Principles of Convective Heat Transfer pp 181-347 | Cite as

# Solid—Fluid Systems with Simple, Continuous Interface

Chapter

## Abstract

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.

## Keywords

Heat Transfer Nusselt Number Heat Transfer Rate Heat Mass Transfer Local Nusselt Number## Preview

Unable to display preview. Download preview PDF.

## References

- 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 - 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 - 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 - 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 - Arpaci, V.S., and Larsen, P.S., 1984,
*Convective Heat Transfer*, Prentice-Hall, Englewood Cliffs, NJ.Google Scholar - 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 - Bau, H.H., 1992, “Controlling Chaotic Convection,” in
*Theoretical and Applied Mechanics 1992*, Bonder, S., et al., Editors, 187–203, Elsevier, Amsterdam.Google Scholar - Bau, H.H., and Wang, Y.-Z., 1992, “Chaos: A Heat Transfer Perspective,”
*Ann. Rev. Heat Transfer*, 4, 1–50.Google Scholar - Bejan, A., 1984,
*Convection Heat Transfer*, John Wiley and Sons, New York.MATHGoogle Scholar - 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 - 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 - 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 - 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 - 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 - Böhme, G.,
*Non-Newtonian Fluid Mechanics*, 1982, North-Holland, Amsterdam.Google Scholar - 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 - 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 - 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 - 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 - Brown, M.A., and Churchill, S.W., 1993, “Transient Behavior of an Impulsively Heated Fluid,”
*Chem. Eng. Technol.*, 16, 82–88.Google Scholar - 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 - Burmeister, L.C., 1983,
*Convective Heat Transfer*, John Wiley and Sons, New York.Google Scholar - Cancaster, J.F., Editor, 1986,
*The Physics of Welding*, Pergamon Press, Oxford.Google Scholar - 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 - Cebeci, T., and Bradshaw, P., 1984,
*Physical and Computational Aspects of Convection Heat Transfer*, Springer-Verlag, New York.Google Scholar - Chandrasekhar, S., 1981,
*Hydrodynamic and Hydromagnetic Stability*, Dover, New York.Google Scholar - 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 - 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 - 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 - Cheng, P., 1978a, “Convective Heat Transfer in Porous Layers by Integral Methods,”
*Commun. Heat Mass Transfer*, 5, 243–252.Google Scholar - Cheng, P., 1978b, “Heat Transfer in Geothermal Systems,”
*Advan. Heat Transfer*, 14, 1–105.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. Geophs. Res.*, 82, 2040–2044.ADSGoogle Scholar - Cho, Y.I., and Hartnett, J.P., 1982, “Non-Newtonian Fluids in Circular Pipe Flow,”
*Advan. Heat Transfer*, 15, 59–141.Google Scholar - Chung, P.M., 1965, “Chemically Reacting Nonequilibrium Boundary Layers,”
*Advan. Heat Transfer*, 2, 109–270.Google Scholar - Churchill, S.W., 1977, “A Comprehensive Correlating Equation for Laminar, Assisting, Forced and Free Convection,”
*AIChE J.*, 23, 10–16.Google Scholar - 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 - 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 - 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 - Cramer, K.R., 1963, “Several Magnetohydrodynamic Free-Convection Solutions,”
*ASME J. Heat Transfer*, 85, 35–40.Google Scholar - Cunningham, R.E., and Williams, R.J.J., 1980,
*Diffusion in Gases and Porous Media*, Plenum Press, New York.Google Scholar - Depew, C.A., and Kramer, T.J., 1973, “Heat Transfer to Flowing Gas-Solid Mixtures,”
*Advan. Heat Transfer*, 9, 113–180.Google Scholar - de Ris, J., 1969, “Spread of a Laminar Diffusion Flame,”
*Twelfth Symposium (International) on Combustion*, 241–252,*The Combustion Institute*, Pittsburgh.Google Scholar - 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 - Eckert, E.R.G., and Drake, R.M., Jr., 1972,
*Analysis of Heat and Mass Transfer*, McGraw-Hill, New York.MATHGoogle Scholar - Ede, A.J., 1967, “Advances in Natural Convection,”
*Advan. Heat Transfer*, 4, 1–64.Google Scholar - Edwards, D.K., 1981,
*Radiation Heat Transfer Notes*, Hemisphere Publishing Company, New York.Google Scholar - 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 - Eichhorn, R., 1960, “The Effect of Mass Transfer on Free Convection,”
*ASME J. Heat Transfer*, 82, 260–263.Google Scholar - Emmons, H.W., 1956, “The Film Combustion of Liquid Fuel,”
*Z. Agnew. Math. Mech., 36*, 60–71.MATHGoogle Scholar - 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 - 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 - 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 - Fujii, T., Poirier, D.R., and Flemings, M.C., 1979, “Macrosegregation in a Multicomponent Low Alloy Steel,”
*Metall. Trans.*, 10B, 331–339.Google Scholar - 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 - Galante, S.R., and Churchill, S.W., 1990, “Applicability of Solutions of Convection in Potential Flows,”
*Advan. Heat Transfer*, 20, 353–388.Google Scholar - Gebhart, B., Jaluria, Y., Mahajan, R.L., and Sammakia, B., 1988,
*Buoyancy-Induced Flows and Transport*, Hemisphere Publishing Corporation, Washington, DC.MATHGoogle Scholar - 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 - 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 - Glassman, I., 1987,
*Combustion*, Second Edition, Academic Press, Orlando.Google Scholar - Goldstein, R.J., 1971, “Film Cooling,”
*Advan. Heat Transfer*, 7, 321–379.Google Scholar - 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 - 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 - 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 - 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 - Hartnett, J.P., 1992, “Viscoelastic Fluids: A New Challenge in Heat Transfer,”
*ASME J. Heat Transfer*, 114, 296–303.Google Scholar - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - Huppert, H.E., 1990, “The Fluid Mechanics of Solidification,”
*J. Fluid Mech.*, 212, 209–240.MathSciNetADSGoogle Scholar - Jaluria, Y., 1980,
*Natural Convection Heat and Mass Transfer*, Pergamon Press, Oxford.Google Scholar - 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 - 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 - 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 - 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 - Kaviany, M., 1985, “Laminar Flow Through a Porous Channel Bounded by Isothermal Parallel Plates,”
*Int. J. Heat Mass Transfer*, 28, 851–858.Google Scholar - 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 - Kaviany, M., 1988, “Heat Transfer About a Permeable Membrane,”
*ASME J. Heat Transfer*, 110, 514–516.Google Scholar - 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 - Kaviany, M., 1999,
*Principles of Heat Transfer in Porous Media*, Corrected Second Edition, Springer-Verlag, New York.Google Scholar - Kaviany, M., 2001,
*Principles of Heat Transfer*, John Wiley and Sons, New York, in pressGoogle Scholar - 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 - 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 - Kays, W.M., and Crawford, M.E., 1993,
*Convective Heat and Mass Transfer*, Third Edition, McGraw-Hill, New York.Google Scholar - 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 - 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 - 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 - Kestin, J., 1966, “The Effects of Free-Stream Turbulence on Heat Transfer Rates,”
*Advan. Heat Transfer*, 3, 1–32.Google Scholar - 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 - 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 - 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 - 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 - 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 - Kogan, M.N., 1973, “Molecular Gas Dynamics,”
*Ann. Rev. Fluid Mech.*, 5, 383–404.ADSGoogle Scholar - Konuma, M., 1992,
*Film Deposition by Plasma Techniques*, Springer-Verlag, New York.Google Scholar - Kurzweg, U.H., 1985, “Enhanced Heat Conduction in Fluids Subjected to Sinusoidal Oscillations,”
*ASME J. Heat Transfer*, 107, 459–462.Google Scholar - Lancaster, J.F., Editor, 1986,
*The Physics of Welding*, Pergamon Press, Oxford.Google Scholar - Launder, B.E., 1988, “On the Computation of Convective Heat Transfer in Complex Turbulent Flows,”
*ASME J. Heat Transfer*, 110, 1112–1128.ADSGoogle Scholar - 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 - 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 - Lemlich, R., 1961, “Vibration and Pulsation Boost Heat Transfer,”
*Chem. Eng.*, 68, 171–176.Google Scholar - Lin, S.-J., and Churchill, S.W., 1978, “Turbulent Free Convection from a Vertical, Isothermal Plate,”
*Num. Heat Transfer*, 1, 129–145.ADSGoogle Scholar - 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 - 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 - 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 - 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 - Lord, R.G., 1992, “Direct Simulation Monte Carlo Calculations of Rarefied Flows with Incomplete Surface Accommodation,”
*J. Fluid Mech.*, 239, 449–459.ADSGoogle Scholar - 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 - 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 - 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 - 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 - 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 - Martin, H., 1977, “Heat and Mass Transfer Between Impinging Gas Jets and Solid Surfaces,”
*Advan. Heat Transfer*, 13, 1–60.Google Scholar - 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 - Meeks, E., Kee, R.J., Dandy, D.S., and Coltrin, M.E., 1993, “Computational Simulation of Diamond Chemical Vapor Deposition in Premixed C
_{2}H_{2}/O_{2}/H_{2}and CH_{4}/O_{2}—Strained Flames,”*Combust. Flame*, 92, 144–160.Google Scholar - 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 - 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 - Merkli, P., and Thomann, H., 1975, “Thermoacoustic Effects in a Resonance Tube,”
*J. Fluid Mech.*, 1970, 161–177.ADSGoogle Scholar - Metzner, A.B., 1965, “Heat Transfer in Non-Newtonian Fluids,”
*Advan. Heat Transfer*, 2, 357–397.Google Scholar - Michaelides, E.E., 1986, “Heat Transfer in Particulate Flows,”
*Int. J. Heat Mass Transfer*, 29, 265–273.Google Scholar - 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 - 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 - 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 - 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 - Muntz, E.P., 1989, “Rarefied Gas Dynamics,”
*Ann. Rev. Fluid Mech.*, 121, 387–417.MathSciNetADSGoogle Scholar - 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 - Nield, D.A., and Bejan, A., 1992,
*Convection in Porous Media*, Springer-Verlag, New York.Google Scholar - 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 - 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 - 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 - Orloff, L., de Ris, J., and Delichatsios, M.A., 1992, “Radiation from Buoyant Turbulent Diffusion Flame,”
*Combust. Sci. Tech.*, 84, 177–186.Google Scholar - 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 - Özisik, M.N., 1985,
*Radiative Transport and Interaction with Conduction and Convection*, Werbel and Peck, New York.Google Scholar - 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 - Paolucci, S., and Chenoweth, D.R., 1987, “Transition to Chaos in a Differentially Heated Vertical Cavity,”
*J. Fluid Mech.*, 201, 379–410.ADSGoogle Scholar - Peters, M., 1992, “A Spectral Closure for Premixed Turbulent Combustion in the Flamelet Regime,”
*J. Fluid Mech.*, 242, 611–629.MathSciNetADSMATHGoogle Scholar - Platten, J.K., and Legros, J.C., 1984,
*Convection in Liquids*, Springer-Verlag, Berlin.MATHGoogle Scholar - Pletcher, R.H., 1988, “Progress in Turbulent Forced Convection,”
*ASME J. Heat Transfer*, 110, 1129–1144.ADSGoogle Scholar - 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 - 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 - Radebaugh, R., 1990, “A Review of Pulse Tube Refrigeration,”
*Adv. Cryog. Eng.*, 35, 1191–1205.Google Scholar - 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 - Rappaz, M., and Voller, V., 1990, “Modeling of Micro-Macrosegregation in Solidification Processes,”
*Metall. Trans.*, 21A, 749–753.Google Scholar - 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 - 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 - Rott, N., 1974, “The Heating Effect Connected with Nonlinear Oscillations in a Resonance Tube,”
*J. Appl. Math. Phys. (ZAMP)*, 25, 619–634.Google Scholar - Rott, N., 1980, “Thermoacoustics,”
*Advan. Appl Mech.*, 20, 135–175.MATHGoogle Scholar - Rott, N., 1984, “Thermoacoustic Heating at the Closed End of an Oscillating Gas Column,”
*J. Fluid Mech.*, 145, 1–9.MathSciNetADSMATHGoogle Scholar - 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 - Schlichting, H., 1979,
*Boundary-Layer Theory*, Seventh Edition, McGraw-Hill, New York.MATHGoogle Scholar - 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 - Shenoy, A.V., and Masheikar, R.A., 1982, “Thermal Convection in Non-Newtonian Fluids,”
*Advan. Heat Transfer*, 15, 143–225.Google Scholar - 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 - Sherman, F.S., 1969, “The Transition from Continuum to Molecular Flow,”
*Ann. Rev. Fluid Mech.*, 1, 317–340.ADSGoogle Scholar - Sherman, F.S., 1990,
*Viscous Flow*, McGraw-Hill, New York.MATHGoogle Scholar - Siegel, R., and Howell, J.R., 1992,
*Thermal Radiation Heat Transfer*, Third Edition, Hemisphere Publishing Company, Washington, DC.Google Scholar - 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 - 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 - 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 - Smith, H., and Jensen, H.H., 1989,
*Transport Phenomena*, Oxford University Press, Oxford.Google Scholar - Soo, S.-L., 1989,
*Particulates and Continuum*, Hemisphere Publishing Corporation, New York.MATHGoogle Scholar - 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 - Spalding, D.B., 1979,
*Combustion and Mass Transfer*, Pergamon Press, Oxford.Google Scholar - 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 - Sparrow, E.M., and Cess, R.D., 1961b, “Free Convection with Blowing or Suction,”
*ASME J. Heat Transfer*, 83, 387–389.Google Scholar - Sparrow, E.M., and Cess, R.D., 1978,
*Radiation Heat Transfer*, Hemisphere Publishing Corporation, Washington, DC.Google Scholar - 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 - Springer, G.S., 1971, “Heat Transfer in Rarefied Gases,”
*Advan. Heat Transfer, 7*, 163–218.Google Scholar - 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 - 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 - 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 - Swift, G.W., 1988, “Thermoacoustic Engines,”
*J. Acoust. Soc. Am.*, 84, 1145–1180.ADSGoogle Scholar - 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 - Tao, Y.-X., and Kaviany, M., 1991, “Burning Rate of Liquid Supplied Through a Wick,”
*Combust. Flame.*, 86, 47–61.Google Scholar - 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 - 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 - Toong, T.-Y., 1983,
*Combustion Dynamics*, McGraw-Hill, New York.Google Scholar - Tsai, C., Nelson, J., and Gerberich, W.W., 1992, “Metal Reinforced Thermal Plasma Diamond Coating,”
*J. Mater. Res.*, 7, 1967–1972.ADSGoogle Scholar - 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 - Turnbull, R.J., 1969, “Free Convection from a Heated Vertical Plate in a Direct-Current Electric Field,”
*Phys. Fluids*, 12, 2255–2263.ADSGoogle Scholar - Turnbull, R.J., 1971a, “Instability of a Thermal Boundary Layer in a Constant Electric Field,”
*J. Fluid Mech.*, 47, 231–239.ADSGoogle Scholar - 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 - Turner, J.S., 1979,
*Buoyancy Effects in Fluids*, Cambridge University Press, Cambridge.MATHGoogle Scholar - 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 - Viskanta, R., 1966, “Radiation Transfer and Interaction of Convection with Radiation Heat Transfer,”
*Advan. Heat Transfer*, 3, 175–251.Google Scholar - 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 - 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 - 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 - Watson, E.J., 1983, “Diffusion in Oscillatory Pipe Flow,”
*J. Fluid Mech.*, 133, 233–244.MathSciNetADSMATHGoogle Scholar - 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 - White, F.M., 1991,
*Viscous Fluid Flow*, Second Edition, McGraw-Hill, New York.Google Scholar - Wichman, I.S., and Argawal, S., 1991, “Wind-Aided Flame Spread over a Thick Solid,”
*Combust. Flame*, 83, 127–145.Google Scholar - Williams, F.A., 1985,
*Combustion Theory*, Addison-Wesley, Redwood City, CA.Google Scholar - Winter, H.H., 1977, “Viscous Dissipation in Shear Flows of Molten Polymers,”
*Advan. Heat Transfer*, 13, 205–267.Google Scholar - Worster, M.G., 1991, “Natural Convection in a Mushy Layer,”
*J. Fluid Mech.*, 224, 335–359.ADSMATHGoogle Scholar - Worster, M.G., 1992, “Instabilities of the Liquid and Mushy Regions During Solidification of Alloys,”
*J. Fluid Mech.*, 237, 649–669.ADSMATHGoogle Scholar - 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 - 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 - 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 - Zappoli, B., 1992, “The Response of a Nearly Supercritical Pure Fluid to a Thermal Disturbance,”
*Phys. Fluids*, A4, 1040–1048.ADSGoogle Scholar - Zaric, Z.P., Editor, 1982,
*Structure of Turbulence in Heat and Mass Transfer*, Hemisphere Publishing Corporation, Washington, DC.Google Scholar - 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 - 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