller, S. Succi, and D. Mansutti Lattice Boltzmann Model for Anisotropic Liquid-Solid Phase Transition, Phys. Rev. Lett., vol. 86, pp. 3578–3581, 2001.
   PubMed Web of Science ®Google Scholar
• M. Eshraghi and S. Felicelli An Implicit Lattice Boltzmann Model for Heat Conduction with Phase Change, Int. J. Heat Mass Transfer, vol. 55, pp. 2420–2428, 2012.
   Web of Science ®Google Scholar
• S. Chakraborty and D. Chatterjee An Enthalpy-Based Hybrid Lattice-Boltzmann Method for Modelling Solid-Liquid Phase Transition in the Presence of Convective Transport, J. Fluid Mech., vol. 592, pp. 155–176, 2007.
   Web of Science ®Google Scholar
• C. Huber, A. Parmigiani, B. Chopard, M. Manga, and O. Bachmann Lattice Boltzmann Model for Melting with Natural Convection, Int. J. Heat Fluid Flow, vol. 29, pp. 1469–1480, 2008.
   Web of Science ®Google Scholar
• D. Gao and Z. Chen Lattice Boltzmann Simulation of Natural Convection Dominated Melting in a Rectangular Cavity Filled with Porous Media, Int. J. Therm. Sci., vol. 50, no. 4, pp. 493–501, 2011.
   Web of Science ®Google Scholar
• Z. Li, M. Yang, and Y. Zhang A Hybrid Lattice Boltzmann and Finite Volume Method for Melting with Natural Convection, Numer. Heat Transfer, Part A: Appl., vol. 66, no. 4, pp. 307–325, 2014.
   Web of Science ®Google Scholar
• M. Ozisik Heat Conduction, 2nd ed., (pp. 398–400), Wiley-Interscience, New York, 1993.
   Google Scholar
• A. Faghri and Y. Zhang Transport Phenomena in Multiphase System, (pp. 426–427), Elsevier, Burlington, MA, 2006.
   Google Scholar
• N. Hannoun, V. Alexiades, and T. Mai A Reference Solution for Phase Change with Convection, Int. J. Numer. Methods Fluids, vol. 48, no. 11, pp. 1283–1308, 2005.
   Web of Science ®Google Scholar
• G. Kosec and B. Sarler Solution of a Low Prandtl Number Natural Convection Benchmark by a Local Meshless Method, Int. J. Numer. Methods Heat Fluid Flow, vol. 23, no. 1, pp. 189–204, 2013.
   Web of Science ®Google Scholar