Evaluation of the interfacial conduction heat transfer coefficient in two-temperature macroscopic models of homogenous porous media using a fully developed unsteady microscopic model in periodic unit cells

References

• K. Vafai (ed.), Handbook of Porous Media, 3rd ed., CRC Press, Taylor and Francis Group, New York, NY, 2015.
   Google Scholar
• D. B. Miracle and S. L. Donaldson (eds.), ASM Handbook, Composites, Vol. 21, ASM International, Materials Park, OH, 2001.
   Google Scholar
• F. A. Dullien, Porous Media: Fluid Transport and Pore Structure, 2nd ed., Academic Press, San Diego, California, 1992.
   Google Scholar
• J. Bear and A. D. Cheng, Modeling Groundwater Flow and Contaminant Transport, Springer Science & Business Media, New York, NY, 2010.
   Google Scholar
• D. A. Nield and A. Bejan, Convection in Porous Media, 4th ed., Springer Science & Business Media, New York, 2013.
   Google Scholar
• N. Wakao and S. Kaguei, Heat Transfer in Packed Beds, Gordon and Breach Science, New York, pp. 264–295, 1982.
   Google Scholar
• K. Vafai, C. P. Desai, and S. C. Chen, An Investigation of Heat Transfer Process in a Chemically Reacting Packed Bed, Numer. Heat Transfer A Appl., vol. 24, pp. 127–142, 1993.
   Web of Science ®Google Scholar
• V. V. Calmidi and R. L. Mahajan, Forced Convection in High Porosity Metal Foams, ASME J. Heat Transfer, vol. 122, pp. 557–565, 2000.
   Web of Science ®Google Scholar
• K. T. Harris, A. Haji-Sheikh, and A. G. Agwu Nnanna, Phase-Change Phenomena in Porous Media—A Non-Local Thermal Equilibrium Model, Int. J. Heat Mass Transfer, vol. 44, pp. 1619–1625, 2001.
   Web of Science ®Google Scholar
• A. R. A. Khaled and K. Vafai, The Role of Porous Media in Modeling Flow and Heat Transfer in Biological Tissues, Int. J. Heat Mass Transfer, vol. 46, pp. 4989–5003, 2003.
   Web of Science ®Google Scholar
• S. Whitaker, The Method of Volume Averaging, Springer Science & Business Media, Dordrecht, Netherlands, 1999.
   Google Scholar
• S. Whitaker, Improved Constraints for the Principle of Local Thermal Equilibrium, Ind. Eng. Chem. Res., vol. 30, pp. 983–997, 1991.
   Web of Science ®Google Scholar
• W. J. Minkowycz, A. Haji-Sheikh, and K. Vafai, On Departure from Local Thermal Equilibrium in Porous Media due to a Rapidly Changing Heat Source: The Sparrow Number, Int. J. Heat Mass Transfer, vol. 42, pp. 3373–3385, 1999.
   Web of Science ®Google Scholar
• P. Vadasz, Explicit Conditions for Local Thermal Equilibrium in Porous Media Heat Conduction, Transport Porous Media, vol. 59, pp. 341–355, 2005.
   Web of Science ®Google Scholar
• L. Virto, M. Carbonell, R. Castilla, and P. J. Gamez-Montero, Heating of Saturated Porous Media in Practice: Several Causes of Local Thermal Non-Equilibrium, Int. J. Heat Mass Transfer, vol. 52, pp. 5412–5422, 2009.
   Web of Science ®Google Scholar
• D. A. S. Rees and I. Pop Local Thermal Non-equilibrium in Porous Medium Convection, in D. B. Ingham and I. Pop (eds.), Transport Phenomena in Porous Media, vol. III, chap. 6, pp. 147–173, Elsevier, Oxford, 2005.
   Google Scholar
• M. Quintard, M. Kaviany, and S. Whitaker, Two-medium Treatment of Heat Transfer in Porous Media: Numerical Results for Effective Properties, Adv. Water Resour., vol. 20, pp. 77–94, 1997.
   Web of Science ®Google Scholar
• A. Amiri and K. Vafai, Transient Analysis of Incompressible Flow through a Packed Bed, Int. J. Heat Mass Transfer, vol. 41, pp. 4259–4279, 1998.
   Web of Science ®Google Scholar
• A. Haji-Sheikh and W. J. Minkowycz Heat Transfer Analysis under local Thermal Non-equilibrium Conditions, in P. Vadasz (ed.), Emerging Topics in Heat and Mass Transfer in Porous Media, Springer, New York, pp. 39–62, 2008.
   Google Scholar
• F. Kuwahara, M. Shirota, and A. Nakayama, A Numerical Study of Interfacial Convective Heat Transfer Coefficient in Two-energy Equation Model for Convection in Porous Media, Int. J. Heat Mass Transfer, vol. 44, pp. 1153–1159, 2001.
   Web of Science ®Google Scholar
• M. B. Saito and M. J. de Lemos, A Correlation for Interfacial Heat Transfer Coefficient for Turbulent Flow over an Array of Square Rods, ASME J. Heat Transfer, vol. 128, pp. 444–452, 2006.
   Web of Science ®Google Scholar
• K. Vafai, A. Bejan, W. J. Minkowycz, and K. Khanafer A Critical Synthesis of Pertinent Models for Turbulent Transport through Porous Media, in W. J. Minkowycz E. M. Sparrow and J. Y. Murthy (eds.), Handbook of Numerical Heat Transfer, 2nd ed., Wiley, New York, pp. 389–416, 2006.
   Google Scholar
• M. Quintard and S. Whitaker, One- and Two-equation Models for Transient Diffusion Processes in Two-Phase Systems, Adv. Heat Transfer, vol. 23, pp. 369–464, 1993.
   Google Scholar
• D. A. S. Rees, Microscopic Modeling of the Two-Temperature Model for Conduction in Heterogeneous Media, J. Porous Media, vol. 13, pp. 125–143, 2010.
   Web of Science ®Google Scholar
• C. T. Hsu, A Closure Model for Transient Heat Conduction in Porous Media, ASME J. Heat Transfer, vol. 121, pp. 733–739, 1999.
   Web of Science ®Google Scholar
• K. Boomsma, D. Poulikakos, and Y. Ventikos, Simulations of Flow through Open Cell Metal Foams using an Idealized Periodic Cell Structure, Int. J. Heat Mass Transfer, vol. 24, pp. 825–834, 2003.
   Google Scholar
• J. Tian, T. Kim, T. J. Lu, H. P. Hodson, D. T. Queheillalt, D. J. Sypeck, and H. N. G. Wadley, The Effects of Topology upon Fluid-Flow and Heat Transfer within Cellular Copper Structures, Int. J. Heat Mass Transfer, vol. 47, pp. 3171–3186, 2004.
   Web of Science ®Google Scholar
• M. P. Sobera and C. R. Kleijn, Hydraulic Permeability of Ordered, and Disordered Single-layer Arrays of Cylinders, Phys. Rev. E, vol. 74, pp. 036301–1–10, 2006.
   Web of Science ®Google Scholar
• A. Tamayol and M. Bahrami, Transverse Permeability of Fibrous Porous Media, Phys. Rev. E, vol. 83, pp. 046314–1–9, 2011.
   Google Scholar
• J. W. Kaczmar K. Pietrzak, and W. Włosiński, The Production and Application of Metal Matrix Composite Materials, J. Mater. Process. Technol. vol. 106, pp. 58–67, 2000.
   Google Scholar
• M. Cimmino and B. R. Baliga, Examination of Two Approaches for Determining Interfacial Conduction Coefficient in Porous Media, Proc. 4th Int. Conf. Comput. Meth. Thermal Prob. (Therma Comp 2016), Georgia Tech., Atlanta, USA, pp. 1–4, 2016.
   Google Scholar
• S. V. Patankar The Concept of a Fully Developed Regime in Unsteady Heat Conduction, in J. P. Hartnett, T. F. Irvine Jr., E. Pfender, and E. M. Sparrow (eds.), Studies in Heat Transfer—A Festschrift for E.R.G. Eckert, McGraw-Hill, New York, pp. 419–431, 1979.
   Google Scholar
• M. Quintard and S. Whitaker, Local Thermal Equilibrium for Transient Heat Conduction: Theory and Comparison with Numerical Experiments, Int. J. Heat Mass Transfer, vol. 38, pp. 2779–2796, 1995.
   Web of Science ®Google Scholar
• B. R. Baliga and N. Atabaki Control‐volume‐based Finite‐difference and Finite‐element Methods, in W. J. Minkowycz E. M. Sparrow and J. Y. Murthy (eds.), Handbook of Numerical Heat Transfer, 2nd ed., chap. 6, pp. 191–224, John Wiley & Sons, New York, 2006.
   Google Scholar
• P. O. Persson and G. Strang, A Simple Mesh Generator in MATLAB, SIAM Rev., vol. 46, pp. 329–345, 2004.
   Web of Science ®Google Scholar
• S. V. Patankar, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, 1980.
   Google Scholar
• Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd ed., Society for Industrial and Applied Mathematics (SIAM), Philadelphia, USA, 2003.
   Google Scholar
• B. R. Baliga and I. Lokhmanets, Generalized Richardson Extrapolation Procedures for Estimating Grid-independent Numerical Solutions, Int. J. Numer. Meth. Heat Fluid Flow, vol. 26, pp. 1121–1144, 2016.
   Web of Science ®Google Scholar