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Convection with Change of Phase

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Convection in Porous Media

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Abstract

In the examples of forced and natural convection discussed until now, the fluid that flowed through the pores did not experience a change of phase, no matter how intense the heating or cooling effect. In this chapter, we turn our attention to situations in which a change of phase occurs, for example, melting or evaporation upon heating and solidification or condensation upon cooling. These convection problems constitute a relatively new and active area in the field of convection in porous media.

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References

  • Adnani, S. G. and Hsiao, K. T. 2005 Transport phenomena in liquid composites molding processes and their roles in process control and optimization. Handbook of Porous Media (ed. K. Vafai), 2nd ed., Taylor and Francis, New York, pp. 573-606. [10.2.3]

    Google Scholar 

  • Agwu Nnanna, A. G., Haji-Sheikh, A. and Harris, K. T. 2004 Experimental study of local thermal non-equilibrium phenomena during phase change in porous media. Int. J. Heat Mass Transfer 43, 4365-4375. [10.1.7]

    Article  MATH  Google Scholar 

  • Ahmad, S. and Pop, I. 2014 Melting effect on mixed convection boundary layer flow about a vertical surface embedded in a porous medium: Opposing flows case. Transp. Porous Media 102, 317-323. [10.1.7]

    Article  Google Scholar 

  • Alexandrov, D. V. and Ivanov, A. O. 2000 Dynamic stability analysis of the solidification of binary melts in the presence of a mushy region: changeover of instability. J. Crystal Growth 210, 797-810. [10.2.3]

    Article  Google Scholar 

  • Alexandrov, D. V., Alexandrova, I. V., Ivanov, A. A., Malygin, A. P. and Nizovtseva, I. G. 2014 Nonlinear analysis of the stability of solidification with a mushy zone. Russian Metallurgy (8), 606-617. [10.2.3]

    Google Scholar 

  • Al-Nimr, M. A. and Alkam, M. K. 1997a Film condensation on a vertical plate embedded in a porous medium. J. Appl. Energy 56, 47-57. [10.4]

    Article  Google Scholar 

  • Amberg, G. and Homsy, G. M. 1993 Nonlinear analysis of buoyant convection in binary solidification with application to channel formation. J. Fluid Mech. 252, 79-98. [10.2.3]

    Article  MATH  Google Scholar 

  • Anderson, D. M. 2003 A model for diffusion-controlled solidification of ternary alloys in mushy layers. J. Fluid Mech. 483, 165-197. [10.2.3]

    Article  MathSciNet  MATH  Google Scholar 

  • Anderson, D. M. and Worster, M. G. 1995 Weakly nonlinear analysis of convection in mushy layers during solidification of binary alloys. J. Fluid Mech. 302, 307-331. [10.2.3]

    Article  MathSciNet  MATH  Google Scholar 

  • Anderson, D. M. and Worster, M. G. 1996 A new oscillatory instability in a mushy layer during the solidification of binary alloys. J. Fluid Mech. 307, 245-267. [10.2.3]

    Article  MATH  Google Scholar 

  • Anderson, D. M., McFadden, G. B., Coriell, S. R. and Murray, B. T. 2010 Convective instabilities during solidification of an ideal ternary alloy in a mushy layer. J. Fluid Mech. 647, 309-333. [10.2.2]

    Article  MathSciNet  MATH  Google Scholar 

  • Anderson, D. M., Schulze, T. P. 2005 Linear and nonlinear convection in solidifying ternary alloys. J. Fluid Mech. 545, 213-243. [10.2.3]

    Article  MathSciNet  MATH  Google Scholar 

  • Asbik, M., Chaynane, R., Boushaba, H., Zeghmati, B. and Khmou, A. 2003 Analytic investigation of forced convection film condensation on a vertical porous-layer coated surface. Heat Mass Transfer 40, 143-155. [10.4]

    Article  Google Scholar 

  • Asbik, M., Zeqhmati, B., Louahlia-Gualos, H. and Yan, W. M. 2007 The effect of thermal dispersion on free convection film condensation on a vertical plate with a thin porous layer. Transp. Porous Media 67, 335-352. [10.4]

    Article  Google Scholar 

  • Aussillous, P., Sederman, A. J., Gladden, L. F., Huppert, H. E. and Worster, M. G. 2006 Magnetic resonance imaging of structure and convection in solidifying mushy layers. J. Fluid Mech. 552, 99-125. [10.2.3]

    Article  MATH  Google Scholar 

  • Bakier, A. Y. 1997 Aiding and opposing mixed convection flow in melting from a vertical flat plate embedded in a porous medium. Transport in Porous Media 29, 127-139. [10.1.7]

    Article  Google Scholar 

  • Bars, M. L. and Worster, M. G. 2006 Interfacial conditions between a pure fluid and a porous medium: Implications for binary alloy solidification. J. Fluid Mech. 550, 149-173. [1.6]

    Article  MathSciNet  MATH  Google Scholar 

  • Bau, H. H. and Torrance, K. E. 1982a Boiling in low permeability porous materials. Int. J. Heat Mass Transfer 25, 45-55. [11.9.2]

    Article  Google Scholar 

  • Bau, H. H. and Torrance, K. E. 1982c Thermal convection and boiling in a porous medium. Lett. Heat Mass Transfer 9, 431-333. [10.3.1]

    Article  Google Scholar 

  • Bautista, O., Mendez, F. and Lizardi, J. 2008 Conjugate heat transfer analysis of the film condensation on a vertical fin immersed in a porous medium. J. Porous Media 11, 145-157. [10.4]

    Article  Google Scholar 

  • Beck, J. L. 1972 Convection in a box of porous material saturated with fluid. Phys. Fluids 15, 1377-1383. [1.5.1, 6.15.1]

    Article  Google Scholar 

  • Beckermann, C. and Viskanta, R. 1988a Natural convection solid/liquid phase change in porous media. Int. J. Heat Mass Transfer 31, 35-46. [10.1.6]

    Article  Google Scholar 

  • Beckermann, C. and Viskanta, R. 1988b Double-diffusive convection during dendritic solidification of a binary mixture. PhysicoChemical Hydrodyn. 10, 195-213. [10.2.2, 10.2.3]

    Google Scholar 

  • Beckermann, C. and Viskanta, R. 1993 Mathematical modeling of transport phenomena during alloy solidification. Appl. Mech. Rev. 46, 1-27. [10.2.3]

    Article  MathSciNet  Google Scholar 

  • Beckermann, C. and Wang, C. Y. 1995 Multiphase/- scale modeling of alloy solidification. Ann. Rev. Heat Transfer 6, 115-198. [10.2.3]

    Article  Google Scholar 

  • Bejan, A. 1984 Convection Heat Transfer, Wiley, New York. [1.1, 4.1, 4.2, 4.5, 4.17, 5.1.4, 5.11.1, 6.9.2, 7.1.1, 7.1.2, 7.3.3, 7.4.2, 9.2.1, 10.1.2]

    MATH  Google Scholar 

  • Bejan, A. 1989 Theory of melting with natural convection in an enclosed porous medium. ASME J. Heat Transfer 111, 407-415. [10.1.3, 10.1.5]

    Article  Google Scholar 

  • Bejan, A., Dincer, I., Lorente, S., Miguel, A. F. and Reis, A. H. 2004 Porous and Complex Flow Structures in Modern Technologies. Springer, New York. [1.5.2, 2.1, 3.3, 3.7, 4.18, 4.19, 6.26, 10.1.7]

    Book  Google Scholar 

  • Bejan, A., Zhang, Z. and Jany, P. 1990 The horizontal intrusion layer of melt in a saturated porous medium. Int. J. Heat Fluid Flow 11, 284-289. [10.1.4]

    Article  Google Scholar 

  • Bennon, W. D. and Incropera, F. P. 1987 A continuum model for momentum, heat and species transport in binary-phase change systems. I. Model formulation. Int. J. Heat Transfer 40, 2161-2170. [10.2.3]

    Article  MATH  Google Scholar 

  • Bergman, M. I., Fearn, D. R., Bloxam, J. and Shannon, M. C. 1997 Convection and channel formation in solidifying Pb-Sn alloys. Metall. Mat. Trans. A 28, 859-866. [10.2.3]

    Google Scholar 

  • Bhatta, D., Muddamallappa, M. S. and Riahi, D. N. 2010 On perturbation and marginal stability analysis of magneto-convection in active mushy layer. Transp. Porous media 82, 385-399. [10.2.3]

    Article  MathSciNet  Google Scholar 

  • Bhatta, D., Riahi, D. N. and Muddamallappa, M. S. 2012 On nonlinear evolution of convective flow in an active mushy layer. J. Engng. Math. 74, 73-89. [10.2.3]

    Article  MathSciNet  MATH  Google Scholar 

  • Bian, W. and Wang, B. X. 1993 Transient freezing and natural convection around a cylinder in saturated porous media. Proc. 6th Int. Sympos. Transport Phenomena in Thermal Engineering, Seoul, Korea, pp. 79-84. [10.2.1.2]

    Google Scholar 

  • Bin-Mansoor, S., Yilbas, B. S. and Al-Haddad, M. 2005 Entropy generation in the porous layer and the condensate film. J. Enhanced Heat Transfer 12, 289-299. [10.4]

    Article  Google Scholar 

  • Butler, S. L., Huppert, H. E. and Worster, M. G. 2006 Numerical modeling of convection in a reactive porous medium with a mobile mush-liquid interface. J. Fluid Mech. 549, 99-129. [10.2.3]

    Article  MathSciNet  Google Scholar 

  • Cao, W. Z. and Poulikakos, D. 1991a Solidification of a binary mixture saturating a bed of glass spheres. Convective Heat and Mass Transfer in Porous Media (eds. S. Kakaç, et al.), Kluwer Academic, Dordrecht, 725-772. [10.2.2]

    Chapter  Google Scholar 

  • Cao, W. Z. and Poulikakos, D. 1991b Freezing of a binary alloy saturating a packed bed of spheres. AIAA J. Thermophys. Heat Transfer 5, 46-53. [10.2.3]

    Article  Google Scholar 

  • Chamkha, A. J., Ahmed, S. E. and Aloraier, A. S. 2010a Melting and radiation effects on mixed convection from a vertical surface embedded in a non-Newtonian fluid saturated in a non-Darcy porous medium for aiding and opposing external flows. Int. J. Phys. Sci. 5, 1212-1224. [10.1.7]

    Google Scholar 

  • Chang, W. J. and Yang, D. F. 1996 Natural convection for the melting of ice in porous media in a rectangular enclosure. Int. J. Heat Mass Transfer 39, 2333-2348. [10.1.7]

    Article  MATH  Google Scholar 

  • Char, M. I, Lin, J. D. and Chen, H. T. 2001 Conjugate mixed convection laminar non-Darcy film condensation along a vertical plate in a porous medium. Int. J. Engng. Sci. 39, 897-912. [10.4]

    Article  MATH  Google Scholar 

  • Char, M. I. and Lin, J. D. 2001 Conjugate film condensation and natural convection between two porous media separated by a vertical plate. Acta Mech. 148, 1-15. [10.4]

    Article  MATH  Google Scholar 

  • Chellaiah, S. and Viskanta, R. 1987 Freezing of water and water-salt solutions around aluminum spheres. Int. Comm. Heat Mass Transfer 14, 437-446. [10.2.1.2]

    Google Scholar 

  • Chellaiah, S. and Viskanta, R. 1989a On the supercooling during freezing of water saturated porous media. Int. Comm. Heat Mass Transfer 16, 163-172. [10.2.1.2]

    Article  Google Scholar 

  • Chellaiah, S. and Viskanta, R. 1989b Freezing of water-saturated porous media in the presence of natural convection: experiments and analysis. ASME J. Heat Transfer 111, 424-432; errata 648. [10.2.1.2]

    Google Scholar 

  • Chellaiah, S. and Viskanta, R. 1990a Natural convection melting of a frozen porous medium. Int. J. Heat Mass Transfer 33, 887-899. [10.2.1.2]

    Article  Google Scholar 

  • Chellaiah, S. and Viskanta, R. 1990b Melting of ice-aluminum ball systems. Expt. Therm. Fluid Sci. 3, 222-231. [10.1.7]

    Article  Google Scholar 

  • Chen, C. F. 1995 Experimental study of convection in a mushy layer during directional solidification. J. Fluid Mech. 293, 81-98. [10.2.3]

    Article  Google Scholar 

  • Chen, F., Lu, J. W. and Yang, T. L. 1994 Convective instability in ammonium chloride solution directionally solidified from below. J. Fluid Mech. 276, 163-187. [10.2.3]

    Article  Google Scholar 

  • Cheng, P. 1981b Film condensation along an inclined surface in a porous medium. Int. J. Heat Mass Transfer 24, 983-990. [10.4]

    Article  MATH  Google Scholar 

  • Cheng, P. and Chui, D. K. 1984 Transient film condensation on a vertical surface in a porous medium. Int. J. Heat Mass Transfer 27, 795-798. [10.4]

    Article  Google Scholar 

  • Cheng, P. and Minkowycz, W. J. 1977 Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike. J. Geophys. Res. 82, 2040-2044. [5.1.1, 10.1.5]

    Article  Google Scholar 

  • Cheng, P. and Verma, A. K. 1981 The effect of subcooled liquid on film boiling about a vertical heated surface in a porous medium. Int. J. Heat Mass Transfer 24, 1151-1160. [10.3.2]

    Article  MATH  Google Scholar 

  • Cheng, P., Betsehorn, M. and Firoozabadi, A. 2012b Effect of permeability anisotropy on buoyancy-driven flow for CO2 sequestration in saline aquifers. Water Resources Res. 48, W0539. [11.11]

    Google Scholar 

  • Cheng, P., Chui, D. K. and Kwok, L. P. 1982 Film boiling about two-dimensional and axisymmetric isothermal bodies of arbitrary shape in a porous medium. Int. J. Heat Mass Transfer 25, 1247-1249. [10.3.2]

    Article  MATH  Google Scholar 

  • Cheng, W. T. and Lin, C. H. 2006 Transient mixed convective heat transfer with melting effect from the vertical plate in a liquid saturated porous medium. Int. J. Engng. Sci. 44, 1023-1036. [10.1.7]

    Article  MATH  Google Scholar 

  • Cheng, W. T. and Lin, C. H. 2007 Melting effect on mixed convective heat transfer with aiding and opposed external flows from a vertical plate in a liquid saturated porous medium. Int. J. Heat Mass Transfer 50, 3026-3034. [10.1.7]

    Article  MATH  Google Scholar 

  • Cheng, W. T. and Lin, C. H. 2009 Unsteady mass transfer in mixed convective flow from a vertical plate embedded in a liquid-saturated porous medium with melting effect. Int. Comm. Heat Mass Transfer 35, 1350-1354. [10.1.7]

    Article  Google Scholar 

  • Cheng, W. T. and Lin, C. H. 2012 Numerical analysis of mass transfer on the melting phenomenon from a vertical plate in a liquid-saturated porous medium. J. Porous Media 15, 485-493. [10.1.7]

    Article  Google Scholar 

  • Chiang, K. C. and Tsai, H. L. 1992 Interaction between shrinkage-induced fluid flow and natural convection during alloy solidification. Int. J. Heat Mass Transfer, 35, 1771-1778. [10.2.3]

    Article  Google Scholar 

  • Chiareli, A. O. P. and Worster, M. G. 1995 Flow focusing instability in a solidifying mushy layer. J. Fluid Mech. 297, 293-305. [10.2.3]

    Article  MATH  Google Scholar 

  • Choi, J. and Viskanta, R. 1992 Freezing of aqueous sodium chloride solution saturated packed bed from above. ASME HTD 206, Vol. 2, 159-166. [10.2.3]

    Google Scholar 

  • Choi, J. and Viskanta, R. 1993 Freezing of aqueous sodium chloride solution saturated packed bed from a vertical wall of a rectangular cavity. Int. J. Heat Mass Transfer 36, 2805-2813. [10.2.3]

    Article  Google Scholar 

  • Christopher, D. M. and Wang, B. X. 1994 Natural convection melting around a horizontal cylinder buried in frozen water-saturated porous media. Heat Transfer 1994, Inst. Chem. Engrs, Rugby, Vol. 4, 19-24. [10.1.7]

    Google Scholar 

  • Chung, C. A. and Chen, F. 2000 Convection in directionally solidifying alloys under inclined rotation. J. Fluid Mech. 412, 93-123. [10.2.3]

    Article  MATH  Google Scholar 

  • Chung, C. A. and Chen, F. 2000b Convection in directionally solidifying alloys under inclined rotation. J. Fluid Mech. 412, 93-123. [10.2.3]

    Article  MATH  Google Scholar 

  • Chung, C. A. and Chen, F. 2000 Onset of plume convection in mushy layers. J. Fluid Mech. 408, 53-82. [10.2.3]

    Article  MATH  Google Scholar 

  • Chung, C. A. and Chen, F. 2001 Morphological instability in a directionally solidifying binary solution with an imposed shear flow. J. Fluid Mech. 436, 85-106. [10.2.3]

    Article  MATH  Google Scholar 

  • Chung, C. A. and Worster, M. G. 2002 Steady-state chimneys in a mushy layer. J. Fluid Mech. 455, 387-411. [10.2.3]

    Article  MATH  Google Scholar 

  • Chung, J. N., Plumb, O. A. and Lee, W. C. 1992 Condensation in a porous region bounded by a cold vertical surface. ASME J. Heat Transfer, 114, 1011-1018. [10.4]

    Article  Google Scholar 

  • Close, D. J. 1983 Natural convection with coupled mass transfer in porous media. Int. Comm. Heat Mass Transfer 10, 465-476. [10.4]

    Article  Google Scholar 

  • Damronglerd, P. and Zhang Y. W. 2006 Transient fluid flow and heat transfer in a porous structure with partial heating and evaporation on the upper surface. J. Enhanced Heat Transfer 13, 53-63. [10.3.1]

    Article  Google Scholar 

  • Damronglerd, P. and Zhang, Y. 2010 Numerical simulation of melting in porous media via modified temperature-transforming model. J. Thermophys. Heat Transfer 24, 340-347. [10.1.7]

    Article  Google Scholar 

  • Dhir, V. K. 1994 Boiling and two-phase flow in porous media. Ann. Rev. Heat Transfer 5, 303-350. [10.3.1]

    Article  Google Scholar 

  • Dhir, V. K. 1997 Heat transfer from heat-generating pools and particulate beds. Adv. Heat Transfer 29, 1-57. [10.3.1]

    Article  Google Scholar 

  • Easterday, O. T., Wang, C. Y. and Cheng, P. 1995 A numerical and experimental study of two-phase flow and heat transfer in a porous formation with localized heating from below. ASME HTD- 321, 723-732. [10.3.2]

    Google Scholar 

  • Ebinuma, C. D. and Nakayama, A. 1990a Non-Darcy transient and steady film condensation in a porous medium. Int. Comm. Heat Mass Transfer 17, 49-58. [10.4]

    Article  Google Scholar 

  • Ebinuma, C. D. and Nakayama, A. 1990b An exact solution for transient film condensation in a porous medium along a vertical surface with lateral mass flux. Int. Comm. Heat Mass Transfer 17, 105-111. [4.6.2, 10.4]

    Article  Google Scholar 

  • Ebinuma, C. D. and Nakayama, A. 1997 Approximate solution for non-Darcy transient film condensation in a porous medium. J. Brazilian Soc. Mech. Sci. 19, 496-503. [10.4]

    Google Scholar 

  • Echaniz, H. L. 1984 Oscillatory convection with boiling in a water-saturated porous medium. MS thesis, Cornell University. [10.3.1]

    Google Scholar 

  • Ellinger, E. A. and Beckerman, C. 1991 On the effect of porous layers on melting heat transfer in an enclosure. Exp. Therm. Fluid Sci. 4, 619-629. [10.1.7]

    Article  Google Scholar 

  • Emms, P. W. 1998 Freckle formation in a solidifying binary alloy. J. Engng. Math. 33, 175-200. [10.2.3]

    Article  MathSciNet  MATH  Google Scholar 

  • Emms, P. W. and Fowler, A. C. 1994 Compositional convection in the solidification of binary alloys. J. Fluid Mech. 262, 111-139. [10.2.3]

    Article  MathSciNet  MATH  Google Scholar 

  • Essome, G. R. and Orozco, J. 1991 An analysis of film boiling on a binary mixture in a porous medium. Int. J. Heat Mass Transfer 34, 757-766. [10.3.2]

    Article  Google Scholar 

  • Fauzi, N. F., Merkin, J. H., Ahmad, S. and Pop, I. 2016 The mixed convection boundary layer on vertical melting front in a non-Darcian porous medium. Transp. Porous Media, to appear. [10.1.7]

    Google Scholar 

  • Felicelli, S. D., Heinrich, J. C. and Poirier, D. R. 1991 Simulation of freckles during vertical solidification of binary alloys. Metall. Trans. B 22, 847-859. [10.2.3]

    Article  Google Scholar 

  • Feltham, D. L and Worster, M. G. 1999 Flow-induced morphological instability of a mushy layer. J. Fluid Mech. 391, 337-357. [10.2.3]

    Article  MATH  Google Scholar 

  • Feltham, D. L., Untersteiner, N., Wettlaufer, J. B. and Worster, M. G. 2006 Sea ice is a mushy layer. Geophys. Res. Lett. 33, #L14501. [10.2.3]

    Article  Google Scholar 

  • Fey, Y. C. and Boies, M. A. 1987 An analytical study of the effect of convection heat transfer on the sublimation of a frozen semi-infinite porous medium. Int. J. Heat Mass Transfer 30, 771-779. [10.1.7]

    Article  MATH  Google Scholar 

  • Fowler, A. C. 1985 The formation of freckles in binary alloys. IMA J. Appl. Maths. 35, 159-174. [10.2.3]

    Article  MATH  Google Scholar 

  • Ganesan, S. and Poirier, D. R. 1990 Conservation of mass and momentum for the flow of interdendritic liquid during solidification. Mettal. Trans. B 21, 173-181. [10.2.3]

    Article  Google Scholar 

  • Gao, D. Y. and Chen, Z. Q. 2011 Lattice Boltzmann simulation of natural convection dominated melting in a rectangular cavity filled with porous media. Int. J. Therm. Sci. 50, 493-501. [10.1.7]

    Article  Google Scholar 

  • Gook, H. I. 2001 Convective instability in porous media during solidification. AIChE J. 47, 1698-1700. [10.2.3]

    Article  Google Scholar 

  • Gook, H. I. 2012 Linear stability of compositional convection in a mushy layer during solidification of ammonium chloride solution. Korean Chem. Engng. Res. 50, 61-65. [10.2.3]

    Article  Google Scholar 

  • Gook, H. I. 2014 Characteristics and stability of compositional convection in binary solidification with a constant solidification velocity. Korean Chem. Engng. Res. 52, 199–204. [10.2.3]

    Article  Google Scholar 

  • Gook, H. I. and Choi, C. K. 2008 Onset of convection in a porous mush during binary solidification. Korean J. Chem. Engng. 25, 199-202. [10.2.3]

    Article  Google Scholar 

  • Gook, H. I. and Choi, C. K. 2009 Stability of buoyancy-driven convection in directional solidification of a binary melt. Korean J. Chem. Engng. 26, 930-934. [10.2.3]

    Article  Google Scholar 

  • Gorla, R. S. R., Mansour, M. A. and Sarhar, M. G. 1999b Natural convection from a vertical plate in a porous medium using Brinkman’s model. Transport Porous Media 36, 357-371. [5.1.7.1]

    Article  Google Scholar 

  • Govender, S. 2003b On the linear stability of large Stephan number convection in rotating mushy layers for a new Darcy equation formulation. Transport Porous Media 51, 173-189. [10.2.3]

    Article  MathSciNet  Google Scholar 

  • Govender, S. 2003d Finite amplitude analysis of convection in rotating mushy layers during solidification of binary alloys. J. Porous Media 6, 137-147. [10.2.3]

    Article  MATH  Google Scholar 

  • Govender, S. 2003e Moderate time scale finite amplitude analysis of large Stephan number convection in rotating mushy layers. Transport Porous Media 53, 357-366. [10.2.3]

    Article  MathSciNet  Google Scholar 

  • Govender, S. 2004c Finite amplitude analysis of convection in rotating mushy layers for small variations in retardability. J. Porous Media 7, 227-238. [10.2.3]

    Article  MATH  Google Scholar 

  • Govender, S. 2005a Moderate Stefan number convection in rotating mushy layers: A new Darcy number formulation. Transport Porous Media 59, 127-137. [10.2.3]

    Article  Google Scholar 

  • Govender, S. 2005b Stefan number effect on the transition from stationary to oscillatory convection in a solidifying mushy layer subjected to rotation; Response to reviewer’s comment. Transport Porous Media 58, 361-369. [10.2.3]

    Article  Google Scholar 

  • Govender, S. 2005c Destabilizing a fluid saturated gravity modulated porous layer heated from above. Transport Porous Media 59, 215-225. [6.24]

    Article  Google Scholar 

  • Govender, S. 2005g Coriolis effect on flow stability in mushy layers solidifying in a microgravity environment. J. Porous Media 8, 355-364. [10.2.3]

    Article  Google Scholar 

  • Govender, S. 2007c Linear stability of solutal convection in solidifying mushy layer: permeable mush-melt interface. Transp. Porous Media 67, 431-439. [10.2.3]

    Google Scholar 

  • Govender, S. 2007a An analogy between a gravity modulated porous layer heated from below and the inverted pendulum with an oscillating pivot point. Transport Porous Media 67, 323-328. [6.24]

    Article  MathSciNet  Google Scholar 

  • Govender, S. 2007b Coriolis effect on the stability of centrifugally driven convection in a rotating anisotropic porous layer subjected to gravity. Transport Porous Media 67, 219-227. [6.22]

    Article  MathSciNet  Google Scholar 

  • Govender, S. 2008a Linear stability of solutal convection in rotating mushy layers: Permeable mush-melt interface. J. Porous Media 11, 683-690. [10.2.3]

    Article  Google Scholar 

  • Govender, S. 2008b Natural convection in gravity-modulated porous layers. In P. Vadasz (ed.) Emerging Topics in Heat and Mass Transfer in Porous Media, Springer, New York, pp. 133-148. [6.24]

    Chapter  Google Scholar 

  • Govender, S. 2011a Stability of moderate Vadasz number solutal convection in a cylindrical mushy layer subjected to vertical vibration. Transport Porous Media 88, 225-234. [10.2.3]

    Article  MathSciNet  Google Scholar 

  • Govender, S. 2011b Stability of solutal convection in a rotating mushy layer solidifying from a vertical surface. Transp. Porous Media 90, 393-402. [10.2.3]

    Article  MathSciNet  Google Scholar 

  • Govender, S. and Vadasz, P. 2002a Weak nonlinear analysis and moderate Stephan number oscillatory convection in rotating mushy layers. Transport Porous Media 48, 353-372. [10.2.3]

    Article  MATH  Google Scholar 

  • Govender, S. and Vadasz, P. 2002b Weak nonlinear analysis and moderate Stephan number stationary convection in rotating mushy layers. Transport Porous Media 49, 247-263. [10.2.3]

    Article  MathSciNet  MATH  Google Scholar 

  • Govender, S. and Vadasz, P. 2002c Moderate time scale linear stability of moderate Stefan number convection in rotating mushy layers. J. Porous Media 5, 113-121. [10.2.3]

    Article  MATH  Google Scholar 

  • Guba, P. 2001 On the finite-amplitude steady convection in rotating mushy layers, J. Fluid Mech. 347, 337-365. [10.2.3]

    MATH  Google Scholar 

  • Guba, P. and Boda, J. 1998 The effect of uniform rotation on convective instability of a mushy layer during binary alloys solidification. Stud. Geophys. Geodaet. 42, 289-296. [10.2.3]

    Article  Google Scholar 

  • Guba, P. and Worster, M. G. 2006a Free convection in laterally solidifying mushy regions. J. Fluid Mech. 558, 69-78. [10.2.3]

    Article  MathSciNet  MATH  Google Scholar 

  • Guba, P. and Worster, M. G. 2006b Nonlinear oscillatory convection in mushy layers. J. Fluid Mech. 553, 419-443. [10.2.3]

    Article  MathSciNet  MATH  Google Scholar 

  • Hallworth, M. A., Huppert, H. E. and Woods, A. W. 2005 Dissolution-driven convection in a reactive porous medium. J. Fluid Mech. 535, 255-285. [10.2.3]

    Article  MathSciNet  MATH  Google Scholar 

  • Hao, Y. L. and Tao, Y. X. 2003a Non-equilibrium melting of granular packed bed in horizontal forced convection. Part I: Experiment. Int. J. Heat Mass Transfer 46, 5017-5030. [10.1.7]

    Article  Google Scholar 

  • Hao, Y. L. and Tao, Y. X. 2003b Non-equilibrium melting of granular packed bed in horizontal forced convection. Part II: Numerical simulation. Int. J. Heat Mass Transfer 46, 5031-5044. [10.1.7]

    Article  Google Scholar 

  • Harris, K.T., Haji-Sheikh, A. and Nhanna, A. G. A. 2001 Phase change phenomena in porous media—a non-local thermal equilibrium model. Int. J. Heat Mass Transfer 44, 1619-1625. [10.1.7]

    Article  MATH  Google Scholar 

  • Hills, R. N., Loper, D. E. and Roberts, P. H. 1983 A thermodynamically consistent model for flow through dendrites. Quart. J. Mech. Appl. Math. 36, 505-539. [10.2.3]

    Article  MATH  Google Scholar 

  • Hong, J. S., Kim, M. C. and Choi, C. K. 2007 The onset of buoyancy-driven instability in porous media melted from below. Transp. Porous Media 67, 229-241. [10.1.7]

    Article  Google Scholar 

  • Hunke, E. C., Notz, D., Turner, A. K. and Vancoppenolle, M. 2011 The multiphase physics of sea ice: A review. Cryosphere 5, 989-1009. [10.2.3]

    Article  Google Scholar 

  • Huppert, H. E. and Worster, M. G. 2012 Flows involving phase change. In Handbook of Environmental Fluid Mechanics (ed. H. J. Fernando), CRC Press. [10.2.3]

    Google Scholar 

  • Jany, P. and Bejan, A. 1988a Scales of melting in the presence of natural convection in a rectangular cavity filled with porous medium. ASME J. Heat Transfer 110, 526-529. [10.1.1, 10.1.2]

    Article  Google Scholar 

  • Jany, P. and Bejan, A. 1988b Scaling theory of melting with natural convection in an enclosure. Int. J. Heat Mass Transfer 31, 1221-1235 [10.1.1]

    Article  Google Scholar 

  • Jha, B. K. and Mohammed, U. 2014 Mixed convection effect on melting from a vertical plate embedded in a porous medium with Soret and Dufour effects. Heat Transfer Asian Res. 43, 667-676. [10.1.7]

    Article  Google Scholar 

  • Jha, B. K., Daramola, D. and Ajibade, A. G. 2013a Steady fully developed mixed convection flow in a vertical parallel plate microchannel with bilateral heating and filled with porous material. Proc. Inst. Mech. Engrs. E. 227, 56-66. [8.3.1]

    Article  Google Scholar 

  • Jha, B. K., Mohammed, U. and Ajidade, A. O. 2013b Dufour and Soret effects on melting from a vertical plate embedded in saturated porous media. J. Appl. Math. 182179. [10.1.7]

    Google Scholar 

  • Kairi, R. R. and Murthy, P. V. S. N. 2012 Effect of melting on mixed convection heat and mass transfer in a non-Newtonian fluid saturated non-Darcy porous medium. ASME J. Heat Transfer 134, 042601. [10.1.7]

    Article  Google Scholar 

  • Kairi, R. R. and Murthy, P. V. S. N. 2013 Soret effect on free convection from a melting vertical surface in a non-Darcy porous medium. J. Porous Media 16, 97-104. [10.1.7]

    Article  Google Scholar 

  • Kameswaran, P. K., Hemalatha, K. and Madhavi, M. V. D. N. S. 2016 Melting effect on convective heat transfer from a vertical plate embedded in a non-Darcy porous medium with variable permeability. Adv. Powder Tech., to appear. [10.1.7]

    Google Scholar 

  • Karcher, C. and Müller, U. 1995 Convection in a porous medium with solidification. Fluid Dyn. Res. 15, 25-42. [10.2.2]

    Article  MathSciNet  MATH  Google Scholar 

  • Katz, R. F. and Worster, M. G. 2008 Simulation of directional solidification, thermochemical convection, and chimney formation in a Hele-Shaw cell. J. Comput. Phys. 227, 9823-9840. [10.2.3]

    Article  MathSciNet  MATH  Google Scholar 

  • Kazmierczak, M. and Poulikakos, D. 1988 Melting of an ice surface in a porous medium. AIAA J. Thermophys. Heat Transfer 2, 352-358. [10.1.7]

    Article  Google Scholar 

  • Kazmierczak, M., Poulikakos, D. and Pop, I. 1986 Melting from a flat plate embedded in a porous medium in the presence of steady natural convection. Numer. Heat Transfer 10, 571-582. [10.1.1, 10.1.5]

    Article  Google Scholar 

  • Kazmierczak, M., Poulikakos, D. and Sadowski, D. 1987 Melting of a vertical plate in porous medium controlled by forced convection of a dissimilar fluid. Int. Comm. Heat Mass Transfer 14, 507-517. [10.1.7]

    Article  Google Scholar 

  • Kazmierczak, M., Sadowski, D. and Poulikakos, D. 1988 Melting of a solid in a porous medium induced by free convection of a warm dissimilar fluid. ASME J. Heat Transfer 110, 520-523. [10.1.7]

    Article  Google Scholar 

  • Khan, A., Khan, I., Ali, F. and Shafie, S. 2014a Effects of wall shear stress on MHD conjugate flow over an inclined plate in a porous medium with ramped wall temperature. Math. Prob. Engng. 861708. [5.3]

    Google Scholar 

  • Khan, A., Khan, I., Ali, F., Ulhaq, S. and Shafie, S. 2014b Effects of wall shear stress on unsteady MHD conjugate flow in a porous medium with ramped wall temperature. PLoS ONE 9, e90280. [5.1.9.10]

    Article  Google Scholar 

  • Khan, W. A., Culham, J. R. Khan, Z. H., and Pop, I. 2014a Triple diffusion along a horizontal plate in a porous medium with convective boundary condition. Int. J. Therm. Sci. 86, 60-67. [9.2.1]

    Article  Google Scholar 

  • Khan, W. A., Uddin, M. J. and Ishmail, A. I. M. 2014b Effects of melting and thermal dispersion on unsteady mixed convection with heat and mass transfer in a non-Darcy porous medium. J. Porous Media 17, 211-223. [10.1.7]

    Article  Google Scholar 

  • Kim, M. C., Yoon, D. Y. and Choi, C. L. 2009a Onset of buoyancy-driven instability in porous medium solidified from above. Transp. Porous Media 78, 295-307. [10.2.2]

    Article  MathSciNet  Google Scholar 

  • Kim, S., Lorente, S. and Bejan, A. 2009 Transient behaviour of vascularized walls exposed to sudden heating. Int. J. Therm. Sci. 48, 2046-2052. [4.19]

    Article  Google Scholar 

  • Kimura, S. 2005 Dynamic solidification in a water-saturated porous medium cooled from above. In Transport Phenomena in Porous Media III, (eds. D. B. Ingham and I. Pop), Elsevier, Oxford, pp. 399-417. [10.2.2]

    Google Scholar 

  • Kokubun, M. A. E. and Fachini, F. F. 2012 Asymptotic analysis of a Hiemenz flow in a low-porosity medium with phase change. J. Fluid Mech. 698, 185-210. [10.3.2]

    Article  MathSciNet  MATH  Google Scholar 

  • Krane, M. J. M. and Incropera, F. P. 1996 A scaling analysis of the unidirectional solidification of a binary alloy. Int. J. Heat Mass Transfer 39, 3567-3579. [10.2.3]

    Article  Google Scholar 

  • Krishnan, S., Murthy, J. Y. and Garimella, S. V. 2005 A two-temperature model for solid-liquid phase change in metal foams. ASME J. Heat Transfer 127, 995-1004. [10.1.7]

    Article  Google Scholar 

  • Krishnan, S., Murthy, J. Y. and Garimella, S. V. 2007 Analysis of solid-liquid phase change under pulsed heating. ASME J. Heat Transfer 129, 395-400. [10.1.7]

    Article  Google Scholar 

  • Krishnan, S., Murthy, J. Y. and Garimella, S. V. 2008 Metal foams as passive thermal control systems. In P. Vadasz (ed.) Emerging Topics in Heat and Mass Transfer in Porous Media, Springer, New York, pp. 261-282. [10.1.7]

    Chapter  Google Scholar 

  • Kumar, A., Zaloznik, M., Combeau, H, Goyeau, B. and Gobin, D. 2013 A numerical simulation of columnar convection: influence of inertia on channel segregation. Modell. Simul. Mater. Sci. Engng. 21, 045016. [10.2.3]

    Article  Google Scholar 

  • Kumar, A., Zaloznik, M., Combeau, H., Goyeau, B. and Gobin, D. 2012 Channel segregation during columnar solidification: influence of inertia. AIP Conf. Proc. 1453, 42-48. [10.2.3]

    Google Scholar 

  • Kumar, N., Gupta, S. and Jain, T. 2013b Combined effects of heat and mass transfer by MHD free-convective flow of micropolar and Newtonian fluids through porous medium in a vertical channel in the presence of thermal radiation. Acta Tech. CSAV 58, 295-313. [9.2.2]

    MathSciNet  Google Scholar 

  • Kumar, S., Sharma, V. and Kishor, K. 2013c Numerical and analytical investigations of thermosolutal instability in rotating Rivlin-Ericksen fluid in porous medium with Hall current. Appl. Math. Mech. – English ed. 34, 501-522. [9.1.6.4]

    Article  MathSciNet  Google Scholar 

  • Kuznetsov, A. 1998e Non-thermal equilibrium forced convection in porous media. Transport Phenomena in Porous Media (eds. D. B. Ingham and I. Pop), Elsevier, Oxford, pp. 103-130. [4.6.4]

    Chapter  Google Scholar 

  • Kuznetsov, A. V. and Vafai, K. 1995b Analytical comparison and criteria for heat and mass transfer models in metal hydride packed beds. Int. J. Heat Mass Transfer 38, 2873-2884. [3.4]

    Article  Google Scholar 

  • Lafdi, K., Mesalhy, O. and Shaikh, S. 2007 Experimental study on the influence of foam porosity and pore size on the melting of phase change materials. J. Appl. Phys. 102, Art. 083549. [10.1.7]

    Article  Google Scholar 

  • Lage, J. L. 1996 Comments on “the effect of turbulence on solidification of a binary metal alloy with electromagnetic stirring.” ASME J. Heat Transfer 118, 996-997. [10.2.3]

    Google Scholar 

  • Lai, F. C. and Kulacki, F. A. 1989b Effects of variable fluid viscosity on film condensation along an inclined surface in saturated porous medium. ASME HTD 127, 7-12. [10.4]

    Google Scholar 

  • Lein, H. and Tankin, R. S. 1992b Natural convection in porous media — II. Freezing. Int. J. Heat Mass Transfer 35, 187-194. [10.2.2]

    Article  Google Scholar 

  • Leu, J. S., Jang, J. Y. and Chou, T. 2006 Heat and mass transfer for liquid film evaporation along a vertical plate covered with a thin porous layer. Int. J. Heat Mass Transfer 49, 1937-1945. [10.3.2]

    Article  MATH  Google Scholar 

  • Leu, J. S., Jang, J. Y. and Chou, T. 2009 Convection heat and mass transfer along a vertical heated plate with film evaporation in a non-Darcian porous medium. Int. J. Heat Mass Transfer 52, 5447-5450. [10.3.2]

    Article  MATH  Google Scholar 

  • Leu, J. S., Jang, J. Y. and Chou, T. 2011 Effects of non-Darcian and inlet conditions on the forced convection along a vertical plate with film evaporation. Heat Transfer Engng. 32, 981-987. [10.3.2]

    Article  Google Scholar 

  • Li, H. Y. and Leong, K. C. 2011 Experimental and numerical study of single and two-phase flow and heat transfer in aluminum foams. Int. J. Heat Mass Transfer 54, 4904-4912. [10.3.1]

    Article  MATH  Google Scholar 

  • Li, H. Y., Leong, K. C., Jin, L. W. and Chai, J. C. 2010b Three dimensional numerical simulation of fluid flow with phase change heat transfer in an asymmetrically heated porous channel. Int. J. Therm. Sci. 49, 2363-2375. [10.3.1]

    Article  Google Scholar 

  • Li, H. Y., Leong, K. C., Jin, L. W. and Chai, J. C. 2010c Transient behaviour of fluid flow and heat transfer with phase change in vertical porous channels. Int. J. Heat Mass Transfer 53, 5209-5222. [10.3.1]

    Article  MATH  Google Scholar 

  • Li, H. Y., Leong, K. C., Jin, L. W. and Chai, J. C. 2010d Transient two-phase flow and heat transfer with localized heating in porous media. Int. J. Therm. Sci. 49, 1115-1127. [10.3.1]

    Article  Google Scholar 

  • Li, J. M. and Wang, B. X. 1998 Investigation on wall effect of condensation in porous media. Heat Transfer 1998, Proc. 11th IHTC, 4, 459-463. [10.4]

    Google Scholar 

  • Li, W. Q., Qu, Z. G., He, H. L. and Tao, W. Q. 2012 Experimental and numerical studies on melting phase change heat transfer in open-cell metallic foams filled with paraffin. Appl. Therm. Engng. 37, 1-9. [10.1.7]

    Article  Google Scholar 

  • Lim, J. S., Fowler, A. J. and Bejan, A., 1993, Spaces filled with fluid and fibers coated with phase-change material. J. Heat Transfer 115, 1044-1050. [10.5]

    Article  Google Scholar 

  • Lindner, F., Mundi, C. and Pfitzner, M. 2015 Fluid flow and heat transfer with phase change and local thermal non-equilibrium in vertical porous channels. Transp. Porous Media 106, 201-220. [10.1.7]

    Article  Google Scholar 

  • Lipnicki, Z. and Weigand, B. 2008 Natural convection flow with solidification between two vertical plates filled with a porous medium. Heat Mass Transfer 44, 1401-1407. [10.2.1.2]

    Article  Google Scholar 

  • Liu, C. Y., Ismail, K. A. R. and Ibinuma, C. D. 1984 Film condensation with lateral mass flux about a body of arbitrary shape in a porous medium. Int. Comm. Heat Mass Transfer 11, 377-384. [10.4]

    Article  Google Scholar 

  • Liu, Q. and He, Y. l. 2015 Double multiple-relaxation time lattice Boltzmann model for solid-liquid phase change with natural convection in porous media. Physica A 438, 94-106. [10.2.1.2]

    Article  MathSciNet  Google Scholar 

  • Loper, D. E. and Roberts, P. H. 2001 Mush-chimney convection. Stud. Appl. Math. 106, 187-227. [10.2.3]

    Article  MathSciNet  MATH  Google Scholar 

  • Lu, J. W. and Chen, F. 1997 Rotation effects on the convection of binary alloys unidirectionally solidified from below. Int. J. Heat Mass Transfer 40, 237-246. [10.2.3]

    Article  MATH  Google Scholar 

  • Ma, J. and Wang, B. X. 1999 Natural convection and its fractal for liquid freezing in a vertical cavity filled with porous medium. Heat Transfer Asian Res. 28, 165-171. [10.2.1.2]

    Article  Google Scholar 

  • Ma, X. H. and Wang, B. X. 1998 Suction effect of a vertical coated plain porous layer on film condensation heat transfer enhancement. Heat Transfer 1998, Proc. 11th IHTC 5, 387-391. [10.4]

    Google Scholar 

  • Maharaj, Y. and Govender, S. 2005 Effects of the Darcy-Prandtl number on the linear stability of stationary convection in rotating mushy layers. J. Porous Media 8, 271-280. [10.2.3]

    Article  Google Scholar 

  • Mahdy, A. 2013a Mixed convection in non-Newtonian fluids along a vertical plate in a liquid-saturated porous medium with melting effect. Engng. Phys. Thermophys. 86, 1117-1126. [10.1.7]

    Article  Google Scholar 

  • Mahmoud, M. A. A. and Waheed, S. E. 2014 Melting heat transfer effects on stagnation point flow of micropolar fluid saturated with internal heat generation (absorption). Appl. Math. Mech. English ed. 35, 979-992. [10.1.7]

    Article  MathSciNet  MATH  Google Scholar 

  • Majumdar, A. and Tien, C. L. 1990 Effects of surface tension on film condensation in a porous medium. ASME J. Heat Transfer 112, 751-757. [10.4]

    Article  Google Scholar 

  • Masoud, S. A., Al-Nimr, M. A. and Alkam, M. K. 2000 Transient film condensation on a vertical plate imbedded in porous medium. Transport Porous Media 40, 345-354. [10.4]

    Article  Google Scholar 

  • Mat, M. D. and Ilegbusi, O. J. 2002 Application of a hybrid model of mushy zone to macrosegregation in alloy solidification. Int. J. Heat Mass Transfer 45, 279-289. [10.2.3]

    Article  MATH  Google Scholar 

  • Matsumoto, K., Okada, M., Murakami, M. and Yabushita, Y. 1993 Solidification of porous medium saturated with aqueous solution in a rectangular cell. Int. J. Heat Mass Transfer 36, 2869-2880. [10.2.3]

    Article  Google Scholar 

  • Matsumoto, K., Okada, M., Murakami, M. and Yabushita, Y. 1995 Solidification of porous medium saturated with aqueous solution in a rectangular cell — II. Int. J. Heat Mass Transfer 38, 2935-2943. [10.2.3]

    Article  Google Scholar 

  • Mbaye, M. and Bilgen, E. 2006 Natural convection in composite systems with phase change materials. Heat Mass Transfer 42, 636-644. [10.5]

    Article  Google Scholar 

  • Mehrabian, R., Keane, M. and Flemings, M. C. 1970 Interdendritic fluid flow and macrosegregation: influence of gravity. Metall. Trans. B 1, 1209-1220. [10.2.3]

    Article  Google Scholar 

  • Merkin, J. H., Pop, I. and Ahmad, S. 2015 Note on the melting effect on mixed convection boundary-layer flow over a vertical flat surface embedded in a porous medium. Int. J. Heat Mass Transfer 84, 786-790. [10.1.7]

    Article  Google Scholar 

  • Mosaad, M. 1999 Natural convection in a porous medium coupled across an impermeable vertical wall with film condensation. Heat Mass Transfer 35, 177-183. [10.4]

    Article  Google Scholar 

  • Muddamallappa, M. S., Bhatta, D. and Riahi, D. N. 2009 Numerical investigation on marginal stability and convection with and without magnetic field in a mushy layer. Transp. Porous Media 79, 301-317. [10.2.3]

    Article  MathSciNet  Google Scholar 

  • Murata, K. 1995 Heat and mass transfer with condensation in a fibrous insulation slab bounded on one side by a cold surface. Int. J. Heat Mass Transfer 38, 3253-3262. [10.4]

    Article  Google Scholar 

  • Najjari, M. and Ben Nasrallah, S. 2002 Numerical study of boiling with mixed convection in a vertical porous layer. Int. J. Therm. Sci. 41, 936-948. [10.3]

    Article  Google Scholar 

  • Najjari, M. and Ben Nasrallah, S. 2005 Numerical study of the effects of geometric dimensions on a liquid-vapor phase change and free convection in a rectangular porous cavity. J. Porous Media 8, 1-12. [10.3]

    Article  MATH  Google Scholar 

  • Najjari, M. and Ben Nasrallah, S. 2006 Liquid-vapor phase-change and mixed convection in a porous layer discretely heated. J. Porous Media 9, 671-681. [10.3.1]

    Article  Google Scholar 

  • Najjari, M. and Ben Nasrallah, S. 2008 Effects of latent heat storage on heat transfer in a forced flow in a porous layer. Int. J. Therm. Sci. 47, 825-833. [10.3.1]

    Article  Google Scholar 

  • Nakayama, A. 1991 A general treatment for non-Darcy film condensation within a porous medium in the presence of gravity and forced flow. Wärme-Stoffübertrag. 27, 119-124. [10.4]

    Article  Google Scholar 

  • Nakayama, A. and Koyama, H. 1988a A similarity transformation for subcooled mixed convection film boiling in a porous medium. Appl. Sci. Res., 45, 129-143. [10.3.2]

    Article  Google Scholar 

  • Nakayama, A. and Koyama, H. 1988b Subcooled forced convection film boiling over a vertical flat plate embedded in a fluid-saturated porous medium. Wärme-Stoffübertrag. 22, 269-273. [10.3.2]

    Article  Google Scholar 

  • Nakayama, A., Koyama, H. and Kuwahara, F. 1987 Two-phase boundary layer treatment for subcooled free-convection film boiling around a body of arbitrary shape in a porous medium. ASME J. Heat Transfer 109, 997-1002. [10.3.2]

    Article  Google Scholar 

  • Nandapurkar, P., Poirier, D. R., Heinrich, J. C. and Felicelli, S. 1989 Thermosolutal convection during dendritic solidification of alloys: Part 1. Linear stability analysis. Metall. Trans. B 20, 711-721. [10.2.3]

    Article  Google Scholar 

  • Nayak, K. C., Saha, S. K., Srinivasan, K. and Dutta, P. 2006 A numerical model for heat sinks with phase change materials and thermal conductivity enhancers. Int. J. Heat Mass Transfer 49, 1833-1844. [10.5]

    Article  MATH  Google Scholar 

  • Neilson, D. G. and Incropera, F. P. 1993 Effect of rotation on fluid motion and channel formation during unidirectional solidification of a binary alloy. Int. J. Heat Mass Transfer 36, 489-505. [10.2.3]

    Article  MATH  Google Scholar 

  • Neufeld, J. A. and Wettlaufer, J. S. 2008 Shear-enhanced convection in a mushy layer. J. Fluid Mech. 612, 339-361. [10.2.3]

    MathSciNet  MATH  Google Scholar 

  • Neufeld, J. A. and Wettlaufer, J. S. 2011 Shear flow, phase change and matched asymptotic expansions: Pattern formation in mushy layers. Physica D 240, 140-149. [10.2.3]

    Article  MathSciNet  MATH  Google Scholar 

  • Nguyen, T. H. and Zhang, X. 1992 Onset and evolution of penetrative convection during the melting process in a porous medium. Heat and Mass Transfer in Porous Media (ed. M. Quintard and M. Todorovic), Elsevier, Amsterdam, 381-392. [10.1.7]

    Google Scholar 

  • Ni, J. and Beckermann, C. 1991b A volume-averaged two-phase model for transport phenomena during solidification. Metall. Trans. B 22, 349-361. [10.2.3]

    Article  Google Scholar 

  • Ni, J. and Incropera, F. P. 1995a Extension of the continuum model for transport phenomena occurring during metal alloy solidification—I. The conservation equations. Int. J. Heat Mass Transfer 38, 1271-1284. [10.2.3]

    Article  MATH  Google Scholar 

  • Ni, J. and Incropera, F. P. 1995b Extension of the continuum model for transport phenomena occurring during metal alloy solidification—II. Microscopic considerations. Int. J. Heat Mass Transfer 38, 1285-1296. [10.2.3]

    Article  MATH  Google Scholar 

  • Nima, M. A. 2016 Numerical study of phase change characteristics in a vertical and inclined channel using thermal nonequilibrium model. J. Porous Media, 19, 1099–1121. [10.1.7]

    Article  Google Scholar 

  • Nishimura, T. and Wakamatsu, M. 2000 Natural convection suppression and crystal growth during unidirectional solidification of a binary system. Heat Transfer Asian Res. 29, 120-131. [10.2.3]

    Article  Google Scholar 

  • Notz, D. and Worster, M. G. 2009 Desalination processes in sea ice revisited. J. Geophys. Res. 114, (C5). [10.2.3]

    Google Scholar 

  • Okada, M., Matsumoto, K. and Yabushita, Y. 1994 Solidification around horizontal cylinder in porous medium saturated with aqueous solution. Heat Transfer 1994, Inst. Chem. Engrs, Rugby, vol. 4, pp. 109-114. [10.2.3]

    Google Scholar 

  • Okhuysen, B. S. and Riahi, D. N. 2008 Flow instabilities of liquid and mushy regions during alloy solidification and under high gravity environment induced by rotation. Int. J. Engng. Sci. 46, 189-201. [10.2.3]

    Article  MathSciNet  MATH  Google Scholar 

  • Okhuysen, B. S. and Riahi, D. N. 2009 Perturbation and stability analyses of flow in a mushy layer with permeable interface. Nonlinear Anal. Real World Appl. 10, 3230-3239. [10.2.3]

    Article  MathSciNet  MATH  Google Scholar 

  • Oosthuizen, P. H. 1988b Mixed convective heat transfer from a heated horizontal plate in a porous medium near an impermeable surface. ASME J. Heat Transfer 110, 390-394. [8.1.4]

    Article  Google Scholar 

  • Orozco, J. 1992 Condensation of a downward flowing vapor on a horizontal cylinder embedded in a porous medium. ASME J. Energy Resour. Tech. 113, 300-304. [10.4]

    Article  Google Scholar 

  • Orozco, J. and Zhu, K. H. 1993 Mixed convection film boiling of a binary mixture on a horizontal cylinder embedded in a porous medium. Chem. Engng Comm. 135, 91-104. [10.3.2]

    Article  Google Scholar 

  • Orozco, J., Stellman, R. and Gutjahr, M. 1988 Film boiling heat transfer from a sphere and a horizontal cylinder embedded in a liquid-saturated porous medium. ASME J. Heat Transfer 110, 961-967. [10.3.2]

    Article  Google Scholar 

  • O'Sullivan, M. J. 1985b Convection with boiling in a porous layer. Convective Flows in Porous Media (eds. R. A. Wooding and I. White), Dept. Sci. Indust. Res., Wellington, N.Z., pp. 141-155. [10.3.1]

    Google Scholar 

  • Oueslati, F., Bennacer, R., Sammouda, H. and Belgith, A. 2008b Thermosolutal convection during melting in a porous medium saturated with aqueous solution. Numer. Heat Transfer 54, 315-330. [10.1.7]

    Article  Google Scholar 

  • Pak, J. and Plumb, O. A. 1997 Melting in a two-component packed bed. ASME J. Heat Transfer 119, 553-559. [10.1.7]

    Article  Google Scholar 

  • Parmentier, E. M. 1979 Two-phase natural convection adjacent to a vertical heated surface in a permeable medium. Int. J. Heat Mass Transfer 22, 849-855. [10.3.2]

    Article  Google Scholar 

  • Peppin, S. S. L., Aussillous, P., Huppert, H. E. and Worster, M.G. 2007 Steady-state mushy layers: experiments and theory. J. Fluid Mech. 570, 69-77. [10.2.3]

    Article  MATH  Google Scholar 

  • Peppin, S. S. L., Huppert, H. E. and Worster, M. G. 2008 Steady-state solidification of aqueous ammonium chloride. J. Fluid Mech. 599, 465-476. [10.2.3]

    Article  MATH  Google Scholar 

  • Pillay, S. K and Govender, S. 2005 Stability of convection in a gravity modulated mushy layer during solidification of binary alloys. Transp. Porous Media 60, 183-197. [6. 24, 10.2.3]

    Article  Google Scholar 

  • Pillay, S. K and Govender, S. 2007 Moderate time scale finite amplitude analysis of large Stefan number convection in a gravity modulated mushy layer during the solidification of binary alloys. Transp. Porous Media 69, 331-341. [10.2.3]

    Article  Google Scholar 

  • Plumb, O. A. 1994a Convective melting of packed beds. Int. J. Heat Mass Transfer 37, 829-836. [10.1.7]

    Article  MATH  Google Scholar 

  • Poirier, D. R., Nandapurkar, P.J. and Ganesan, S. 1991 The energy and solute conservation equations for dendritic solidification. Metall. Trans. B 22, 889-900. [10.2.3]

    Article  Google Scholar 

  • Prescott, P. J. and Incropera, F. P. 1995 The effect of turbulence on solidification of binary metal alloy with electromagnetic stirring. ASME J. Heat Transfer 117, 716-724. [1.8, 10.2.3]

    Article  Google Scholar 

  • Prescott, P. J. and Incropera, F. P. 1996 Convection heat and mass transfer in alloy solidification. Advances in Heat Transfer 28, 231-329. [10.2.3]

    Article  Google Scholar 

  • Ramesh, P. S. and Torrance, K. E. 1990 Stability of boiling in porous media. Int. J. Heat Mass Transfer 33, 1895-1908. [10.3.1]

    Article  MATH  Google Scholar 

  • Ramesh, P. S. and Torrance, K. E. 1993 Boiling in a porous layer heated from below: effects of natural convection and a moving liquid/ two-phase surface. J. Fluid Mech. 257, 289-309. [10.3.1]

    Article  MATH  Google Scholar 

  • Rees Jones, D. W. and Worster, M. G. 2013 Fluxes through steady chimneys in a mushy layer during binary alloy solidification. J. Fluid Mech. 714, 127-151. [10.2.3]

    Article  MathSciNet  MATH  Google Scholar 

  • Rees Jones, D. W. and Worster, M. G. 2015 On the thermodynamic boundary conditions of a solidifying mushy layer with outflow. J. Fluid Mech. 762, #R1. [10.2.3]

    Google Scholar 

  • Renken, K. J and Raich, M. R. 1996 Forced convection steam condensation experiments within thin porous coatings. Int. J. Heat Mass Transfer 39, 2937-2945. [10.4]

    Article  Google Scholar 

  • Renken, K. J. and Aboye, M. 1993a Analysis of film condensation promotion within thin inclined porous coatings. Int. J. Heat Fluid Flow 14, 48-53. [10.4]

    Article  Google Scholar 

  • Renken, K. J. and Aboye, M. 1993b Experiments on film condensation promotion within thin porous coatings. Int. J. Heat Mass Transfer 36, 1347-1355. [10.4]

    Article  Google Scholar 

  • Renken, K. J., Carneiro, M. J. and Meechan, K. 1994 Analysis of laminar forced convection condensation within porous coatings. AIAA J. Thermophys. Heat Transfer 8, 303-308. [10.4]

    Article  Google Scholar 

  • Renken, K. J., Soltykiewicz, D. J. and Poulikakos, D. 1989 A study of laminar film condensation on a vertical surface with a porous coating. Int. Comm. Heat Mass Transfer 16, 181-192. [10.4]

    Article  Google Scholar 

  • Riahi, D. N. 1993b Effect of rotation on the stability of the melt during the solidification of a binary alloy. Acta Mech. 99, 95-101. [10.2.3]

    Article  MATH  Google Scholar 

  • Riahi, D. N. 1997 Effects of centrifugal and Coriolis forces on chimney convection during alloy solidification. J. Crystal Growth 179, 287-296. [10.2.3]

    Article  Google Scholar 

  • Riahi, D. N. 1998a On the structure of an unsteady convecting mushy layer. Acta Mech. 127, 83-96. [10.2.3]

    Article  MATH  Google Scholar 

  • Riahi, D. N. 1998b High gravity convection in a mushy layer during alloy solidification. In Nonlinear Instability, Chaos and Turbulence, Vol. 1 (L. Debnath and D. N. Riahi, eds.) WIT Press, Boston, pp. 301-336. [10.2.3]

    Google Scholar 

  • Riahi, D. N. 2002a Effects of rotation on convection in a porous layer during alloy solidification. In Transport Phenomena in Porous Media II (D. B. Ingham and I. Pop, eds.) Elsevier, Oxford, pp. 316-340. [10.2.3]

    Chapter  Google Scholar 

  • Riahi, D. N. 2002b On nonlinear convection in mushy layers. Part 1. Oscillatory modes of convection. J. Fluid Mech. 467, 331-359. [10.2.3]

    Google Scholar 

  • Riahi, D. N. 2003a Nonlinear steady convection in rotating mushy layers. J. Fluid Mech. 485, 279-306. [10.2.3]

    Google Scholar 

  • Riahi, D. N. 2003b On stationary and oscillatory modes of flow instability during alloy solidification. J. Porous Media 6, 177-188. [10.2.3]

    Google Scholar 

  • Riahi, D. N. 2004 On nonlinear convection in mushy layers. Part 2. Mixed oscillatory and stationary modes of convection. J. Fluid Mech. 517, 71-101. [10.2.3]

    Article  MATH  Google Scholar 

  • Riahi, D. N. 2005 Flow instabilities in a horizontal dendrite layer rotating about an inclined axis. J. Porous Media 8, 327-342. [10.2.3]

    Article  Google Scholar 

  • Riahi, D. N. 2006a Effect of permeability on steady flow in a dendrite layer. J. Porous Media 9, 135-153. [10.2.3]

    Article  Google Scholar 

  • Riahi, D. N. 2006b Nonlinear oscillatory convection in rotating mushy layers. J. Fluid Mech. 553, 389-400. [10.2.3]

    Article  MathSciNet  MATH  Google Scholar 

  • Riahi, D. N. 2007a Inertial and Coriolis effects on oscillatory flow in a horizontal dendrite layer. Transp. Porous Media 69, 301-312. [10.2.3]

    Article  MathSciNet  Google Scholar 

  • Riahi, D. N. 2007b Inertial effects on rotating flow in a porous layer. J. Porous Media 10, 343-356. [10.2.3]

    Article  Google Scholar 

  • Riahi, D. N. 2010 On nonlinear evolution approach for convective flow during alloy solidification. Transp. Porous Media 84, 655-662. [10.2.3]

    Article  MathSciNet  Google Scholar 

  • Riahi, D. N. 2012a Effect of a vertical magnetic field on nonlinear convection in a mushy layer. J. Porous Media 15, 805-821. [10.2.3]

    Article  Google Scholar 

  • Riahi, D. N. 2012b Stability and perturbation analysis for nonlinear convection in a mushy layer and in the presence of viscous heating. Mech. Res. Commun. 39, 18-22. [10.2.3]

    Article  MATH  Google Scholar 

  • Riahi, D. N. 2013 Nonlinear evolution analysis and stability for convection in a mushy layer with permeable interface. Mech. Res. Commun. 50, 22-26. [10.2.3]

    Article  Google Scholar 

  • Riahi, D. N. 2014 On the three-dimensional non-linear buoyant convection in ternary solidification. Transp. Porous Media 103, 249-277. [9.1.6.4]

    Article  MathSciNet  Google Scholar 

  • Riahi, D. N. 2016 Effect of low rotation rate on steady convection during the solidification of a ternary alloy. Transp. Porous media, to appear. [10.2.3]

    Google Scholar 

  • Riahi, D. N. and Sayre, T. L. 1996 Effect of rotation on the structure of a convecting mushy layer. Acta Mech. 118, 109-119. [10.2.3]

    Article  MATH  Google Scholar 

  • Roberts, P. H. and Loper, D. E. 1983 Towards a theory of the structure and evolution of a dendrite layer. Stellar and Planetary Magnetism (ed. A. M. Soward), Gordon and Braech, New York, 329-349. [10.2.3]

    Google Scholar 

  • Roberts, P. H., Loper, D. E. and Roberts, M. F. 2003 Convective instability of a mushy layer: I. Uniform permeability. Geophys. Astrophys. Fluid Dyn. 97, 97-134. [10.2.3]

    Article  MathSciNet  MATH  Google Scholar 

  • Rocha, L. A. O., Neagu, M., Bejan, A. and Cherry, R. S. 2001 Convection with phase change during gas formation from methane hydrates via depressurization of porous layers. J. Porous Media 4, 283-295. [10.1.7]

    Article  MATH  Google Scholar 

  • Rodrigues, J. F. and Urbano, J. M. 1999 Darcy-Stefan problem arising in freezing and thawing of saturated porous media. Cont. Mech. Thermodyn. 11, 181-191. [10.2.1.2]

    Article  MathSciNet  MATH  Google Scholar 

  • Roper, S. M., Davis, S. H. and Voorhees, P. W. 2007 Convection in a mushy zone forced by sidewall heat losses. Metall. Mater. Trans. A. 38, 1069-1079. [10.2.3]

    Article  Google Scholar 

  • Roper, S. M., Davis, S. H. and Voorhees, P. W. 2011 Localization of convection in mushy layers by weak background flow. J. Fluid Mech. 675, 518-528. [10.2.3]

    Article  MathSciNet  MATH  Google Scholar 

  • Sahli, A., Moyne, C. and Stemmelen, D. 2010 Boiling stability in a porous medium heated from below. Transp. Porous Media 82, 527-545. [10.3.1]

    Article  MathSciNet  Google Scholar 

  • Saija, U. K., Udaya, K. and Felicelli, S. D. 2011 Modeling freckle segregation with mesh adaptation. Metal. Mat. Trans. B 42, 1118-1129. [10.2.3]

    Article  Google Scholar 

  • Sasaguchi, K. 1995 Effect of density inversion of water on the melting process of frozen porous media. Proc. ASME/JSME Thermal Engineering Joint Conf.,. vol. 3, pp.371-378. [10.1.7]

    Google Scholar 

  • Sasaki, A., Aiba, S. and Fukusako, S. 1990 Numerical study on freezing heat transfer in water-saturated porous media. Numer. Heat Transfer A 18, 17-32. [10.2.1.2]

    Article  Google Scholar 

  • Sasaki, A., and Aiba, S. 1992 Freezing heat transfer in water-saturated porous media in a vertical rectangular vessel. Wärme-Stoffübertrag., 27, 289-298. [10.2.1.2]

    Article  Google Scholar 

  • Sayre, T. L. and Riahi, D. N. 1996 Effect of rotation on flow instabilities during solidification of a binary alloy. Int. J. Engng Sci. 34, 1631-1645. [10.2.3]

    Article  MATH  Google Scholar 

  • Sayre, T. L. and Riahi, D. N. 1997 Oscillatory instabilities of the liquid and mushy layers during solidification of alloys under rotational constraint. Acta Mech. 121, 143-152. [10.2.3]

    Article  MATH  Google Scholar 

  • Schneider, M. C. and Beckermann, C. 1995 A numerical study of the combined effects of microsegregation, mushy zone permeability and flow, caused by volume contraction and thermosolutal convection, on macrosegregation and eutectic formation in binary alloy solidification. Int. J. Heat Mass Transfer 38, 3455-3473. [10.2.3]

    Article  MATH  Google Scholar 

  • Schubert, G. and Straus, J. M. 1977 Two-phase convection in a porous medium. J. Geophys. Res. 82, 3411-3421. [10.3.1]

    Article  Google Scholar 

  • Schubert, G. and Straus, J. M. 1980 Gravitational stability of water over steam in vapor-dominated geothermal systems. J. Geophys. Res. 85, 6505-6512. [10.3.1]

    Article  Google Scholar 

  • Schulze, T. P. and Worster, M. G. 1998 A numerical investigation of steady convection in mushy layers during the directional solidification of binary alloys. J. Fluid Mech. 356, 199-220. [10.2.3]

    Article  MATH  Google Scholar 

  • Schulze, T. P. and Worster, M. G. 1999 Weak convection, liquid inclusions and the formation of chimneys in mushy layers. J. Fluid Mech. 388, 197-215. [10.2.3]

    Article  MATH  Google Scholar 

  • Shao, J. Liu, Y. and Xu, Y. 2011 Lattice Boltzmann simulation on natural convection heat transfer for phase change with heterogeneously porous medium. Adv. Mater. Res. 322, 61-67. [10.1.7]

    Article  Google Scholar 

  • Shih, M. H., Huang, M. J. and Chen, C. K. 2005 A study of the liquid evaporation with Darcian resistance effect on mixed convection in porous media. Int. Comm. Heat Mass Transfer 32, 685-694. [10.3.2]

    Article  Google Scholar 

  • Shih, M. H., Luo, W. J. and Yu, K. C. 2008 Evaporation of non-Newtonian fluid in porous medium under mixed convection. J. Mech. 24, 153-162. [10.3.2]

    Article  Google Scholar 

  • Sinha, S. K., Sundararajan, T. and Garg, V. K. 1992 A variable property analysis of alloy solidification using the anisotropic porous medium approach. Int. J. Heat Mass Transfer 35, 2865-2877. [10.2.3]

    Article  MATH  Google Scholar 

  • Sinha, S. K., Sundararajan, T. and Garg, V. K. 1993 A study of the effects of macrosegregation and buoyancy-driven flow in binary mixture solidification. Int. J. Heat Mass Transfer 36, 2349-2358. [10.2.3]

    Article  MATH  Google Scholar 

  • Skudarnov, P. V., Lin, C. X., Wang, M. H., Pradeep, N. and Ebadian, M. A. 2002 Evolution of convection pattern during the solidification process of a binary mixture: effect of initial solutal concentration. Int. J. Heat Mass Transfer 45, 5191-5200. [10.2.3]

    Article  Google Scholar 

  • Smith, C. 2006 Influence of density inversion on thawing round a cylinder in a frozen saturated porous medium. Transport Porous Media 63, 223-237. [10.1.7]

    Article  Google Scholar 

  • Solomon, T. H. and Hartley, R. R. 1998 Measurements of the temperature field of mushy and liquid regions during solidification of aqueous ammonium chloride. J. Fluid Mech. 358, 87-106. [10.2.3]

    Article  Google Scholar 

  • Sondergeld, C. H. and Turcotte, D. L. 1977 An experimental study of two-phase convection in a porous medium with applications to geological problems. J. Geophys. Res. 82, 2045-2053. [10.3.1]

    Article  Google Scholar 

  • Sondergeld, C. H. and Turcotte, D. L. 1978 Flow visualization studies of two-phase thermal convection in a porous layer. Pure Appl. Geophys. 117, 321-330. [10.3.1]

    Article  Google Scholar 

  • Song, M. and Viskanta, R. 2001 Lateral freezing of an anisotropic porous medium saturated with an aqueous salt solution. Int. J. Heat Mass Transfer 44, 733-751. [10.2.1.2]

    Article  MATH  Google Scholar 

  • Song, M., Choi, J. and Viskanta, R. 1993 Upward solidification of a binary solution saturated porous medium. Int. J. Heat Mass Transfer 36, 3687-3695. [10.2.3]

    Article  Google Scholar 

  • Sözen, M. and Vafai, K. 1990 Analysis of the non-thermal equilibrium condensing flow of a gas through a packed bed. Int. J. Heat Mass Transfer 33, 1247-1261. [4.6.5, 10.4]

    Article  Google Scholar 

  • Srivastava, A. K. and Bhadauria, B. S. 2011 Linear stability of solutal convection in a mushy layer subjected to gravity modulation. Comm. Nonlinear Sci. Numer. Simul. 16, 3548-3558. [10.2.3]

    Article  MathSciNet  MATH  Google Scholar 

  • Stemmelen, D., Moyne, C. and Degiovanni, A. 1992 Thermoconvective instability of a boiling liquid in porous medium. C.R. Acad. Sci. Paris, Sér. II, 314, 769-775. [10.3.1]

    Google Scholar 

  • Sugawara, M., Inaba, H. and Seki, N. 1988 Effect of maximum density of water on freezing of a water-saturated horizontal porous layer. ASME J. Heat Transfer 110, 155-159. [10.2.2]

    Article  Google Scholar 

  • Sura Ram Prasad J. and Hemalatha, K. 2016 A study on mixed convective MHD flow from a vertical plate embedded in a non -Newtonian fluid saturated non-Darcy porous medium with melting effect. [10.1.7]

    Google Scholar 

  • Tait, S. and Jauport, C. 1992 Compositional convection in a reactive crystalline mush and melt differentiation. J. Geophys. Res. 97, 6735-6756. [10.2.3]

    Article  Google Scholar 

  • Tait, S., Jahrling, K. and Jaupart, C. 1992 The platform of compositional convection and chimney formation in a mushy layer. Nature 359, 406-408. [10.2.3]

    Article  Google Scholar 

  • Tashtoush, B. 2005 Magnetic and buoyancy effects on melting from a vertical plate embedded in saturated porous media. Energy Conv. Manag. 46, 2566-2577. [10.1.7]

    Article  Google Scholar 

  • Tewari, P. K. 1982 A study of boiling and convection in fluid-saturated porous media. MS thesis, Cornell University. [10.3.1]

    Google Scholar 

  • Thompson, A. F., Huppert, H. E., Worster, G. M. and Aitta, A. 2003 Solidification and compositional convection of a ternary alloy. J. Fluid Mech. 497, 167-199. [10.2.3]

    Article  MathSciNet  MATH  Google Scholar 

  • Tian, Y. and Zhao, C. Y. 2011a A numerical investigation of heat transfer in phase change materials (PCMs) embedded in porous metals. Energy 36, 5539-5546. [10.1.7]

    Article  Google Scholar 

  • Tian, Y. and Zhao, C. Y. 2011b Natural convection investigations in porous phase change materials. Nanoscience Nanotech. Lett. 3, 769-772. [10.1.7]

    Article  Google Scholar 

  • Toda, S., Hsu, W. S., Hashizume, H. and Kawaguchi, T. 1998 Unsteady heat transfer of steam flow with condensation in porous media. Heat Transfer 1998, Proc. 11 th IHTC, 6, 463-468. [10.4]

    Google Scholar 

  • Tong, X., Khan, J. A. and Amin, M. R. 1996 Enhancement of heat transfer by inserting a metal matrix into a phase change material. Numer. Heat Transfer 30, 125-141.[10.1.7]

    Article  Google Scholar 

  • Tsuchiya, K. and Okada, M. 1995 Solidification around a horizontal cylinder in a porous medium saturated with aqueous solution (influence of natural convection and forced convection). Trans. Japan Soc. Mech. Engnrs. B 61, 4123-4129. [10.2.1.2]

    Article  Google Scholar 

  • Vafai, K. and Sarkar, S. 1986 Condensation effects in a fibrous insulation slab. ASME J. Heat Transfer 108, 667-675. [10.4]

    Article  Google Scholar 

  • Vafai, K. and Sarkar, S. 1987 Heat and mass transfer in partial enclosures. AIAA J. Thermophys. Heat Transfer 1, 253-259. [10.4]

    Article  Google Scholar 

  • Vafai, K. and Whitaker, S. 1986 Simultaneous heat and mass transfer accompanied by phase change in porous insulation. ASME J. Heat Transfer 108, 132-140. [10.4]

    Article  Google Scholar 

  • Veinberg, A. K. 1967 Permeability, electrical conductivity, dielectric constant and thermal conductivity of a medium with spherical and ellipsoidal inclusions. Soviet Phys. Dokl. 11, 593-595. [10.1.6]

    Google Scholar 

  • Verma, S. and Dewan, A. 2016 Solidification with buoyancy induced convection: Evaluation of different mushy zone formulations. Proc. Indian Nat. Sci. Acad. 82, 309–319. [10.2.3]

    Google Scholar 

  • Vigo, T. L. and Bruno, J. S., 1987 Temperature-adaptable textiles containing durably bound polyethylene glycols. Textile Res. J. 57, 427-429. [10.5]

    Article  Google Scholar 

  • Wang, C. Y. 1998b Onset of natural convection in a fluid-saturated porous medium inside a cylindrical enclosure bottom heated by constant flux. Int. Comm. Heat Mass Transfer 25, 593-598. [6.16.1]

    Article  Google Scholar 

  • Wang, C. Y. and Beckermann, C. 1993 A two-phase model of liquid-gas flow and heat transfer in capillary porous media. — II. Application to pressure-driven boiling flow adjacent to a vertical heated plate. Int. J. Heat Mass Transfer 36, 2759-2768. [10.3.1]

    Article  MATH  Google Scholar 

  • Wang, C. Y. and Beckermann, C. 1995 Boundary layer analysis of buoyancy driven two-phase flow in capillary porous media. ASME J. Heat Transfer 117, 1082-1087. [10.3.1, 10.4]

    Article  Google Scholar 

  • Wang, C. Y., Beckermann, C. and Fan, C. 1994a Transient natural convection and boiling in a porous layer heated from below. Heat Transfer 1994, Inst. Chem. Engrs, Rugby, vol 5, pp. 411-416. [10.3.1]

    Google Scholar 

  • Wang, C. Y., Beckermann, C. and Fan, C. 1994b Numerical study of boiling and natural convection in capillary porous media using the two-phase mixture model. Numer. Heat Transfer A 26, 375-398. [10.3.1]

    Article  Google Scholar 

  • Wang, C. Y., Wu, C. Z., Tu, C. J. and Fukusako, S. 1990a Freezing around a vertical cylinder immersed in porous media incorporating the natural convection effect. Wärme-Stoffübertrag. 26, 7-15. [10.2.1.2]

    Article  Google Scholar 

  • Wang, C., Tu, C. and Zhang, X. 1990b Mixed convection of non-Newtonian fluids from a vertical plate embedded in a porous medium. Acta Mech. Sinica 6, 214-220. [8.1.1]

    Article  MATH  Google Scholar 

  • Wang, S. C., Yang, Y. T. and Chen, C. K. 2003d Effect of uniform suction on laminar filmwise condensation on a finite-size horizontal flat surface in a porous medium. Int. J. Heat Mass Transfer 46, 4003-4011. [10.4]

    Article  MATH  Google Scholar 

  • Ward, J. C. 1964 Turbulent flow in porous media. ASCE J. Hydraul. Div. 90 (HY5), 1-12. [1.5.2, 10.1.6]

    Google Scholar 

  • Weaver, J. A. and Viskanta, R. 1986 Freezing of liquid saturated porous media. ASME J. Heat Transfer 108, 654-659. [10.2.2]

    Article  Google Scholar 

  • Weber, J. E. 1975a Thermal convection in a tilted porous layer. Int. J. Heat Mass Transfer 18, 474-475. [7.8]

    Article  Google Scholar 

  • Wells, A. J., Wettlaufer, J. S. and Orszag, S. A. 2013 Nonlinear mushy layer convection with chimneys: stability and optimal heat fluxes. J. Fluid Mech. 716, 203-227. [10.2.3]

    Article  MathSciNet  MATH  Google Scholar 

  • Wells, A. J., Wettlaufer, J. S. and Orszag, S. A. 2010 Maximal potential energy transport: A variational principle for solidification problems. Phys. Rev. Lett. 105, #254502. [10.2.3]

    Article  Google Scholar 

  • Wettlaufer, J. S., Worster, M. G. and Huppert, H. E. 1997 Natural convection during solidification of an alloy from above with application to the evolution of sea ice. J. Fluid Mech. 344, 291-316. [10.2.3]

    Article  Google Scholar 

  • White, S. M. and Tien, C. L. 1987 Analysis of laminar film condensation in a porous medium. Proceedings 1987 ASME JSME Thermal Engineering Joint Conference, ASME, New York, vol. 2, pp. 401-406. [10.4]

    Google Scholar 

  • Worster, M. G. 1991 Natural convection in a mushy layer. J. Fluid Mech. 224, 335-359. [10.2.3]

    Article  MATH  Google Scholar 

  • Worster, M. G. 1992 Instabilities of the liquid and mushy regions during solidification of alloys. J. Fluid Mech. 237, 649-669. [10.2.3]

    Article  MATH  Google Scholar 

  • Worster, M. G. 1997 Convection in mushy layers. Annu. Rev. Fluid Mech. 29, 91-122. [10.2.3]

    Article  MathSciNet  Google Scholar 

  • Worster, M. G. 2000 Solidification of fluids. Perspectives in Fluid Dynamics (eds. G. K. Batchelor, H. K. Moffat and M. G. Worster), Cambridge University press, Cambridge, UK, pp. 393-446. [10.2.3]

    Google Scholar 

  • Worster, M. G. and Kerr, R. C. 1994 The transient behavior of alloys solidified from below prior to the formation of chimneys. J. Fluid Mech. 269, 23-44. [10.2.3]

    Article  Google Scholar 

  • Yang, C. H., Rastrogi, S. K. and Poulikakos, D. 1993a Freezing of a water-saturated inclined packed bed of beads. Int. J. Heat Mass Transfer 36, 3583-3592. [10.2.1.2]

    Article  Google Scholar 

  • Yang, C. H., Rastrogi, S. K. and Poulikakos, D. 1993b Solidification of a binary mixture saturating an inclined bed of packed spheres. Int. J. Heat Fluid Flow 14, 268-278. [10.2.3]

    Article  Google Scholar 

  • Yang, Z. and Garimella, S. V. 2010 Melting of phase change materials with volume change in metal foams. ASME J. Heat Transfer 132, #062301. [10.1.7]

    Google Scholar 

  • Yih, K. A. 1999b Uniform transpiration effect of coupled heat and mass transfer, in mixed convection about inclined surfaces in porous media: the entire regime. Acta Mech. 132, 229-240. [9.6.1,10.3.2]

    Article  MATH  Google Scholar 

  • Yoo, H and Viskanta, R. 1992 Effect of anisotropic permeability in the transport process during solidification of a binary mixture. Int. J. Heat Mass Transfer 35, 2335-2346. [10.2.3]

    Article  Google Scholar 

  • Zhang, X. 1993 Natural convection and heat transfer in a vertical cavity filled with an ice-water saturated porous medium. Int. J. Heat Mass Transfer 36, 2881-2890. [10.1.7]

    Article  Google Scholar 

  • Zhang, X. and Nguyen, T. H. 1990 Development of convective flow during the melting of ice in a porous medium heated from above. ASME HTD 156, 1-6. [10.1.7]

    Google Scholar 

  • Zhang, X. L. and Nguyen, T. H. 1994 Numerical study of convection heat transfer during the melting of ice in a porous layer. Numer. Heat Transfer A 25, 559-574. [10.1.7]

    Article  Google Scholar 

  • Zhang, X. L. and Nguyen, T. H. 1999 Solidification of a superheated fluid in a porous medium: effects of convection. Int. J. Numer. Meth. Heat Fluid Flow 9, 72-91. [10.2.2]

    Article  MATH  Google Scholar 

  • Zhang, X. L., Nguyen, T. H. and Kawawita, R. 1997 Effects of anisotropy in permeability on two-phase flow and heat transfer in porous cavity. Heat Mass Transfer 32, 167-174. [10.1.7]

    Article  Google Scholar 

  • Zhang, X., Nguyen, T. H. and Kahawita, R. 1991a Melting of ice in a porous medium heated from below. Int. J. Heat Mass Transfer 34, 389-405. [10.1.7]

    Article  Google Scholar 

  • Zhang, Z., Bejan, A. and Lage, J. L 1991b Natural convection in a vertical enclosure with internal permeable screen. ASME J. Heat Transfer 113, 377-383. [7.7].

    Article  Google Scholar 

  • Zhao, T. S. 1999 Coupled heat and mass transfer of a stagnation point flow in a heated porous bed with liquid film evaporation. Int. J. Heat Mass Transfer 42 861-872. [10.3.2]

    Article  MATH  Google Scholar 

  • Zhong, J. Q., Fragaso, A. T., Wells, A. J. and Wettlaufer, J. S. 2012 Finite-sample-size effects on convection in mushy layers. J. Fluid Mech. 704, 89-108. [10.2.3]

    Article  MATH  Google Scholar 

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  1. Department of Engineering Science, University of Auckland, Auckland, New Zealand

    Donald A. Nield

  2. Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC, USA

    Adrian Bejan

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Nield, D.A., Bejan, A. (2017). Convection with Change of Phase. In: Convection in Porous Media. Springer, Cham. https://doi.org/10.1007/978-3-319-49562-0_10

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  • Online ISBN: 978-3-319-49562-0

  • eBook Packages: EngineeringEngineering (R0)

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