The CRC Handbook of Mechanical Engineering. Chapter 4. Heat and Mass Transfer (776127), страница 23
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Trans.ASME 84, 969–975.Rossen, H.F. and Meyers, J.A. 1965. Point values of condensing film coefficients inside a horizontaltube. Chem. Eng. Prog. Symp. Ser. 61(59), 190–199.© 1999 by CRC Press LLC4-98Section 4Seban, R. 1954. Remarks on film condensation with turbulent flow. Trans. ASME 76, 299–303.Selin, G. 1961. Heat transfer by condensing pure vapors outside inclined tubes, in Proc. First Int. HeatTransfer Conf., University of Colorado, Boulder, Part II, 279–289.Sparrow, E.M.
and Gregg, J.L. 1959. A boundary-layer treatment of laminar film condensation. J. HeatTransfer 81, 13–23.Stephen, K. 1992. Heat Transfer in Condensation and Boiling. Springer-Verlag, New York.Tanaka, H. 1975. A theoretical study of dropwise condensation. J. Heat Transfer 97, 72–78.Tanaka, H. 1979. Further developments of dropwise condensation theory. J.
Heat Transfer 101, 603–611.Traviss, D.P., Rohsenow, W.M., and Baron, A.B. 1973. Forced convection condensation in tubes: a heattransfer correlation for condenser design. ASHRAE Trans. 79(I), 157–165.Witte, L.C. and Lienhard, J.H. 1982. On the existence of two “transition” boiling curves. Int. J. HeatMass Transfer 25, 771–779.Zuber, N. 1959. Hydrodynamic aspects of boiling heat transfer. AEC Rep. AECU-4439.Further InformationThe texts Heat Transfer in Condensation and Boiling by K. Stephan (Springer-Verlag, New York, 1992)and Liquid-Vapor Phase Change Phenomena by V.P.
Carey (Taylor and Francis, Washington, D.C., 1992)provide an introduction to the physics of boiling and condensation processes. The text by J.G. Collier,Convective Boiling and Condensation (2nd ed., McGraw-Hill, New York, 1981), summarizes moreadvanced elements of convective boiling and condensation processes. The ASHRAE Handbook of Fundamentals (American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Atlanta, GA,1993) provides some information on boiling and condensation heat transfer and is a good source ofthermophysical property data needed to analyze boiling and condensation processes.Particle Gas ConvectionJohn C.
ChenIntroductionHeat transfer in two-phase systems involving gas and solid particles are encountered in several types ofoperations important in chemical, power, and environmental technologies. Chief among these are gasfluidized beds which are widely used to achieve either physical processing or chemical reactions thatrequire interfacial contact between gas and solid particles. Currently, fluidized beds operate in either thebubbling regime or the fast-circulating regime.
In the first case, particles are retained in the fluidizedbed while the gas passes upward past the particles, partially as rising bubbles. In the second case, gasvelocities exceed terminal velocity for the individual particles and the two phases flow through thefluidized bed in cocurrent upward flow. For those applications which require thermal control, convectiveheat transfer between the fluidized medium and heat transfer surfaces (either immersed tubes or thevessel walls) is an essential element of the process design.Bubbling Fluidized BedsBubbling fluidization occurs when the superficial gas velocity exceeds a critical value wherein thegravitational body force on the solid particles is balanced by the shear force between particles andflowing gas.
The superficial gas velocity at this condition, commonly called the minimum fluidizationvelocity (Umf), marks the boundary between gas flow through packed beds and gas flow in fluidizedbeds. Wen and Yu (1966) derived the following general equation to estimate Umf for spherical particles:[2Re mf = (33.7) + 0.0408Arwhere© 1999 by CRC Press LLC12]- 33.7(4.4.21)4-99Heat and Mass TransferRe mf = particle Reynolds number at U mf =Ar = Archimedes number =(U mf d p r gmg)d p3r g r s - r g gm2gIncreasing gas velocity beyond minimum fluidization causes the excess gas to collect into discrete bubblesthat grow and rise through the fluidized matrix of solid particles.
In this bubbling fluidization regime,the total pressure drop over the height of the fluidized bed, H, is equal to the hydrostatic pressure of thesolid mass,DP = gr s (1 - e) H(4.4.22)where e = volume fraction of gas (void fraction).Tubes carrying cooling or heating fluids are often immersed in bubbling fluidized beds to extract oradd thermal energy. The effective heat transfer coefficient at the surface of such tubes has been theobjective of numerous experimental and analytical investigations. Data for the circumferentially averagedheat transfer coefficient for horizontal tubes are shown in Figure 4.4.10 for various types of solid particles.Characteristics representative of such systems areFIGURE 4.4.10 Average heat transfer coefficients for horizontal tubes immersed in bubbling fluidized beds.
(FromBiyikli, Tuzla and Chen, 1983.)• The heat transfer coefficient increases sharply as the gas velocity exceeds minimum fluidizationvelocity,• After the initial increase, the heat transfer coefficient remains fairly constant over a significantrange of the gas velocity beyond minimum fluidization velocity,• The absolute magnitude of the heat transfer coefficient is severalfold greater than single-phasegas convection at the same superficial velocity,• The heat transfer coefficient increases as particle size decreases.Kunii and Levenspiel (1991) have shown that increasing gas pressure and density significantlyincreases the magnitude of the heat transfer coefficient as well as promoting the occurrence of minimumfluidization at a lower value of superficial gas velocity.
The effect of bundle spacing is insignificant at1-atm pressure but becomes increasingly more important as gas pressure and density increase. The data© 1999 by CRC Press LLC4-100Section 4of Jacob and Osberg (1957) indicate that the convective heat transfer coefficient in fluidized beds increaseswith increasing thermal conductivity of the gas phase, for any given particle size.Several different types of correlations have been suggested for predicting convective heat transfercoefficients at submerged surfaces in bubbling fluidized beds. The first type attributes the enhancementof heat transfer to the scouring action of solid particles on the gas boundary layer, thus decreasing theeffective film thickness. These models generally correlate a heat transfer Nusselt number in terms of thefluid Prandtl number and a modified Reynolds number with either the particle diameter or the tubediameter as the characteristic length scale.
Examples areLeva’s correlation for vertical surfaces and larger particles (Leva and Gummer, 1952);Nu d p =hc d pkg( )= 0.525 Re p0.75(4.4.23)whereRe p =d p r gUmgVreedenberg’s (1958) correlation for horizontal tubes refers to the particle of diameter Dt.Nu D t =æröhc Dt= 420ç s Re t ÷kgè rgø0.3æ m 2g öç gr2 d 3 ÷è s pø0.3(Pr )g0.3(4.4.24)foröæ rsç r Re t ÷ > 2250è gøwhereRe t =Dt r gUmgMolerus and Schweinzer (1989) developed an alternative type of correlation based on the suppositionthat the heat transfer is dominated by gas convection through the matrix of particles in the vicinity ofthe heat transfer surface.
Their correlation takes the form:Nu =hc d pkg= 0.0247 (Ar )0.4304(Pr )0.33(4.4.25)Figure 4.4.11 shows comparison of this model with experimental data obtained at three differentpressures. The solid curve represents the relationship for fixed beds, while the dashed lines representthe behavior for fluidized beds (i.e., Equation 4.4.25) upon exceeding minimum fluidization.A third type of model considers the heat transfer surface to be contacted alternately by gas bubblesand packets of packed particles, leading to a surface renewal process for heat transfer.
Mickley andFairbanks (1955) provided the first analysis of this renewal mechanism. Ozkaynak and Chen (1980)© 1999 by CRC Press LLC4-101Heat and Mass TransferFIGURE 4.4.11 Correlation of Molerus and Schweinzer compared with experimental data (1989).showed that if experimentally measured values of the packet contact time and residence times are usedin the packet model analysis, excellent agreement is obtained.Fast-Circulating Fluidized BedsFast fluidization occurs when the superficial gas velocity exceeds the terminal velocity of the solidparticles, causing the particles to be suspended in cocurrent upward flow with the gas.
This upward flowoccurs in “rise reactors” wherein desired physical or chemical reactions occur. In most applications, thetwo-phase flow exits the top of the riser into a cyclone where the gas phase is separated and exhaustedwhile the solid particles are captured and returned for reinjection at the bottom of the riser. The volumetricconcentration of solid particles in these fast fluidized beds (FFBs) tend to be fairly dilute, often withaverage concentrations of less than 2%. Heat exchange with the particle/gas suspension is usuallyaccomplished through the vertical wall surfaces or through vertical tubes immersed in the duct.The heat transfer coefficient at vertical surfaces FFBs has been found to increase with increasing solidconcentration, aside from other second-order parametric effects. Figure 4.4.12 shows heat transfercoefficients experimentally measured by Dou et al.
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