Solid—Fluid Systems with Simple, Continuous Interface

  • Massoud Kaviany
Part of the Mechanical Engineering Series book series (MES)


When the assumption of local thermal equilibrium between the solid and the fluid is not valid, i.e., when the main heat transfer is between the two adjacent phases, the two-medium treatment of the heat transfer is needed. In this chapter interfacial geometries that are simple and continuous (as compared to discrete, which is discussed in Chapter 5), such as planar and curved surfaces, are considered.


Heat Transfer Nusselt Number Heat Transfer Rate Heat Mass Transfer Local Nusselt Number 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Al-Sanea, S., 1992, “A Numerical Study of the Flow and Heat Transfer Characteristics of an Impinging Laminar Slot-Jet Including Crossflow Effects,” Int. J. Heat Mass Transfer, 35, 2501–2513.Google Scholar
  2. 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.ADSMATHGoogle Scholar
  3. Antonia, R.A., and Kim, J., 1991, “Reynolds Shear Stress and Heat Flux Calculations in a Fully Developed Turbulent Duct Flow,” Int. J. Heat Mass Transfer, 34, 2013–2018.ADSGoogle Scholar
  4. Apte, V.B., Bilger, R.W., Green, A.R., and Quintere, J.G., 1991, “Wind-Aided Turbulent Flame Spread and Burning over Large-Scale Horizontal PMMA Surfaces,” Combust. Flame, 85, 169–184.Google Scholar
  5. Arpaci, V.S., and Larsen, P.S., 1984, Convective Heat Transfer, Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
  6. Banerjee, S., 1991, “Turbulence/Interface Interactions”, in Phase-Interface Phenomena in Multiphase Flow, Hewitt, G.F., Mayinger, F., and Riznic, J.R., Editors, Hemisphere Publishing Corporation, New York.Google Scholar
  7. Bau, H.H., 1992, “Controlling Chaotic Convection,” in Theoretical and Applied Mechanics 1992, Bonder, S., et al., Editors, 187–203, Elsevier, Amsterdam.Google Scholar
  8. Bau, H.H., and Wang, Y.-Z., 1992, “Chaos: A Heat Transfer Perspective,” Ann. Rev. Heat Transfer, 4, 1–50.Google Scholar
  9. Bejan, A., 1984, Convection Heat Transfer, John Wiley and Sons, New York.MATHGoogle Scholar
  10. Bennen, W.D., and Incropera, F.P., 1987, “A Continuum Model for Momentum, Heat and Species Transport in Binary Solid-Liquid Phase Change Systems. I. and II.” Int. J. Heat Mass Transfer, 30, 2161–2187.Google Scholar
  11. Bergeies, G., Gosman, A.D., and Launder, B.E., 1981, “The Prediction of Three-Dimensional Discrete-Hole Cooling Processes,” ASME J. Heat Transfer, 103, 141–145.ADSGoogle Scholar
  12. Bhattacharjee, S., 1993, “A Comparison of Numerical and Analytical Solutions of the Creeping Flame Spread Over Thermally Thin Material,” Combust. Flame, 93, 434–444.Google Scholar
  13. Bird, R.B., Armstrong, R.C., and Hassager, O., 1987, Dynamics of Polymeric Liquids, Volume 1: Fluid Mechanics, Volume 2: Kinetic Theory, Second Edition, John Wiley and Sons, New York.Google Scholar
  14. Biswas, G., and Chattopadhyay, H., 1992, “Heat Transfer in a Channel with Built-in Wing-Type Vortex Generators,” Int. J. Heat Mass Transfer, 35, 803–814.ADSMATHGoogle Scholar
  15. Böhme, G., Non-Newtonian Fluid Mechanics, 1982, North-Holland, Amsterdam.Google Scholar
  16. Bouillard, J.X., and Berry, G.F., 1992, “Performance of a Multigrid Three-Dimensional Magnetohydrodynamic Generator Calculation Procedure,” Int. J. Heat Mass Transfer, 35, 2219–2232.ADSMATHGoogle Scholar
  17. Branover, H., Lykoudis, P.S., and Mond, M., 1985, Single- and Multiphase Flows in an Electromagnetic Field. Energy, Metallurgical, and Solar Applications, Vol. 100, Progress in Astronautics and Aeronautics, American Institute of Aeronautic and Astronautics, New York.Google Scholar
  18. Bray, K.N.C., Champion, M., and Libby, P.A., 1992, “Premixed Flames in Stagnation Turbulence. Part III—The k̄-ϵ̄ Theory for Reactants Impinging on a Wall,” Combust. Flame, 91, 165–186.Google Scholar
  19. Brown, M.A., 1992, Thermally Induced Pressure Waves in a Gas: Experimental Observation and Theoretical Prediction of Thermoacoustic Convection, Ph.D. Thesis, University of Pennsylvania.Google Scholar
  20. Brown, M.A., and Churchill, S.W., 1993, “Transient Behavior of an Impulsively Heated Fluid,” Chem. Eng. Technol., 16, 82–88.Google Scholar
  21. Brown, M.A., and Churchill, S.W., 1995, “Experimental Measurements of Pressure Waves Generated by Impulsive Heating of a Surface,” AIChE J., 41, 205–213.Google Scholar
  22. Burmeister, L.C., 1983, Convective Heat Transfer, John Wiley and Sons, New York.Google Scholar
  23. Cancaster, J.F., Editor, 1986, The Physics of Welding, Pergamon Press, Oxford.Google Scholar
  24. Carey, V.P., 1992, “Monte Carlo Simulation of the Operating Characteristics of an Ultraminature Hot-Film Sensor in High-Speed Gas Flow,” in Heat Transfer on the Microscale, HTD-Vol. 200, 45–54, American Society of Mechanical Engineers, New York.Google Scholar
  25. Cebeci, T., and Bradshaw, P., 1984, Physical and Computational Aspects of Convection Heat Transfer, Springer-Verlag, New York.Google Scholar
  26. Chandrasekhar, S., 1981, Hydrodynamic and Hydromagnetic Stability, Dover, New York.Google Scholar
  27. Chen, F., Lu, J.W., and Yang, T.L., 1994, “Convective Instability in Ammonium Chlorida Solution Directionally Solidified from Below,” J. Fluid Mech., 276, 163–167.ADSGoogle Scholar
  28. Chen, X., 1990, “Heat Transfer and Flow in a Radio Frequency Plasma Torch-A New Modeling Approach,” Int. J. Heat Mass Transfer, 33, 815–826.Google Scholar
  29. Chen, Y.-M., 1985, “Heat Transfer of a Laminar Flow Passing a Wedge at Small Prandtl Number: A New Approach,” Int. J. Heat Mass Transfer, 28, 1517–1523.ADSMATHGoogle Scholar
  30. Cheng, P., 1978a, “Convective Heat Transfer in Porous Layers by Integral Methods,” Commun. Heat Mass Transfer, 5, 243–252.Google Scholar
  31. Cheng, P., 1978b, “Heat Transfer in Geothermal Systems,” Advan. Heat Transfer, 14, 1–105.Google Scholar
  32. 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. Geophs. Res., 82, 2040–2044.ADSGoogle Scholar
  33. Cho, Y.I., and Hartnett, J.P., 1982, “Non-Newtonian Fluids in Circular Pipe Flow,” Advan. Heat Transfer, 15, 59–141.Google Scholar
  34. Chung, P.M., 1965, “Chemically Reacting Nonequilibrium Boundary Layers,” Advan. Heat Transfer, 2, 109–270.Google Scholar
  35. Churchill, S.W., 1977, “A Comprehensive Correlating Equation for Laminar, Assisting, Forced and Free Convection,” AIChE J., 23, 10–16.Google Scholar
  36. Churchill, S.W., and Brown, M.A., 1987, “Thermoacoustic Convection and the Hyperbolic Equation of Convection,” Int. Commun. Heat Mass Transfer, 14, 647–655.Google Scholar
  37. Coleman, H.W., Moffat, R.J., and Kays, W.M., 1981, “Heat Transfer in the Accelerated Fully Rough Turbulent Boundary Layer,” ASME J. Heat Transfer, 103, 153–158.ADSGoogle Scholar
  38. Craft, T.J., Graham, L.J.W., and Launder, B.E., 1993, “Impinging Jet Studies of Turbulence Model Assessment. II. An Examination of the Performance of Four Turbulence Models,” Int. J. Heat Mass Transfer, 36, 2685–2697.Google Scholar
  39. Cramer, K.R., 1963, “Several Magnetohydrodynamic Free-Convection Solutions,” ASME J. Heat Transfer, 85, 35–40.Google Scholar
  40. Cunningham, R.E., and Williams, R.J.J., 1980, Diffusion in Gases and Porous Media, Plenum Press, New York.Google Scholar
  41. Depew, C.A., and Kramer, T.J., 1973, “Heat Transfer to Flowing Gas-Solid Mixtures,” Advan. Heat Transfer, 9, 113–180.Google Scholar
  42. de Ris, J., 1969, “Spread of a Laminar Diffusion Flame,” Twelfth Symposium (International) on Combustion, 241–252, The Combustion Institute, Pittsburgh.Google Scholar
  43. Dietz, P.W., and Melcher, J.R., 1975, “Field Controlled Heat Transfer Involving Macroscopic Charged Particles in Liquids,” ASME J. Heat Transfer, 97, 429–434.Google Scholar
  44. Eckert, E.R.G., and Drake, R.M., Jr., 1972, Analysis of Heat and Mass Transfer, McGraw-Hill, New York.MATHGoogle Scholar
  45. Ede, A.J., 1967, “Advances in Natural Convection,” Advan. Heat Transfer, 4, 1–64.Google Scholar
  46. Edwards, D.K., 1981, Radiation Heat Transfer Notes, Hemisphere Publishing Company, New York.Google Scholar
  47. Eibeck, P.A., and Eaton, J.K., 1987, “Heat Transfer Effects of a Longitudinal Vortex Embedded in a Turbulent Boundary Layer,” ASME J. Heat Transfer, 109, 16–24.Google Scholar
  48. Eichhorn, R., 1960, “The Effect of Mass Transfer on Free Convection,” ASME J. Heat Transfer, 82, 260–263.Google Scholar
  49. Emmons, H.W., 1956, “The Film Combustion of Liquid Fuel,” Z. Agnew. Math. Mech., 36, 60–71.MATHGoogle Scholar
  50. Faraco-Medeiros, M.A., and Silva-Preire, A.P., 1992, “The Transfer of Heat in Turbulent Boundary Layers with Injection or Suction: Universal Laws and Stanton Number Equations,” Int. J. Heat Mass Transfer, 35, 991–995.ADSGoogle Scholar
  51. Farber, L., and Depew, C.A., 1963, “Heat Transfer Effects to Gas-Solids Mixtures Using Solid Spherical Particles of Uniform Size,” I & EC Fundamentals, 2, 130–135.Google Scholar
  52. Fray, A.E., and T’ien, J.S., 1979, “A Theory of Flame Spread over a Solid Fuel Including Finite-Rate Chemical Reactants,” Combust. Flame, 36, 263–289.Google Scholar
  53. Fujii, T., Poirier, D.R., and Flemings, M.C., 1979, “Macrosegregation in a Multicomponent Low Alloy Steel,” Metall. Trans., 10B, 331–339.Google Scholar
  54. Fujino, T., Yokohama, Y., and Mori, Y.H., 1989, “Augmentation of Laminar Forced-Convective Heat Transfer by the Application of a Transverse Electric Field,” ASME J. Heat Transfer, 111, 345–351.Google Scholar
  55. Galante, S.R., and Churchill, S.W., 1990, “Applicability of Solutions of Convection in Potential Flows,” Advan. Heat Transfer, 20, 353–388.Google Scholar
  56. Gebhart, B., Jaluria, Y., Mahajan, R.L., and Sammakia, B., 1988, Buoyancy-Induced Flows and Transport, Hemisphere Publishing Corporation, Washington, DC.MATHGoogle Scholar
  57. Giedt, W.H., and Willis, D.R., 1985, “Rarefied Gases,” in Handbook of Heat Transfer, Fundamentals, Rohsenow, W.M., et al., Editors, Second Edition, McGraw-Hill, New York.Google Scholar
  58. Girshick, S.L., and Yu, W., 1990, “Radio-Frequency Induction Plasmas at Atmospheric Pressure: Mixtures of Hydrogen, Nitrogen, and Oxygen with Argon,” Plasma Chem. Plasma Process., 10, 515–529.Google Scholar
  59. Glassman, I., 1987, Combustion, Second Edition, Academic Press, Orlando.Google Scholar
  60. Goldstein, R.J., 1971, “Film Cooling,” Advan. Heat Transfer, 7, 321–379.Google Scholar
  61. Goldstein, R.J., Behbahani, A.I., and Heppelmann, K.K., 1986, “Streamwise Distribution of the Recovery Factor and the Local Heat Transfer Coefficient for an Impinging Circular Air Jet,” Int. J. Heat Mass Transfer, 29, 1227–1235.Google Scholar
  62. Goldstein, R.J., and Seol, W.S., 1991, “Heat Transfer to a Row of Impinging Circular Air Jets Including the Effect of Entrainment,” Int. J. Heat Mass Transfer, 34, 2133–2147.ADSGoogle Scholar
  63. Grassman, P., and Turna, M., 1979, “Critical Reynolds Number for Oscillating and Pulsating Tube Flow,” (in German), Thermo-Fluid Dyn., 12, 203–209.Google Scholar
  64. Greenberg, J.B., and Ronrey, P.D., 1993, “Analysis of Lewis Number Effects in Flame Spread,” Int. J. Heat Mass Transfer, 36, 315–323.Google Scholar
  65. Hartnett, J.P., 1992, “Viscoelastic Fluids: A New Challenge in Heat Transfer,” ASME J. Heat Transfer, 114, 296–303.Google Scholar
  66. Hartnett, J. P., and Kostic, M., 1989, “Heat Transfer to Newtonian and Non-Newtonian Fluids in Rectangular Ducts,” Advan. Heat Transfer, 19, 247–356.Google Scholar
  67. Henkes, R.A.W.M., and Hoogendoorn, C.J., 1989, “Comparison of Turbulence Models for the Natural Convection Boundary Layer Along a Heated Vertical Plate,” Int. J. Heat Mass Transfer, 32, 157–169.ADSMATHGoogle Scholar
  68. Hills, R.N., Loper, D.E., and Roberts, P.H., 1992, “On Continuum Models for Momentum, Heat and Species Transport in Solid-Liquid Phase Change Systems,” Int. Commum. Heat Mass Transfer, 19, 585–594.Google Scholar
  69. Hirano, T., and Kinoshita, M., 1974, “Gas Velocity and Temperature Profiles of a Diffusion Flame Stabilized in the Stream over Liquid Fuel,” Fifteenth Symposium (International) on Combustion, 379–387, The Combustion Institute, Pittsburgh.Google Scholar
  70. Hollworth, B.R., and Gero, L.R., 1985, “Entrainment Effect on Impingement Heat Transfer: Part II. Local Heat Transfer Measurements,” ASME J. Heat Transfer, 107, 910–915.Google Scholar
  71. Hong, J.-T., Tien, C.-L., and Kaviany, M., 1985, “Non-Darcean Effects on Vertical Plate Natural Convection in Porous Media with High Porosity,” Int. J. Heat Mass Transfer, 28, 2149–2157.Google Scholar
  72. Hosni, M.H., Coleman, H.W., Garner, J.W., and Taylor, R.P., 1993, “Roughness Element Shape Effects on Heat Transfer and Skin Friction in Rough-Wall Turbulent Boundary Layers,” Int. J. Heat Mass Transfer, 36, 147–153.ADSGoogle Scholar
  73. Huang, Y., and Bau, H.H., 1993, “Thermoacoustic Convection,” in Heat Transfer in Micro Gravity, ASME HTD-Vol. 269, 1–9, American Society of Mechanical Engineers, New York.Google Scholar
  74. Huppert, H.E., 1990, “The Fluid Mechanics of Solidification,” J. Fluid Mech., 212, 209–240.MathSciNetADSGoogle Scholar
  75. Jaluria, Y., 1980, Natural Convection Heat and Mass Transfer, Pergamon Press, Oxford.Google Scholar
  76. Joshi, S.V., Liang, Q., Park, J.Y., and Batdorf, J.A., 1990, “Effect of Quenching Conditions on Particle Formation and Growth in Thermal Plasma Synthesis of Fine Powders,” Plasma Chem. Plasma Process., 10, 339–358.Google Scholar
  77. Kang, S.H., and Grief, R., 1993, “Thermophoretic Transport in the Outside Vapor Deposition Process,” Int. J. Heat Mass Transfer, 36, 1007–1018.Google Scholar
  78. Kasagi, N., Kuroda, A., and Hirata, M., 1989, “Numerical Investigation of Near-Wall Turbulent Heat Transfer Taking into Account the Unsteady Heat Transfer in the Solid Wall,” ASME J. Heat Transfer, 111, 385–392.Google Scholar
  79. Kasagi, N., Tomita, Y., and Kuroda, A., 1992, “Direct Numerical Simulation of Passive Scalar Fields in a Turbulent Channel Flow,” ASME J. Heat Transfer, 114, 598–606.ADSGoogle Scholar
  80. Kaviany, M., 1985, “Laminar Flow Through a Porous Channel Bounded by Isothermal Parallel Plates,” Int. J. Heat Mass Transfer, 28, 851–858.Google Scholar
  81. Kaviany, M., 1987, “Boundary Layer Treatment of Forced Convection Heat Transfer from a Semi-Infinite Flat Plate Embedded in Porous Media,” ASME J. Heat Transfer, 109, 345–349.Google Scholar
  82. Kaviany, M., 1988, “Heat Transfer About a Permeable Membrane,” ASME J. Heat Transfer, 110, 514–516.Google Scholar
  83. Kaviany, M., 1990, “Performance of a Heat Exchanger Based on Enhanced Heat Diffusion in Fluids by Oscillation: Analysis,” ASME J. Heat Transfer, 112, 49–55.Google Scholar
  84. Kaviany, M., 1999, Principles of Heat Transfer in Porous Media, Corrected Second Edition, Springer-Verlag, New York.Google Scholar
  85. Kaviany, M., 2001, Principles of Heat Transfer, John Wiley and Sons, New York, in pressGoogle Scholar
  86. Kaviany, M., and Miltal, M., 1987, “Natural Convection Heat Transfer from a Vertical Plate to High Permeability Porous Media: An Experiment and an Approximate Solution,” Int. J. Heat Mass Transfer, 30, 967–977.MATHGoogle Scholar
  87. Kaviany, M., and Reckker, M., 1990, “Performance of a Heat Exchanger Based on Enhanced Heat Diffusion in Fluids by Oscillation: Experiment,” ASME J. Heat Transfer, 112, 56–63.Google Scholar
  88. Kays, W.M., and Crawford, M.E., 1993, Convective Heat and Mass Transfer, Third Edition, McGraw-Hill, New York.Google Scholar
  89. Keanini, R., and Rubinsky, B., 1993, “Three-Dimensional Simulation of the Plasma Arc Welding Process,” Int. J. Heat Mass Transfer, 36, 3283–3298.MATHGoogle Scholar
  90. Kececioglu, I., and Rubinsky, B., 1989, “A Continuum Model for the Propagation of Discrete Phase-Change Fronts in Porous Media in the Presence of Coupled Heat Flow, Fluid Flow and Species Transport Processes,” Int. J. Heat Mass Transfer, 32, 1111–1130.MATHGoogle Scholar
  91. Kerstein, A.R., 1992, “Linear Eddy Modeling of Turbulent Transport. Part 7. Finite-Rate Chemistry and Multi-Stream Mixing,” J. Fluid Mech., 240, 289–313.ADSGoogle Scholar
  92. Kestin, J., 1966, “The Effects of Free-Stream Turbulence on Heat Transfer Rates,” Advan. Heat Transfer, 3, 1–32.Google Scholar
  93. Kestin, J., Maeder, P.F., and Wang, H.E., 1961, “On Boundary Layers Associated with Oscillating Streams,” Appl. Sci. Res., A10, 1–22.Google Scholar
  94. Kim, J.-K., and Aihara, T., 1992, “A Numerical Study of Heat Transfer due to an Axisymmetric Laminar Impinging Jet of Supercritical Carbon Dioxide,” Int. J. Heat Mass Transfer, 35, 2515–2526.Google Scholar
  95. Kim, J., and Moin, P., 1989, “Transport of Passive Scalars in a Turbulent Channel Flow,” in Turbulent Shear Flows VI, André, J.-C., et al., Editors, Springer-Verlag, Berlin.Google Scholar
  96. Kim, J., Simon, T.W., and Russ, S.G., 1992, “Free-Stream Turbulence and Concave Curvature Effects on Heated, Transitional Boundary Layers,” ASME J. Heat Transfer, 114, 338–347.Google Scholar
  97. Klebanoff, P.S., Cleveland, W.G., and Tidstrom, K.D., 1992, “On the Evolution of a Turbulent Boundary Layer Induced by a Three-Dimensional Roughness Element,” J. Fluid Mech., 237, 101–182.ADSGoogle Scholar
  98. Kogan, M.N., 1973, “Molecular Gas Dynamics,” Ann. Rev. Fluid Mech., 5, 383–404.ADSGoogle Scholar
  99. Konuma, M., 1992, Film Deposition by Plasma Techniques, Springer-Verlag, New York.Google Scholar
  100. Kurzweg, U.H., 1985, “Enhanced Heat Conduction in Fluids Subjected to Sinusoidal Oscillations,” ASME J. Heat Transfer, 107, 459–462.Google Scholar
  101. Lancaster, J.F., Editor, 1986, The Physics of Welding, Pergamon Press, Oxford.Google Scholar
  102. Launder, B.E., 1988, “On the Computation of Convective Heat Transfer in Complex Turbulent Flows,” ASME J. Heat Transfer, 110, 1112–1128.ADSGoogle Scholar
  103. Lazarenko, B.R., Grosu, F.P., and Bologa, M.K., 1975, “Convective Heat Transfer Enhancement by Electric Fields,” Int. J. Heat Mass Transfer, 18, 1433–1441.ADSMATHGoogle Scholar
  104. Lee, S.T., and T’ien, J.S., 1982, “A Numerical Analysis of Flame Flashback in a Premixed Laminar System,” Combust. Flame, 48, 273–285.Google Scholar
  105. Lemlich, R., 1961, “Vibration and Pulsation Boost Heat Transfer,” Chem. Eng., 68, 171–176.Google Scholar
  106. Lin, S.-J., and Churchill, S.W., 1978, “Turbulent Free Convection from a Vertical, Isothermal Plate,” Num. Heat Transfer, 1, 129–145.ADSGoogle Scholar
  107. Liu, C.N., and Shih, T.M., 1980, “Laminar, Mixed-Convection, Boundary-Layer, Nongray-Radiative Diffusion Flame,” ASME J. Heat Transfer, 102, 724–730.ADSGoogle Scholar
  108. Liu, K.V., Lloyed, J.R., and Yang, K.J., 1981, “An Investigation of a Laminar Diffusion Flame Adjacent to a Vertical Flat Plate Burner,” Int. J. Heat Mass Transfer, 24, 1959–1970.Google Scholar
  109. Liu, K.V., Yang, K.T., and Lloyed, J.R., 1982, “Elliptic Field Calculation of a Laminar Diffusion Flame Adjacent to a Vertical Flat Plate Burner,” Int. J. Heat Mass Transfer, 25, 863–870.MATHGoogle Scholar
  110. Lloyed, J.R., and Sparrow, E.M., 1970, “Combined Forced and Free Convection Flow on Vertical Surfaces,” Int. J. Heat Mass Transfer, 13, 434–438.Google Scholar
  111. Lord, R.G., 1992, “Direct Simulation Monte Carlo Calculations of Rarefied Flows with Incomplete Surface Accommodation,” J. Fluid Mech., 239, 449–459.ADSGoogle Scholar
  112. Louge, M., Yusef, M.J., and Jenkins, J.T., 1993, “Heat Transfer in the Pneumatic Transport of Massive Particles,” Int. J. Heat Mass Transfer, 36, 265–275.ADSMATHGoogle Scholar
  113. Lykoudis, P.S., 1962, “Natural Convection of an Electrically Conducting Fluid in the Presence of a Magnetic Field,” Int. J. Heat Mass Transfer, 5, 23–34.Google Scholar
  114. Lykoudis, P.S., and Yu, C.P., 1963, “The Influence of Electrostrictive Forces in Natural Thermal Convection,” Int. J. Heat Mass Transfer, 6, 853–862.Google Scholar
  115. Maciejewski, P.K., and Moffat, R.J., 1992, “Heat Transfer with Very High Free-Stream Turbulence. Part I. Experimental Data; Part II. Analysis of Results,” ASME J. Heat Transfer, 114, 827–839.ADSGoogle Scholar
  116. Martin, B.W., 1984, “An Appreciation of Advances in Natural Convection Along an Isothermal Vertical Surface,” Int. J. Heat Mass Transfer, 27, 1583–1586.Google Scholar
  117. Martin, H., 1977, “Heat and Mass Transfer Between Impinging Gas Jets and Solid Surfaces,” Advan. Heat Transfer, 13, 1–60.Google Scholar
  118. Martin, P.J., and Richardson, A.T., 1984. “Conductivity Models of Electrothermal Convection in a Plane Layer of Dielectric Liquid,” ASME J. Heat Transfer, 106, 131–142.Google Scholar
  119. Meeks, E., Kee, R.J., Dandy, D.S., and Coltrin, M.E., 1993, “Computational Simulation of Diamond Chemical Vapor Deposition in Premixed C2H2/O2/H2 and CH4/O2—Strained Flames,” Combust. Flame, 92, 144–160.Google Scholar
  120. Mehendale, A.B., and Han, J.C., 1992, “Influence of High Mainstream Turbulence on Leading Edge Film Cooling Heat Transfer: Effect of Film Hole Spacing,” Int. J. Heat Mass Transfer, 35, 2593–2604.ADSGoogle Scholar
  121. Merkin, J.H., 1969, “The Effect of Buoyancy Forces on the Boundary-Layer Flow over a Semi-Infinite Vertical Flat Plate in a Uniform Free Stream,” J. Fluid Mech., 35, 439–450.ADSMATHGoogle Scholar
  122. Merkli, P., and Thomann, H., 1975, “Thermoacoustic Effects in a Resonance Tube,” J. Fluid Mech., 1970, 161–177.ADSGoogle Scholar
  123. Metzner, A.B., 1965, “Heat Transfer in Non-Newtonian Fluids,” Advan. Heat Transfer, 2, 357–397.Google Scholar
  124. Michaelides, E.E., 1986, “Heat Transfer in Particulate Flows,” Int. J. Heat Mass Transfer, 29, 265–273.Google Scholar
  125. Mironov, B.P., Vasechkin, V.N., Mamonov, V.N., and Yarygina, N.J., 1982, “Transport Processes in Turbulent Boundary Layer Under High-Level Free Stream Turbulence,” in Structure of Turbulence in Heat and Mass Transfer, 221–243, Hemisphere Publishing Corporation, Washington, DC.Google Scholar
  126. Mittal, M.L., Natarja, H.R., and Naidu, V.G., 1987, “Fluid Flow and Heat Transfer in the Duct of an MHD Power Generator,” Int. J. Heat Mass Transfer, 30, 527–535.MATHGoogle Scholar
  127. Mohandi, R.B., and Gilligan, J.G., 1990, “Electrical Conductivity and Thermodynamic Functions of Weakly Nonideal Plasma,” J. Appl. Phys., 68, 5044–5051.ADSGoogle Scholar
  128. Molodtsof, Y., and Muzyka, D.W., 1989, “General Probabilistic Multiphase Flow Equations for Analyzing Gas-Solid Mixtures,” Int. J. Eng. Fluid Mech., 2, 1–24.Google Scholar
  129. Muntz, E.P., 1989, “Rarefied Gas Dynamics,” Ann. Rev. Fluid Mech., 121, 387–417.MathSciNetADSGoogle Scholar
  130. Murayama, M., and Uchida, K., 1992, “Synthesis of Uniform Diamond Films by Flat Flame Combustion of Acetylene/Hydrogen/Oxygen Mixtures,” Combust. Flame, 91, 239–245.ADSGoogle Scholar
  131. Nield, D.A., and Bejan, A., 1992, Convection in Porous Media, Springer-Verlag, New York.Google Scholar
  132. Nielson, D.G., and Incropera, F.P., 1993a, “Three-Dimensional Consideration of Unidirectional Solidification in a Binary Liquid,” Num. Heat Transfer, 23A, 1–20.ADSGoogle Scholar
  133. Nielson, D.G., and Incropera, F.P., 1993b, “Effect of Rotation on Fluid Motion and Channel Formation During Unidirectional Solidification of a Binary Alloy,” Int. J. Heat Mass Transfer, 36, 489–505.Google Scholar
  134. Oliver, F.W.J., 1972, “Bessel Functions of Integer Order,” Handbook of Mathematical Functions, Abramowitz, M., and Stegun, X., Editors, U.S. Government Printing Office, Washington, DC.Google Scholar
  135. Orloff, L., de Ris, J., and Delichatsios, M.A., 1992, “Radiation from Buoyant Turbulent Diffusion Flame,” Combust. Sci. Tech., 84, 177–186.Google Scholar
  136. özdemir, I.B., and Whitelaw, J.H., 1992, “Impingement of an Axisymmetric Jet on Unheated and Heated Flat Plates,” J. Fluid Mech., 240, 503–532.ADSGoogle Scholar
  137. Özisik, M.N., 1985, Radiative Transport and Interaction with Conduction and Convection, Werbel and Peck, New York.Google Scholar
  138. Ozoe, H., Sato, N., and Churchill, S.W., 1980, “The Effect of Various Parameters on Thermoacoustic Convection,” Chem. Eng. Comm., 5, 203–221.Google Scholar
  139. Paolucci, S., and Chenoweth, D.R., 1987, “Transition to Chaos in a Differentially Heated Vertical Cavity,” J. Fluid Mech., 201, 379–410.ADSGoogle Scholar
  140. Peters, M., 1992, “A Spectral Closure for Premixed Turbulent Combustion in the Flamelet Regime,” J. Fluid Mech., 242, 611–629.MathSciNetADSMATHGoogle Scholar
  141. Platten, J.K., and Legros, J.C., 1984, Convection in Liquids, Springer-Verlag, Berlin.MATHGoogle Scholar
  142. Pletcher, R.H., 1988, “Progress in Turbulent Forced Convection,” ASME J. Heat Transfer, 110, 1129–1144.ADSGoogle Scholar
  143. Poirier, D.R., Mandapurkar, P.J., and Ganesan, S., 1991, “The Energy and Solute Conservation Equations for Dendritic Solidification,” Metall. Trans., 22B, 889–900.Google Scholar
  144. Puzach, V.G., 1992, “Heat and Mass Transfer on a Rough Surface with Gas Blowing at the Wall,” Int. J. Heat Mass Transfer, 35, 981–986.Google Scholar
  145. Radebaugh, R., 1990, “A Review of Pulse Tube Refrigeration,” Adv. Cryog. Eng., 35, 1191–1205.Google Scholar
  146. Ramesham, R., and Ellis, C., 1992, “Selective Growth of Diamond Crystals on the Apex of Silicon Pyramids,” J. Mater. Res., 7, 1189–1194.ADSGoogle Scholar
  147. Rappaz, M., and Voller, V., 1990, “Modeling of Micro-Macrosegregation in Solidification Processes,” Metall. Trans., 21A, 749–753.Google Scholar
  148. Romig, M.F., 1964, “The Influence of Electric and Magnetic Fields on Heat Transfer to Electrically Conducting Fluids,” Advan. Heat Transfer, 1, 267–354.Google Scholar
  149. Rossow, V.J., 1957, On Flow of Electrically Conducting Fluids over a Flat Plate in the Presence of a Magnetic Field, NASA Technical Note 3971.Google Scholar
  150. Rott, N., 1974, “The Heating Effect Connected with Nonlinear Oscillations in a Resonance Tube,” J. Appl. Math. Phys. (ZAMP), 25, 619–634.Google Scholar
  151. Rott, N., 1980, “Thermoacoustics,” Advan. Appl Mech., 20, 135–175.MATHGoogle Scholar
  152. Rott, N., 1984, “Thermoacoustic Heating at the Closed End of an Oscillating Gas Column,” J. Fluid Mech., 145, 1–9.MathSciNetADSMATHGoogle Scholar
  153. Sahraoui, M., and Kaviany, M., 1994, “Slip and No-Slip Temperature Boundary Conditions at Interface of Porous, Plain Media: Convection,” Int. J. Heat Mass Transfer, 37, 1029–1044.MATHGoogle Scholar
  154. Schlichting, H., 1979, Boundary-Layer Theory, Seventh Edition, McGraw-Hill, New York.MATHGoogle Scholar
  155. Shadid, J.N., and Eckert, E.R.G., 1992, “Viscous Heating of a Cylinder with Finite Length by a High Viscosity Fluid in Steady Longitudinal Flow. II. Non-Newtonian Carreau Model Fluids,” Int. J. Heat Mass Transfer, 35, 2739–2749.MATHGoogle Scholar
  156. Shenoy, A.V., and Masheikar, R.A., 1982, “Thermal Convection in Non-Newtonian Fluids,” Advan. Heat Transfer, 15, 143–225.Google Scholar
  157. Sherman, F.S., 1955, A Low-Density Wind-Tunnel Study of Shock-Wave Structure and Relaxation Phenomena in Gases, NASA Technical Report 3298.Google Scholar
  158. Sherman, F.S., 1969, “The Transition from Continuum to Molecular Flow,” Ann. Rev. Fluid Mech., 1, 317–340.ADSGoogle Scholar
  159. Sherman, F.S., 1990, Viscous Flow, McGraw-Hill, New York.MATHGoogle Scholar
  160. Siegel, R., and Howell, J.R., 1992, Thermal Radiation Heat Transfer, Third Edition, Hemisphere Publishing Company, Washington, DC.Google Scholar
  161. Siegel, R., and Snyder, A., 1984, “Shape of Porous Region to Control Cooling Along Curved Exit Boundary,” Int. J. Heat Mass Transfer, 27, 243–252.ADSMATHGoogle Scholar
  162. Simpkins, P.G., Greenberg-Kosinski, S., and MacChesney, J.B., 1979, “Ther-mophoresis: The Mass Transfer Mechanism in Modified Chemical Vapor Deposition,” J. Appl. Phys., 50, 5676–5681.ADSGoogle Scholar
  163. Sinai, Y.L., 1987, “A Wall Function for the Temperate Variance in Turbulent Flow Adjacent to a Diabatic Wall,” ASME J. Heat Transfer, 109, 861–865.MathSciNetGoogle Scholar
  164. Smith, H., and Jensen, H.H., 1989, Transport Phenomena, Oxford University Press, Oxford.Google Scholar
  165. Soo, S.-L., 1989, Particulates and Continuum, Hemisphere Publishing Corporation, New York.MATHGoogle Scholar
  166. Soo, S.-L., Trezek, G.J., Dimick, R.C., and Hohnstreiter, G.F., 1964, “Concentration and Mass Flow Distribution in a Gas-Solid Suspension,” Ind. Eng. Chem. Fundam., 3, 98–104.Google Scholar
  167. Spalding, D.B., 1979, Combustion and Mass Transfer, Pergamon Press, Oxford.Google Scholar
  168. Sparrow, E.M., and Cess, R.D., 1961a, “The Effect of a Magnetic Field on Free Convection Heat Transfer,” Int. J. Heat Mass Transfer, 3, 267–274.Google Scholar
  169. Sparrow, E.M., and Cess, R.D., 1961b, “Free Convection with Blowing or Suction,” ASME J. Heat Transfer, 83, 387–389.Google Scholar
  170. Sparrow, E.M., and Cess, R.D., 1978, Radiation Heat Transfer, Hemisphere Publishing Corporation, Washington, DC.Google Scholar
  171. Sparrow, E.M., and Lin, S.H., 1962, “Laminar Heat Transfer in Tubes Under Slip-Flow Conditions,” ASME J. Heat Transfer, 84, 363–369.Google Scholar
  172. Springer, G.S., 1971, “Heat Transfer in Rarefied Gases,” Advan. Heat Transfer, 7, 163–218.Google Scholar
  173. Stadler, K.R., and Sharpless, R.L., 1990, “Plasma Properties of a Hydrocarbon Arc Jet Used in the Plasma Deposition of Diamond Thin Films,” J. Appl. Phys., 68, 6189–6190.ADSGoogle Scholar
  174. Striegl, S.A., and Diller, T.E., 1984, “An Analysis of the Effect of Entrainment Temperature on Jet Impingement Heat Transfer,” ASME J. Heat Transfer, 106, 804–810.Google Scholar
  175. Sundarraj, S., and Voller, V.R., 1993, “The Binary Alloy Problem in an Expanding Domain: The Microsegregation Problem,” Int. J. Heat Mass Transfer, 36, 713–723.Google Scholar
  176. Swift, G.W., 1988, “Thermoacoustic Engines,” J. Acoust. Soc. Am., 84, 1145–1180.ADSGoogle Scholar
  177. Takhar, H.S., and Soundalgekar, V.M., 1977, “Effect of Viscous Dissipation on Heat Transfer in an Oscillating Flow Past a Flat Plate,” Appl. Sci. Res., 33, 101–111.ADSMATHGoogle Scholar
  178. Tao, Y.-X., and Kaviany, M., 1991, “Burning Rate of Liquid Supplied Through a Wick,” Combust. Flame., 86, 47–61.Google Scholar
  179. Taylor, R.P., Coleman, H.W., and Hodge, B.K., 1989, “Prediction of Heat Transfer in Turbulent Flow over Rough Surfaces,” ASME J. Heat Transfer, 111, 569–572.Google Scholar
  180. To, W.M., and Humphrey, J.A.C., 1986, “Numerical Simulation of Buoyant, Turbulent Flow. I. Free Convection Along a Heated, Vertical, Flat Plate,” Int. J. Heat Mass Transfer, 29, 573–592.ADSMATHGoogle Scholar
  181. Toong, T.-Y., 1983, Combustion Dynamics, McGraw-Hill, New York.Google Scholar
  182. Tsai, C., Nelson, J., and Gerberich, W.W., 1992, “Metal Reinforced Thermal Plasma Diamond Coating,” J. Mater. Res., 7, 1967–1972.ADSGoogle Scholar
  183. Tsai, M.C., and Kou, S., 1990, “Heat Transfer and Fluid Flow in Welding Arcs Produced by Sharpened and Flat Electrodes,” Int. J. Heat Mass Transfer, 33, 2089–2098.Google Scholar
  184. Turnbull, R.J., 1969, “Free Convection from a Heated Vertical Plate in a Direct-Current Electric Field,” Phys. Fluids, 12, 2255–2263.ADSGoogle Scholar
  185. Turnbull, R.J., 1971a, “Instability of a Thermal Boundary Layer in a Constant Electric Field,” J. Fluid Mech., 47, 231–239.ADSGoogle Scholar
  186. Turnbull, R.J., 1971b, “Effect of Non-uniform Alternating Electric Field on the Thermal Boundary Layer Near a Heated Vertical Plate,” J. Fluid Mech., 49, 693–703.ADSMATHGoogle Scholar
  187. Turner, J.S., 1979, Buoyancy Effects in Fluids, Cambridge University Press, Cambridge.MATHGoogle Scholar
  188. Vafai, K., and Tien, C.-L., 1981, “Boundary and Inertia Effects on Flow and Heat Transfer in Porous Media,” Int. J. Heat Mass Transfer, 24, 195–203.MATHGoogle Scholar
  189. Viskanta, R., 1966, “Radiation Transfer and Interaction of Convection with Radiation Heat Transfer,” Advan. Heat Transfer, 3, 175–251.Google Scholar
  190. Wadsworth, DC., and Erwin, D.A., 1993, “Numerical Simulation of Rarefied Flow Through a Slit. Part I: Direct Simulation Monte Carlo Results,” Phys. Fluids, 5, 235–242.ADSGoogle Scholar
  191. Wadsworth, DC., Erwin, D.A., and Muntz, E.P., 1993, “Transient Motion of a Confined Gas Due to Wall Heating or Cooling,” J. Fluid Mech., 248, 219–235.ADSMATHGoogle Scholar
  192. Walker, K.L., Homsy, G.M., and Geyling, F.T., 1979, “Thermophoretic Deposition of Small Particles in Laminar Tube Flow,” J. Colloid Interface Sci., 69, 138–147.Google Scholar
  193. Watson, E.J., 1983, “Diffusion in Oscillatory Pipe Flow,” J. Fluid Mech., 133, 233–244.MathSciNetADSMATHGoogle Scholar
  194. Wheatley, J., Hofler, T., Swift, G.W., and Migliori, A., 1985, “Understanding Some Simple Phenomena in Thermoacoustics with Applications to Acoustical Heat Engines,” Am. J. Phys., 53, 147–162.ADSGoogle Scholar
  195. White, F.M., 1991, Viscous Fluid Flow, Second Edition, McGraw-Hill, New York.Google Scholar
  196. Wichman, I.S., and Argawal, S., 1991, “Wind-Aided Flame Spread over a Thick Solid,” Combust. Flame, 83, 127–145.Google Scholar
  197. Williams, F.A., 1985, Combustion Theory, Addison-Wesley, Redwood City, CA.Google Scholar
  198. Winter, H.H., 1977, “Viscous Dissipation in Shear Flows of Molten Polymers,” Advan. Heat Transfer, 13, 205–267.Google Scholar
  199. Worster, M.G., 1991, “Natural Convection in a Mushy Layer,” J. Fluid Mech., 224, 335–359.ADSMATHGoogle Scholar
  200. Worster, M.G., 1992, “Instabilities of the Liquid and Mushy Regions During Solidification of Alloys,” J. Fluid Mech., 237, 649–669.ADSMATHGoogle Scholar
  201. Yen, S.M., 1984, “Numerical Solution of the Nonlinear Boltzmann Equation for Nonequilibrium Gas Flow Problems,” Ann. Rev. Fluid Mech., 16, 67–97.ADSGoogle Scholar
  202. Youssef, M.S., Nagano, Y., and Tagawa, M., 1992, “A Two-Equation Heat Transfer Model for Predicting Turbulent Thermal Fields Under Arbitrary Wall Thermal Conditions,” Int. J. Heat Mass Transfer, 35, 3095–3104.Google Scholar
  203. Yuan, T.D., and Liburdy, J.A., 1992, “Application of a Surface Renewal Model to the Prediction of Heat Transfer in an Impinging Jet,” Int. J. Heat Mass Transfer, 35, 1905–1912.ADSGoogle Scholar
  204. Zappoli, B., 1992, “The Response of a Nearly Supercritical Pure Fluid to a Thermal Disturbance,” Phys. Fluids, A4, 1040–1048.ADSGoogle Scholar
  205. Zaric, Z.P., Editor, 1982, Structure of Turbulence in Heat and Mass Transfer, Hemisphere Publishing Corporation, Washington, DC.Google Scholar
  206. Zhao, G.Y., Dassanayake, M., and Etemadi, K., 1990, “Numerical Simulation of a Free-Burning Argon Arc with Copper Evaporation from the Anode,” Plasma Chem. Plasma Process., 10, 87–98.Google Scholar
  207. Zhao, G.Y., Mostaghimi, J., and Boulos, M.I., 1990, “The Induction Plasma Chemical Reactor: Part I. Equilibrium Model, and Part II. Kinetic Model,” Plasma Chem. Plasma Process., 10, 133–167.Google Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Massoud Kaviany
    • 1
  1. 1.Department of Mechanical Engineering and Applied MechanicsUniversity of MichiganAnn ArborUSA

Personalised recommendations