Melting and Freezing

Advances in Heat Transfer

Volumn 19, Issue C, 1989, Pages 1-95

  Yao, L S ^a   Prusa, J ^b  

^a ARIZONA STATE UNIVERSITY   (United States)

^b IOWA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0344407902     PISSN: 00652717     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0065-2717(08)70211-9     Document Type: Article

References (280)

1. Lunardini, V.J., “Heat Transfer in Cold Climate, 1981, Van Nostrand-Reinhold, Princeton, New Jersey.
2. Bankoff, S.G., Heat conduction or diffusion with change of phase. Adv. Chem. Eng., 5, 1964, 75.
3. Goodman, T.R., Application of integral methods to transient nonlinear heat transfer. Adv. Heat Transfer, 1, 1964, 71.
4. Rubinstein, L.I., The Stefan problem. Am. Math. Soc. Transl. Math. Monogr., 27, 1971.
5. Ockendon, J.R., Hodgkins, W.R., “Moving Boundary Problems in Heat Flow and Diffusion”, 1975, Oxford Univ. Press (Clarendon), London and New York.
6. Wilson, D.G., Solomon, A.D., Boggs, P.T., “Moving Boundary Problems”, 1978, Academic Press, New York.
7. Crank, J., “Free and Moving Boundary Problems”, 1984, Oxford Univ. Press (Clarendon), London and New York.
8. Viskanta, R., Phase change heat transfer. Lane, G.A., (eds.) “Solar Heat and Storage: Latent Heat Materials”, 1983, CRC Press, Boca Raton, Florida, 153.
9. Viskanta, R., Natural convection in melting and solidification. Kakac, S., Aung, W., Viskanta, R., (eds.) “Natural Convection: Fundamentals and Applications, 1985, Hemisphere, Washington, D.C., 845.
10. Epstein, M., Cheung, F.B., Complex freezing-melting interfaces in fluid flow. Annu. Rev. Fluid Mech., 15, 1983, 293.
11. Cheung, F.B., Epstein, M., Solidification and melting in fluid flow. Adv. Transp. Processes, 3, 1984, 35.
12. Carslaw, H.S., Jaeger, J.C., “Conduction of Heat in Solids”, 2nd Ed., 1959, Oxford Univ. Press, London and New York, 283–353.
13. Muehlbauer, J.C., Sunderland, J.E., Heat conduction with a freezing or melting. Appl. Mech. Rev., 18, 1965, 951.
14. Stefan, J., Ueber die Theorie der, Eisbildung, Insbesondere ueber die Eisbildung im Polarmeere. Ann. Phys. Chem., N. S., 42, 1891, 269.
15. Boltzmann, L., Zur Integration der Diffusiongleichung bei variabeln Diffusionscoefficienten. Ann. Phys. Chem., S.3, 1894, 53 959.
16. Taylor, A.B., The mathematical formulation of Stefan problems. “Moving Boundary Problems in Heat Flow and Diffusion”. Proc. Univ. Oxford, 1974, 120 March 25-27.
17. Fox, L., What are the best numerical methods? “Moving Boundary Problems in Heat Flow and Diffusion”. Proc. Univ. Oxford, 1974, 210 March 25-27.
18. Yao, L.S., Cherney, W., Transient phase-change around a horizontal cylinder. Int. J. Heat Mass Transfer, 24, 1981, 1971.
19. Budhia, H., Kreith, F., Heat transfer with melting or freezing in a wedge. Int. J. Heat Mass Transfer, 16, 1973, 195.
20. Cho, S.H., Sunderland, J.E., Approximate temperature distribution for phase change of a semi-infinite body. J. Heat Transfer, 103, 1981, 401.
21. Tokuda, N., An asymptotic, large time solution of the convection Stefan problem with surface radiation. Int. J. Heat Mass Transfer, 29, 1986, 135.
22. Prusa, J., A spatial Stefan problem modified by natural convection. Melting around a horizontal cylinder, 1983, Univ. of Illinois at Urbana-Champaign Ph. D. Dissertation.
23. Tao, L.N., On free boundary problems with radiation boundary conditions,”. Q. J. Mech. Appl. Math., 37, 1979, 1.
24. Tao, L.N., The exact solutions of some Stefan problems with prescribed heat flux. J. Heat Transfer, 48, 1981, 732.
25. Tao, L.N., On free boundary problems with arbitrary initial and flux conditions. J. Appl. Math. Phys. (ZAMP), 30, 1979, 416.
26. Evans, G.W., Isaacson, E., MacDonald, J.K.L., Stefan-like problems. Q. J. Appl. Math., 8, 1950, 312.
27. Boley, B.A., The embedding technique in melting and solidification problems. “Moving Boundary Problems in Heat Flow and Diffusion”. Proc. Conf. Univ. Oxford, March 25-27, 1974, 150.
28. Elliot, C.M., Ockendon, J.R., “Weak and Variational Methods for Moving Boundary Problems”, 1982 Research Notes in Mathematics 59. Pitman Advanced Publishing Program, Boston.
29. Ockendon, J.R., Techniques of analysis. “Moving Boundary Problems in Heat Flow and Diffusion”. Proc. Conf. Univ. Oxford, March 25-27, 1974, 138.
30. Sikarskie, D.L., Boley, B.A., The solution of a class of two-dimensional melting and solidification problems. Int. J. Solids Struct., 1, 1965, 207.
31. Prandtl, L., AurBerechung der Grenzschichten. Z. Angew. Math. Mech., 18, 1938, 77.
32. Rosenhead, L., (eds.) “Laminar Boundary Layers,”, 1963, Oxford Univ. Press (Clarendon), London and New York Also.
33. Zener, C., Theory of growth of spherical precipitates from solid solution. J. Appl. Phys., 20, 1949, 950.
34. Landau, H.G., Heat conduction in a melting solid. Q. Appl. Math., 8, 1949, 81.
35. Yang, K.T., Formation of ice in plane stagnation flow. Appl. Sci. Res., 17, 1967, 377.
36. Duda, J.L., Malone, M.F., Notter, R.H., Vrentas, J.S., Analysis of two-dimensional diffusion-controlled moving boundary problems. Int. J. Heat Mass Transfer, 18, 1975, 901.
37. Saitoh, T., Numerical method for multidimensional freezing problems in arbitrary domains. J. Heat Transfer, 100, 1978, 294.
38. Sparrow, E.M., Ramadhyani, S., Patankar, S.V., Effect of subcooling on cylindrical melting. J. Heat Transfer, 100, 1978, 395.
39. Tien, L.C., Churchill, S.W., Freezing front motion and heat transfer outside an infinite, isothermal cylinder. AIChE J., 11, 1965, 790.
40. Hill, J.M., Kucera, A., Freezing a saturated liquid inside a sphere. Int. J. Heat Mass Transfer, 26, 1983, 1631.
41. Kassinos, A., Prusa, J., Effects of density change and subcooling on the melting of a solid in a rectangular enclosure. Proc. Int. Heat Transfer Conf., 8th, San Francisco, 4, 1986, 1787.
42. Furzeland, R.M., A comparative study of numerical methods for moving boundary problems. J. Inst. Math. Appl., 26, 1980, 411.
43. Yao, L.S., Analysis of heat transfer in slightly eccentric annuli. J. Heat Transfer, 102, 1980, 279.
44. Murray, W.D., Landis, F., Numerical and machine solutions of transient heatconduction problems involving melting or freezing; Part I - Method of analysis and sample solutions. J. Heat Transfer, 81, 1959, 106.
45. Pujado, P.R., Stermole, F.J., Golden, J.O., Melting of a finite paraffin slab as applied to phase-change thermal control. J. Space Rockets, 6, 1969, 280.
46. Lynch, D.R., O' Neill, K., Continuously deforming finite elements for the solution of parabolic problems, with and without phase change. Int. J. Numer. Methods Eng., 17, 1981, 81.
47. Duda, J.L., Vrentas, J.S., Perturbation solutions of diffusion-controlled moving boundary problems. Chem. Eng. Sci., 24, 1969, 461.
48. Crank, J., Two methods for the numerical solution of moving-boundary problems in diffusion and heat flow. Q. J. Mech. Appl. Math., 10, 1957, 220.
49. Atthey, D.R., A finite difference scheme for melting problems based on the method of weak solutions. “Moving Boundary Problems in Heat Flow and Diffusion”. Proc. Conf. Univ. Oxford. March 25-27, 1974, 182.
50. Furzeland, R.M., Symposium on free and moving boundary problems in heat flow and diffusion, University of Durham, July, 1978. Inst. Math. Appl., 15, 1979, 172.
51. Baxter, D.C., The fusion times of slabs and cylinders. J. Heat Transfer, 84, 1962, 317.
52. Shamsundar, N., Sparrow, E.M., Analysis of multidimensional conduction phase change via the enthalpy model. J. Heal Transfer, 97, 1975, 333.
53. Boucheron, E.A., Smith, R.N., An enthalpy formulation of the simple algorithm for phase change heat transfer problems. ASME/AIChE Natl. Heat Transfer Conf., 23rd, Denver, August 4-7 85-HT-7, 1985.
54. Schneider, G.E., Raw, M.J., An implicit solution procedure for finite difference modeling of the Stefan problem. AIAA J., 22, 1984, 1685.
55. Voller, V., Cross, M., Accurate solutions of moving boundary problems using the enthalpy method. Int. J. Heat Mass Transfer, 24, 1981, 545.
56. Goodrich, L.E., Efficient numerical technique for one-dimensional thermal problems with phase change. Int. J. Heat Mass Transfer, 21, 1978, 615.
57. Pham, Q.T., A fast, unconditionally stable finite-difference scheme for heat conduction with phase change. Int. J. Heat Mass Transfer, 28, 1985, 2079.
58. Pham, Q.T., The use of lumped capacitance in the finite-element solution of heat conduction problems with phase change. Int. J. Heat Mass Transfer, 29, 1986, 285.
59. Weinbaum, S., Jiji, L.M., Singular perturbation theory for melting or freezing in finite domains not at the fusion temperature. J. Appl. Meek, 44, 1977, 25.
60. Charach, Ch., Zoglin, P., Solidification in a finite, initially overheated slab. Int. J. Heat Mass Transfer, 28, 1985, 2261.
61. Pedroso, R.I., Domoto, G.A., Exact solution by perturbation method for planar solidification of a saturated liquid with convection at the wall. Int. J. Heat Mass Transfer, 16, 1973, 1816.
62. Jiji, L.M., Weinbaum, S., Perturbation solutions for melting or freezing in annular regions initially not at the fusion temperature. Int. J. Heat Mass Transfer, 21, 1978, 581.
63. Pedroso, R.I., Domoto, G.A., Inward spherical solidification-solution by the method of strained coordinates. Int. J. Heat Mass Transfer, 16, 1973, 1037.
64. Tao, L.C., Generalized numerical solution of freezing in a saturated liquid in cylinders and spheres. A. I. Ch. E. J., 13, 1967, 165.
65. Van Dyke, M., “Perturbation Methods in Fluid Mechanics”, 1975, The Parabolic Press, Stanford, California.
66. Riley, D.S., Smith, F.T., Poots, G., The inward solidification of spheres and circular cylinders. Int. J. Heat Mass Transfer, 17, 1974, 1507.
67. Seeniraj, R.V., Bose, T.K., One-dimensional phase-change problems with radiation convection. J. Heat Transfer, 104, 1982, 811.
68. Yan, M.M., Huang, P.N.S., Perturbation solutions to phase-change problem subject to convection and radiation. J. Heat Transfer, 101, 1979, 96.
69. Seeniraj, R.V., Perturbation solutions to phase-change problem subject to convection and radiation. Letter to the Editor. J. Heat Transfer, 102, 1980, 395.
70. Goodman, T.R., The heat-balance integral and its application to problems involving a change of phase. ASME Trans., 80, 1958, 335.
71. Mennig, J., Ozisik, M.N., Coupled integral equation approach for solving melting or solidification. Int. J. Heat Mass Transfer, 28, 1985, 1481.
72. Steward, W.E., Smith, K.L., Inward solidification of water in a cylinder-An analytical and experimental study. ASME/AIChE Natl. Heat Transfer Conf., 23rd. Denver. August 4-7 85-HT-2, 1985.
73. Bell, G.E., Solidification of a liquid about a cylindrical pipe. Int. J. Heat Mass Transfer, 22, 1979, 1681.
74. Lunardini, V.J., Phase change around a circular cylinder. J. Heat Transfer, 103, 1981, 598.
75. Milanez, L.F., Ismail, K.A.R., Solidification in spheres-theoretical and experimental investigation. Veziroglu, T.N., Bergles, A.E., (eds.) “Multi-Phase Flow and Heat Tranfer III. Part B: Applications”, 1984, Elsevier, Amsterdam, 565.
76. Rao, V.D., Sarma, P.K., Direct contact heat transfer in spherical geometry associated with phase transformation-A closed-form solution. Int. J. Heat Mass Transfer, 28, 1985, 1956.
77. Chung, B.T.F., Yeh, L.T., Solidification and melting of materials subject to convection and radiation. J. Spacecraft, 12, 1975, 329.
78. Habib, I.S., Solidification of semi-transparent materials by conduction and radiation. Int. J. Heat Mass Transfer, 14, 1971, 2161.
79. Habib, I.S., Solidification of a semi-transparent cylindrical medium by conduction and radiation. J. Heat Transfer, 95, 1973, 37.
80. Breinan, E.M., Kear, B.H., Banas, C.M., Processing materials with lasers. Phys. Today, 29, 1976, 44.
81. Giles, G.E., Kirkpatrick, J.R., Wood, R.F., Laser annealing of solar cell wafers. ASME Natl. Heat Transfer Conf, 19th, Orlando, July 27-30 80-HT-13, 1980.
82. Gelder, D., Guy, A.C., Current problems in the glass industry. Ockendon, J.R., Hodgkins, W.R., (eds.) “Moving Boundary Melting and Freezing Problems in Heat Flow and Diffusion”, 1975, Oxford Univ. Press (Clarendon), London and New York.
83. Smith, R.N., Ebersole, T.E., Griffi, E.P., Exchanger performances in latent heat thermal storage. ASME J. Sol. Energy, 102, 1980.
84. Maeno, N., Integral and surface melting of ice. Low-Temp. Sci., 28, 1978, 22.
85. Seki, N., Sugawara, M., Fukusako, S., Radiative melting of ice layer adhering to a vertical surface. Wärme-Stoffubertrag., 12, 1979, 137.
86. Chan, S.H., Cho, D.H., Kocamustafaogullari, G., Melting and solidification with internal radiative transfer-A generalized phase change model. Int. J. Heat Mass Transfer, 26, 1983, 621.
87. Oruma, F.O., Ozisik, M.N., Boles, M.A., Effects of non-grayness on melting and solidification of a semi-infinite, semi-transparent medium. J. Franklin Inst., 319, 1985, 459.
88. Oruma, F.O., Ozisik, M.N., Boles, M.A., Effects of anisotropic scattering on melting and solidification of a semi-infinite, semi-transparent medium. Int. J. Heat Mass Transfer, 28, 1985, 441.
89. Siegel, R., Boundary perturbation methods for free boundary problem in convectively cooled continuous casting. J. Heat Transfer, 108, 1986, 230.
90. Siegel, R., Free boundary shape of a convectively cooled solidified region. Int. J. Heat Mass Transfer, 29, 1986, 309.
91. Agrawal, H.C., Biot's variational principle for moving boundary problems. “Moving Boundary Problems in Heat Flow and Diffusion.”. Proc. Conf. Univ. Oxford, March 25-27, 1974, 242.
92. Duvaut, G., The solution of a two-phase Stefan problem by a variational inequality. “Moving Boundary Problems in Heat Flow and Diffusion.”. Proc. Conf. Univ. Oxford, March 25-27, 1974, 173.
93. Crank, J., Finite-difference methods. “Moving Boundary Problems in Heat Flow and Diffusion.”. Proc. Conf. Univ. Oxford. March 25-27, 1975, 192.
94. Crank, J., Gupta, R.S., Isotherm migration method in two dimensions. Int. J. Heat Mass Transfer, 18, 1975, 1101.
95. Frederick, D., Greif, R., A method for the solution of heat transfer problems with a change of phase. J. Heat Transfer, 107, 1985, 520.
96. Goodling, J.S., Khader, M.S., Inward solidification with radiation-convection boundary condition. J. Heat Transfer, 96, 1974, 114.
97. Abrams, M., Viskanta, R., The effects of radiative heat transfer upon the melting and solidification of semi-transparent crystals. J. Heat Transfer, 96, 1974, 184.
98. Seki, N., Sugawara, M., Fukusako, S., Back-melting of a horizontal cloudy ice layer with radiative heating. J. Heat Transfer, 101, 1979, 90.
99. Diaz, L.A., Viskanta, R., Experiments and analysis on the melting of a semi-transparent material by radiation. Wärme Stoffiibertrag., 20, 1986, 311.
100. Chuang, Y.K., Szekely, J., On the use of greens function for solving melting and solidification problems. Int. J. Heat Mass Transfer, 14, 1971, 1285.
101. Banerjee, P.K., Shaw, R.P., Boundary element formulation for melting and solidification problems. Banerjee, P.K., Shaw, R.P., (eds.) “Developments in Boundary Element Methods-2, 1982, Applied Science Publ, London, 1.
102. Sadegh, A.M., Jiji, L.M., Weinbaum, S., Boundary integral equation technique with application to freezing around a buried pipe. ASME Winter Annu. Meet., Miami Beach, November 17-22 85-WA/HT-73, 1985.
103. Tien, C., Yen, Y.-C., Approximate solution of a melting problem with natural convection. AIChE J., 62, 1966, 166.
104. Boger, D.V., Westwater, J.W., Effect of buoyancy on the melting and freezing process. J. Heat Transfer, 89, 1967, 81.
105. Heitz, W.L., Westwater, J.W., Extension of the numerical method for melting and freezing problems. Int. J. Heat Mass Transfer, 13, 1970, 1371.
106. Hale, N.W. Jr., Viskanta, R., Solid-liquid phase-change heat transfer and interface motion in materials cooled or heated from above or below. Int. J. Heat Mass Transfer, 23, 1980, 283.
107. Bathelt, A.G., Viskanta, R., Leidenfrost, W., An experimental investigation of natural convection in the melted region around a heated horizontal cylinder. J. Fluid Mech., 90, 1979, 227.
108. Bathelt, A.G., Viskanta, R., Heat transfer at the solid-liquid interface during melting from a horizontal cylinder. Int. J. Heat Mass Transfer, 23, 1980, 1493.
109. Bathelt, A.G., Viskanta, R., Leindenfrost, W., Latent heat-of-fusion energy storage: Experiments on heat transfer from cylinders during melting. J. Heat Transfer, 101, 1979, 453.
110. Sparrow, E.M., Schmidt, R.R., Ramsey, J.W., Experiments on the role of natural convection in the melting of solids. J. Heat Transfer, 100, 1978, 11.
111. Abdel-Wahed, R.M., Ramsey, J.W., Sparrow, E.M., Photographic study of melting about an embedded horizontal heating cylinder. Int. J. Heat Mass Transfer, 22, 1979, 171.
112. Sparrow, E.M., Patankar, S.V., Ramadhyani, S., Analysis of melting in the presence of natural convection in the melt region. J. Heat Transfer, 99, 1977, 520.
113. Kemink, R.G., Sparrow, E.M., Heat transfer coefficients for melting about a vertical cylinder with or without subcooling and for open or closed containment. Int. J. Heat Mass Transfer, 24, 1981, 1699.
114. Goldstein, R.J., Ramsey, J.W., Heat transfer to a melting solid with application to thermal energy storage systems. “Heat Transfer Studies: Festschrift for E. R. G. Eckert”, 1979, Hemisphere, New York.
115. Sparrow, E.M., Ramsey, J.W., Kemink, R.G., Freezing controlled by natural convection. J. Heat Transfer, 101, 1979, 578.
116. Bathelt, A.G., Van Buren, P.D., Viskanta, R., Heat transfer during solidification around a cooled horizontal cylinder. AlChE J., 75, 1979, 103.
117. Yao, L.S., Chen, F.F., Effects of natural convection in the melted region around a heated horizontal cylinder. J. Heat Transfer, 102, 1980, 667.
118. Prusa, J., Yao, L.S., Natural convection heat transfer between eccentric horizontal cylinders. J. Heat Transfer, 105, 1983, 108.
119. Rieger, H., Projahn, U., Beer, H., Analysis of the heat transport mechanisms during melting around a horizontal circular cylinder. Int. J. Heat Mass Transfer, 25, 1982, 137.
120. Thompson, J.F., Thames, F.C., Mastin, C.W., Automatic numerical generation of body fitted curvilinear coordinate system for field containing any number of arbitrary two dimensional bodies. J. Comp. Phys., 15, 1974, 299.
121. Prusa, J., Yao, L.S., Melting around a horizontal heated cylinder: Part I - Perturbation and numerical solution for constant heat flux boundary condition. J. Heat Transfer, 106, 1984, 376.
122. Prusa, J., Yao, L.S., Melting around a horizontal heated cylinder: Part II-Numerical solution for isothermal boundary condition. J. Heat Transfer, 106, 1984, 469.
123. Roberts, A.S., Rothgeb, T.M., An experimental investigation of melting about an isothermal horizontal cylinder. ASME/AIChE Natl. Heat Transfer Conf., 22nd, Niagara Falls, August 84-HT-9, 1984.
124. Prusa, J., Yao, L.S., Effects of density change and sub-cooling on the melting of a solid around a horizontal heated cylinder. J. Fluid Mech., 155, 1985, 193.
125. Prusa, J., Vandekamp, L., A numerical solution for melting around multiple horizontal heated cylinders. ASME/AIChE Natl. Heat Transfer Conf, 23rd, Denver August 4-7 85-HT 12, 1985.
126. Bathelt, A.G., Viskanta, R., Heat transfer and interface motion during melting and solidification around a finned heat source/sink. J. Heat Transfer, 103, 1981, 720.
127. Betzel, T., Beer, H., Experimental investigation of heat transfer during melting around a horizontal tube with and without axial fins. Tech. Note Inst. Tech. Therodyn, 1987.
128. Sparrow, E.M., Larson, E.D., Ramsey, J.W., Freezing on a finned tube for either conduction-controlled or natural-convection-controlled heat transfer. Int. J. Heat Mass Transfer, 24, 1981, 273.
129. Kalhori, B., Ramadhyani, S., Studies on heat transfer from a vertical cylinder, with or without fins, embedded in a solid phase change medium. J. Heat Transfer, 107, 1985, 44.
130. Rieger, H., Projahn, U., Bareiss, M., Beer, H., Heat transfer during melting inside a horizontal tube. J. Heat Transfer, 105, 1983, 226.
131. Bareiss, M., Beer, H., Experimental investigation of melting heat transfer with regard to different geometric arrangements. Int. Commun. Heat Mass Transfer, 11, 1984, 323.
132. Ho, C.J., Viskanta, R., Heat transfer during inward melting in a horizontal tube. Int. J. Heat Mass Transfer, 27, 1984, 705.
133. Pannu, J., Joglekar, G., Rice, P.A., Natural convection heat transfer to cylinders of phase change material used for thermal storage. AIChE J., 76, 1980, 47.
134. Saitoh, T., Hirose, K., High Rayleigh number solutions to problems of latent heat thermal energy storage in a horizontal cylinder capsule. J. Heat Transfer, 104, 1982, 545.
135. Viskanta, R., Gau, C., Inward solidification of a superheated liquid in a cooled horizontal tube. Wärme Stoffübertrag., 17, 1982, 39.
136. Guenigault, R., Poots, G., Effects of natural convection on the inward solidification of spheres and cylinders. Int. J. Heat Mass Transfer, 28, 1985, 1229.
137. Yao, L.S., Natural convection effects in the continuous casting of a horizontal cylinder. Int. J. Heat Mass Transfer, 27, 1984, 697.
138. Sparrow, E.M., Broadbent, J.A., Inward melting in a vertical tube which allows free expansion of the phase-change medium. J. Heat Transfer, 104, 1982, 309.
139. Sparrow, E.M., Gurtcheff, G.A., Myrum, T.A., Correlation of melting results for both pure substances and impure substances. J. Heat Transfer, 108, 1986, 649.
140. Menon, A.S., Weber, M.E., Mujumdar, A.S., The dynamics of energy storage for paraffin wax in cylindrical containers. Can. J. Chem. Eng., 61, 1983, 647.
141. Sparrow, E.M., Broadbent, J.A., Freezing in a vertical tube. J. Heat Transfer, 105, 1983, 217.
142. Larson, E.D., Sparrow, E.M., Effect of inclination on freezing in a sealed cylindrical capsule. J. Heat Transfer, 106, 1984, 394.
143. Hale, N.W. Jr., Viskanta, R., Photographic observation of the solid-liquid interface motion during melting of a solid heated from an isothermal vertical wall. Lett. Heat Mass Transfer, 5, 1978, 329.
144. Van Buren, P.D., Viskanta, R., Interferometric measurement of heat transfer during melting from a vertical surface. Int. J. Heat Mass Transfer, 23, 1980, 568.
145. Benard, C., Gobin, D., Martinez, F., Melting in rectangular enclosures: Experiments and numerical simulations. J. Heat Transfer, 107, 1985, 794.
146. Ho, C.-J., Viskanta, R., Heat transfer during melting from an isothermal vertical wall. J. Heal Transfer, 106, 1984, 12.
147. Gau, C., Viskanta, R., Melting and solidification of a pure metal on a vertical wall. J. Heat Transfer, 108, 1986, 174.
148. Huang, S.C., Analytical solution for the buoyancy flow during the melting of vertical semiinfinite region. Int. J. Heat Mass Transfer, 28, 1985, 1231.
149. Okada, M., Analysis of heat transfer during melting from a vertical wall. Int. J. Heat Mass Transfer, 11, 1984, 2059.
150. Gadgil, A., Gobin, D., Analysis of two-dimensional melting in rectangular enclosures in presence of convection. J. Heat Transfer, 106, 1984, 20.
151. G. E. Schneider Computation of heat transfer with solid/liquid phase change including free convection AIAA Aerospace Sci. Meet., 23rd, Reno, Nevada, January 14-17 AIAA-85-0404 1985.
152. Benard, C., Gobin, D., Zanoli, A., Numerical simulation of transient melting in two dimensions by coupling of natural convection in the melt and heat conduction in the solid phase. ASME/AIChE Natl. Heat Transfer Conf., 22rd, Niagara Falls, August 5-8 84-HT-5, 1984.
153. Ramachandran, N., Gupta, J.P., Jaluria, Y., Thermal and fluid flow effects during solidification in a rectangular enclosure. Int. J. Heat Mass Transfer, 25, 1982, 187.
154. Ramachandran, N., Gupta, J.P., Jaluria, Y., Experiments on solidification with natural convection in a rectangular enclosed region. Int. J. Heat Mass Transfer, 25, 1982, 595.
155. Ho, C.-J., Viskanta, R., Inward solid-liquid phase-change heat transfer in a rectangular cavity with conducting vertical walls. Int. J. Heat Mass Transfer, 27, 1984, 1055.
156. Gau, C., Viskanta, R., Melting and solidification of a metal system in a rectangular cavity. Int. J. Heat Mass Transfer, 27, 1984, 113.
157. Webb, B.W., Viskanta, R., Natural-convection-dominated melting heat transfer in an inclined rectangular enclosure. Int. J. Heat Mass Transfer, 29, 1986, 183.
158. Wilson, N.W., Lee, J.J., Melting of a vertical ice wall by free convection into fresh water. J. Heat Transfer, 103, 1981, 13.
159. White, D., Viskanta, R., Leidenfrost, W., Heat transfer during the melting of ice around a horizontal, isothermal cylinder. Exp. Fluids, 4, 1986, 171.
160. Rieger, H., Beer, H., The melting process of ice inside a horizontal cylinder: Effects of density anomaly. J. Heat Transfer, 108, 1986, 166.
161. Moore, F.E., Bayazitoglu, Y., Melting within a spherical enclosure. J. Heat Transfer, 104, 1982, 19.
162. Bareiss, M., Beer, H., An analytical solution of the heat transfer process during melting of an unfixed solid phase change material inside a horizontal tube. Int. J. Heat Mass Transfer, 27, 1984, 739.
163. Sparrow, E.M., Geiger, G.T., Melting in a horizontal tube with the solid either constrained or free to fall under gravity. Int. J. Heat Mass Transfer, 29, 1986, 1007.
164. Betzel, Th., Beer, H., Prediction and measurement of melting heat transfer to an unfixed phase change material heated in a horizontal concentric annulus. Proc. Int. Heat Transfer Conf., 8th, San Francisco, August 17-22, 4, 1986, 1793.
165. Webb, B.W., Moallemi, M.K., Viskanta, R., Phenomenology of melting of unfixed phase change material in a horizontal cylindrical capsule. AIAA/ASME Natl. Thermophys. Heat Transfer Conf, Boston, June 2-4 86-HT-10, 1986.
166. Moallemi, M.K., Viskanta, R., Experiments on fluid flow induced by melting around a migrating heat source. J. Fluid Mech., 157, 1985, 35.
167. Moallemi, M.K., Viskanta, R., Analysis of close-contact melting heat transfer. Int. J. Heat Mass Transfer, 29, 1986, 855.
168. Moallemi, M.K., Viskanta, R., Analysis of melting around a moving heat source. Int. J. Heat Mass Transfer, 29, 1986, 1271.
169. Emerman, S.H., Turcotte, D.L., Stokes' problem with melting. Int. J. Heat Mass Transfer, 26, 1983, 1625.
170. Bott, M.H.P., “The Interior of The Earth: Its Structure, Constitution and Evolution, 2nd. Ed., 1982, Elsevier, New York, 164.
171. Sadeghipour, M.S., Ozisik, M.N., Mulligan, J.C., Transient freezing of a liquid in a convectively cooled tube. J. Heat Transfer, 104, 1982, 316.
172. Cevantes, J., Trevino, C., Rodriguez, M., Transient freezing and laminar flow in a circular pipe. Int. Symp. Heat Mass Transfer Cryoeng. Refrig., 1986 18th, Dubrovnik, September 1-5.
173. Toda, S., Sugiyama, H., Owada, H., Kurokawa, M., Hori, Y., Laminar flow heat transfer in a tube with internal solidification. Proc. Int. Heat Transfer Conf., 8th, San Francisco, August 17-22, 4, 1986, 1745.
174. Epstein, M., Cheung, F.B., On the prediction of pipe freeze-shut in turbulent flow. J. Heat Transfer, 104, 1982, 381.
175. Sampson, P., Gibson, R.D., A mathematical model of nozzle blockage by freezing-II. Turbulent flow. Int. J. Heat Mass Transfer, 25, 1982, 119.
176. Gilpin, R.R., Ice formation in a pipe containing flows in the transition and turbulent regimes. J. Heat Transfer, 103, 1981, 363.
177. Hirata, T., Ishihara, M., Freeze-off conditions of a pipe containing a flow of water. Int. J. Heat Mass Transfer, 28, 1985, 331.
178. Morton, B.R., Laminar convection in uniformly heated horizontal pipes at low Rayleigh numbers. J. Mech. Appl. Math., 12, 1959, 410.
179. Seki, N., Fukusako, S., Younan, G.W., Ice-formation phenomena for water flow between two cooled parallel plates. J. Heat Transfer, 106, 1984, 498.
180. Cheung, F.B., Analysis of freeze coating on a nonisothermal moving plate by a perturbation method. J. Heat Transfer, 107, 1985, 549.
181. Cheng, K.C., Inaba, H., Gilpin, R.R., An experimental investigation of ice formation around an isothermally cooled cylinder in crossflow. J. Heat Transfer, 103, 1981, 733.
182. Lock, G.S.H., Kaiser, T.M.V., Icing on submerged tubes: A study of occlusion. Int. J. Heat Mass Transfer, 28, 1985, 1689.
183. Cheng, K.C., Sabhapathy, P., Determination of local heat transfer coefficients at the solid-liquid interface by heat conduction analysis of the solidification region. J. Heat Transfer, 107, 1985, 703.
184. Shiina, Y., Kroeger, P.G., Transient moisture migration and phase change front propagation in porous media. ASME/AIChE Natl. Heat Transfer Conf., 22nd, Niagara Falls, August 5-8 84-HT-7, 1984.
185. Weaver, J.A., Viskanta, R., Freezing of liquid-saturated porous media. J. Heat Transfer, 108, 1986, 654.
186. Torrance, K.E., Phase-change heat transfer in porous media. Proc. Int. Heat Transfer Conf., 8th, San Francisco, 1, 1986, 181.
187. Frivik, P.E., Comini, G., Seepage and heat flow in soil freezing. J. Heat Transfer, 104, 1982, 323.
188. Boles, M.A., Ozisik, M.N., Exact solution for freezing in cylindrically symmetric porous moist media. J. Heat Transfer, 105, 1983, 401.
189. Inaba, H., Heat transfer behavior of frozen soils. J. Heat Transfer, 105, 1983, 680.
190. Couvillion, R.J., Hartly, J.G., Drying front movement near low-density, impermeable underground heat sources. J. Heat Transfer, 108, 1986, 182.
191. Vauclin, M., Giakoumakis, S., Gaudet, J.P., Albergel, A., Experimental and numerical analysis of coupled heat and mass transfer in a partially saturated frozen soil. Symp. Heat Mass Transfer Cryoeng. Refrig., I8th, Dubrovnik, September 1-5, 1986.
192. Zhang, G.-P., Jiji, L.M., Weinbaum, S., Quasi-three-dimensional steady-state analytic solution for melting or freezing around a buried pipe in a semi-infinite medium. J. Heat Transfer, 107, 1985, 245.
193. G. -P. Zhang, S. Weinbaum, and L. M. Jiji An approximate three-dimensional solution for melting or freezing around a buried pipe beneath a free surface ASME Winter Annu. Meet, Miami Beach, November 17-22 85-WA/HT-74 1985.
194. Rubinsky, B., Solidification of a conglomerate of particles. J. Heat Transfer, 104, 1982, 193.
195. Raymond, J.F., Rubinsky, B., A numerical study of the thawing process of a frozen coal particle. J. Heat Transfer, 105, 1983, 197.
196. Moog, D.B., Rubinsky, B., An analytical model of thermal and vapor diffusion in freezing of wet coal. J. Heat Transfer, 107, 1985, 5.
197. Elliot, R., Eutectic solidification. Int. Met. Rev., 219, 1977, 161.
198. Wollhover, K., Korber, Ch., Scheiwe, M.W., Hartmann, U., Unidirectional freezing of binary aqueous solutions: An analysis of transient diffusion of heat and mass. Int. J. Heat Mass Transfer, 28, 1985, 761.
199. Wollhover, K., Scheiwe, M.W., Hartmann, U., Korber, Ch., On morphological stability of planar phase boundaries during unidirectional transient solidification of binary aqueous solutions. Int. J. Heat Mass Transfer, 28, 1985, 897.
200. Weiss, P.A., Desalination by freezing. Bakish, R., Noyes, R., (eds.) “Practice of Desalination”, 1973, Noyes Data Corp., Park Ridge, New Jersey, 260.
201. Carey, V.P., Gebhart, B., Transport near a vertical ice surface melting in saline water: Some numerical calculations. J. Fluid Mech., 117, 1982, 379.
202. Gradon, L., Orlicki, D., Separation of liquid mixtures in the freezing-out processmathematical description and experimental verification. Int. J. Heat. Mass Transfer, 28, 1985, 1983.
203. Fang, L.J., Cheung, F.B., Linehan, J.H., Pedersen, D.R., Selective freezing of a dilute salt solution on a cold ice surface. J. Heat Transfer, 106, 1984, 385.
204. Chawla, T.C., Pedersen, D.R., Leaf, G., Minkowycz, W.J., Shouman, A.R., Adaptive collocation method for simultaneous heat and mass diffusion with phase change. J. Heat Transfer, 106, 1984, 491.
205. Mullins, W.W., Sekerka, R.K., Stability of a planar interface during solidification of a dilute binary alloy. J. Appl. Phys., 35, 1964, 4444.
206. Glicksman, M.E., Coriell, S.R., McFadden, G.B., Interaction of flows with the crystalmelt interface. Annu. Rev. Fluid Mech., 18, 1986, 307.
207. Tien, R.H., Geiger, G.E., A heat transfer analysis of the solidification of a binary eutectic system. J. Heat Transfer, 89, 1967, 230.
208. Cho, S.H., Sunderland, J.E., Heat conduction problems with melting and freezing. J. Heat Transfer, 91, 1969.
209. Hayashi, Y., Komori, T., Investigation of freezing of salt solutions in cells. J. Heat Transfer, 101, 1979, 459.
210. O'Callaghan, M.G., Cravalho, E.G., Huggins, C.E., An analysis of the heat and solute transport during solidification of an aqueous binary solution. Int. J. Heat Mass Transfer, 25, 1982, 553.
211. Webb, B.W., Viskanta, R., An experimental and analytical study of solidification of a binary mixture. Proc. Int. Heat Transfer Conf., 8th, San Francisco, 4, 1986, 1739.
212. Kehtarnavaz, H., Bayazitoglu, Y., Solidification of binary mixture in a finite planar medium: Saline water. J. Heat Transfer, 107, 1985, 964.
213. Sparrow, E.M., Lee, L., Shamsundar, N., Convective instability in the melt layer heated from below. J. Heat Transfer, 98, 1976, 88.
214. Seki, N., Fukusako, S., Sugawara, M., A criterion of onset of free convection in a horizontal melted water layer with free surface. J. Heat Transfer, 99, 1977, 92.
215. Yao, L.S., Catton, I., The effects of phase change on the onset of thermal instability in an internally heated pool. Natl. Heat Transfer Conf., 17th, Salt Lake City Reprints of AlChe Paps, 1977, 176–181.
216. Yao, L.S., Catton, I., Thermal instability of a volumetrically heated pool with phase change and a free upper surface. J. Heat Transfer, 100, 1978, 376.
217. Langlois, W.E., Buoyancy-driven flows in crystal-growth melts. Annu. Rev. Fluid Mech., 17, 1985, 191.
218. Cheung, F.B., Periodic growth and decay of a frozen crust over a heat generating liquid layer. J. Heat Transfer, 103, 1981, 369.
219. Davis, S.H., Muller, U., Dietsche, C., Pattern selection in single-component systems coupling Bernard convection and solidification. J. Fluid Mech., 144, 1984, 133.
220. Dietsche, C., Muller, U., Influence of Bernard convection on solid-liquid interfaces. J. Fluid Mech., 161, 1985, 249.
221. Fang, Q.T., Glicksman, M.E., Coriell, S.R., McFadden, G.B., Boisdert, R.F., Convective influence on the stability of a cylindrical solid-liquid interface. J. Fluid Mech., 151, 1985, 121.
222. Gau, C., Viskanta, R., Effect of natural convection on solidification from above and melting from below. Int. J. Heat Mass Transfer, 28, 1985, 573.
223. Englberger, W., Winter, E.R.F., Onset of natural convection and heat transfer in a layer of water below melting ice. Proc. Int. Heat Transfer Conf., 8th, San Francisco, 4, 1986, 1799.
224. Ostrach, S., Low-gravity fluid flows. Annu. Rev. Fluid Mech., 14, 1982, 313.
225. Davis, S.H., Thermocapillary instabilities. Annu. Rev. Fluid Mech., 19, 1987, 403.
226. Farhadieh, R., Baker, L. Jr., Heat transfer phenomenology of a hydrodynamically unstable melting system. J. Heat Transfer, 100, 1978, 305.
227. Catton, I., Brinsfield, W.A., Ghiaasiaan, S.M., Heat transfer from a heated pool to a melting miscible substrate. J. Heat Transfer, 105, 1983, 447.
228. Eck, G., Werle, H., Experimental studies of penetration of a hot liquid pool into a melting miscible substrate. Nucl. Technol., 64, 1984, 275.
229. Epstein, M., Grolmes, M.A., Natural convection characteristics of pool penetration into a melting miscible substrate. J. Heat Transfer, 108, 1986, 190.
230. Chen, M.M., Farhadieh, R., Baker, L. Jr., On free convection melting of a solid immersed in a hot dissimilar fluid. Int. J. Heat Mass Transfer, 29, 1986, 1087.
231. Taghavi-Tafreshi, K., Dhir, V.K., Analytical and experimental investigation of simultaneous melting-condensation on a vertical wall. J. Heat Transfer, 104, 1982, 24.
232. Taghavi-Tafreshi, K., Dhir, V.K., Shape change of an initially vertical wall undergoing condensation-driven melting. J. Heat Transfer, 105, 1982, 235.
233. Galamba, D., Dhir, V.K., Transient simultaneous condensation and melting of a vertical surface. J. Heat Transfer, 107, 1985, 812.
234. Peifer, W.A., Levitation melting, a survey of the state-of-art. J. Met., 17, 1965, 487.
235. Vives, C., Perry, C., Effects of electromagnetic stirring during the controlled solidification of tin. Int. J. Heat Mass Transfer, 29, 1986, 21.
236. Kroeger, P.G., Ostrach, S., The solution of a two-dimensional freezing problem including convection effects in the liquid region. Int. J. Heat Mass Transfer, 17, 1974, 1191.
237. Rubinsky, B., Thermal stresses during solidification processes. J. Heat Transfer, 104, 1982, 196.
238. Landram, C.S., Measurement of fusion boundary energy transport during arc welding. J. Heat Transfer, 105, 1983, 550.
239. Oreper, G.M., Szekely, J., Heat and fluid-flow phenomena in weld pools. J. Fluid Mech., 147, 1984, 53.
240. Wang, P., Lin, S., Kahawita, R., The cubic spline integration technique for solving fusion welding problems. J. Heat Transfer, 107, 1985, 485.
241. Salcudean, M., Choi, M., Greif, R., A study of heat transfer during arc welding. Int. J. Heat Mass Transfer, 29, 1986, 215.
242. Francis, A., Craine, R.E., On a model for frictioning stage in friction welding of thin tubes. Int. J. Heat Mass Transfer, 28, 1985, 1747.
243. Dowden, J., Davis, M., Kapadia, P., Some aspects of the fluid dynamics of laser welding. J. Fluid Mech., 126, 1983, 123.
244. Beckett, P.M., Laser heating of a solid with change of phase. ASME/AIChE Natl. Heat Transfer Conf., 22nd, Niagara Falls, August 5-8 84-HT-6, 1984.
245. Modest, M.F., Abakians, H., Evaporative cutting of a semi-infinite body with a moving cw laser. ASME/AIChE Natl. Heat Transfer Conf, 23rd, Denver, August 4-7 85-HT-25, 1985.
246. Modest, M.F., Abakians, H., Heat conduction in a moving semi-infinite solid subjected to pulsed laser irradiation. J. Heat Transfer, 108, 1986, 597.
247. Srinivasan, J., Basu, B., A numerical study of thermocapillary flow in a rectangular cavity during laser melting. Int. J. Heat Mass Transfer, 29, 1986, 563.
248. White, J.E., Cremers, C.J., Prediction of growth parameters of frost deposits in forced convection. J. Heat Transfer, 103, 1981, 3.
249. Cremers, C.J., Mehra, V.K., Frost formation on vertical cylinders in free convection. J. Heat Transfer, 104, 1982, 3.
250. Tokura, I., Saito, H., Kishinami, K., Study on properties and growth rate of frost layers on cold surfaces. J. Heat Transfer, 105, 1983, 895.
251. Steinhagen, H.P., Myers, G.E., Numerical solution to axisymmetric thawing and heating of frozen logs. J. Heat Transfer, 105, 1983, 195.
252. Thompson, D.R., Frost formation on cryogenic heat exchangers with atmospheric heat sources. ASME/AIChE Natl. Heat Transfer Conf., 23rd, Denver, August 4-7 85-HT-3, 1985.
253. Auracher, H., Effective thermal conductivity of frost. Int. Symp. Heat Mass Transfer Cryoeng. Refrig., 18th, Dubrovick, Sept. 1-5, 1986.
254. Chung, P.M., Bywater, R., Role of the liquid layer in ice accumulation on flat surfaces. J. Heat Transfer, 106, 1984, 5.
255. Chung, B.T.F., Chang, T.Y., Hsiao, J.S., Chang, C.T., Heat transfer with ablation in a half-space subjected to time-variant heat fluxes. J. Heat Transfer, 105, 1983, 200.
256. Chung, B.T.F., Hsiao, J.S., Heat transfer with ablation in a finite slab subjected to timevariant heat fluxes. AIAA J., 23, 1985, 145.
257. Park, C., Lundell, J.H., Green, M.J., Winovich, W., Covington, M.A., Ablation of carbonaceous materials in a hydrogen-helium arcjet flow. AIAA J., 22, 1984, 1491.
258. Hogge, M., Gerrekens, P., Two-dimensional deforming finite element methods for surface ablation. AIAAJ., 23, 1985, 465.
259. Park, C., Balakrishnan, A., Ablation of Galileo probe heat-shield models in a ballistic range. AIA A J., 23, 1985, 301.
260. Lin, S., An exact solution of the sublimation problem in a porous medium. J. Heat Transfer, 104, 1982, 808.
261. Sakly, M., Aguirre-Puente, J., Lambrinos, G., Experimental study of the sublimation of pure ice under very low temperature and relative humidity conditions. Int. Symp. Heat Mass Transfer Cryoeng. Refrig., 18th, Dubrovnik, Sept 1-5, 1986.
262. Turcotte, D.L., Hsui, A.T., Torrance, K.E., Schubert, G., Influence of viscous dissipation on Benard convection. J. Fluid Mech., 64, 1974, 369.
263. Hewitt, J.M., McKenzie, D.P., Weise, N.O., Dissipative heating in convective flows. J. Fluid Mech., 68, 1975, 721.
264. Nitsan, U., Viscous heat production in a slab. J. Geophys. Res., 78, 1973, 1395.
265. Yuen, D.A., Schubert, G., On the stability of frictionally heated shaw flows in the asthenosphere. Geophys. J. R. Astron. Soc., 57, 1979, 189.
266. Melosh, M.J., Ebel, J., A simple model for thermal instability in the asthenosphere. Geophys. J. R. Astron. Soc., 59, 1979, 419.
267. Ockendon, J.R., layler, A.B., Emerman, S.H., Turcotte, D.L., Geodynamic thermal runaway with melting. J. Fluid Mech., 152, 1985, 301.
268. Oversby, W.M., Ringwood, A.E., Time formation of the earth's core. Nature (London), 234, 1971, 463.
269. Grossman, L., Larimer, J.W., Early chemical history of the solar system. Rev. Geophys. Space Phys., 12, 1974, 71.
270. Ringwood, A.E., “Composition and petrology of the earth's mantle”, 1975, McGraw-Hill, New York.
271. Spera, F.J., Aspects of magma transport. Hargraves, R.B., (eds.) Physics of Magma Processes, 1980, Princeton University Press, New Jersey, 263.
272. Turcotte, D.L., Magma migration. Annu. Rev. Earth Planet. Sci., 10, 1982, 397.
273. Marsh, B.D., Kantha, L.L., On the heat and mass transfer from an ascending magma. Earth Planet. Sci. Lett., 39, 1978, 435.
274. Marsh, B.D., On the mechanics of igneous diapirism, stoping and zone melting. Am. J. Sci., 282, 1982, 808.
275. Huang, S.C., Melting of semi-infinite region with viscous heating. Int. J. Heat Mass Transfer, 37, 1984, 1337.
276. Schneider, S.H., Dickinson, R.E., Climate modeling. Rev. Geophys. Space Phys., 12, 1974, 447.
277. Drazin, P.G., Griffel, D.H., On the branching structure of diffusive climatological models. J. Atmos. Sci., 34, 1977, 1696.
278. Pollard, D., An investigation of the astronomical theory of the ice ages using a simple climate-ice-sheet model. Nature (London), 272, 1978, 233.
279. Kallen, C., Craft, C., Ghil, M., Free oscillations in a climate model with ice-sheet dynamics. J. Atmos. Sci., 36, 1979, 2292.
280. Nicolis, C., A free boundary value problem arising in climate dynamics. Int. J. Heat Mass Transfer, 25, 1982, 371.