The CRC Handbook of Mechanical Engineering. Chapter 4. Heat and Mass Transfer (776127), страница 24
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(1994) for an FFB operating with sand particles of124 mm mean diameter. Figure 4.4.12b shows that the heat transfer coefficient increased with solid massflux, for a constant superficial gas velocity. Figure 4.4.12a shows that the heat transfer coefficientdecreased parametrically with superficial gas velocity for a constant solid mass flux. Both figures indicatethat heat transfer coefficients decrease with increasing elevation in the riser duct.
These three parametrictrends are all consistent with the hypothesis that heat transfer in FFBs increases with increasing concentration of the solid phase.It is generally accepted that the effective heat transfer coefficient for surfaces in FFBs have contributions for gas-phase convection, particle-induced convection, and radiation:h = hg + h p + hr© 1999 by CRC Press LLC(4.4.26)4-102Section 4FIGURE 4.4.12 Heat transfer coefficients in fast fluidized beds; Vg is superficial gas velocity, Gs is mass flux ofparticles, and Z is elevation in FFB.
(From Dou, Tuzla and Chen, 1992.)© 1999 by CRC Press LLC4-103Heat and Mass TransferIn contrast to the situation in dense-bubbling fluidized beds, the relatively dilute concentration of solidparticles in FFBs often results in significant contributions from all three heat transfer mechanisms. Theradiation coefficient can be obtained by a gray body model suggested by Grace (1985). The contributionof the gas phase convection (hg) is commonly estimated based on correlations for gas flow alone at thesame superficial gas velocity.
Although the presence of particles may alter the turbulence characteristicof this gas flow, any errors caused by this procedure are usually small since hg is generally smaller thanthe particle-phase convective coefficient hp.For most FFBs, the particle convective contribution to heat transfer is most important and the predictionof hp is the major concern in thermal design. Unfortunately, mechanistically based models are still lackingand most design methods rely on empirical correlations which often combine the contributions of gasand particle phases into a single convective heat transfer coefficient (hc). One such correlation proposedby Wen and Miller (1961) isNu d p =hc d pkgæ C pp ö æ rsusp ö=ç÷ç÷è C pg ø è r p ø0.3æ Vt öç gd ÷è pø0.21Prg(4.4.27)where Vt = terminal velocity of particle.Other correlations have been proposed by Fraley (1992) and Martin (1984).
These correlations areuseful as a starting point but have not yet been verified over wide parametric ranges. Large deviationscan occur when compared with measurements obtained outside of the experimental parametric ranges.ReferencesBiyikli, K., Tuzla, K., and Chen, J.C. 1983. Heat transfer around a horizontal tube in freeboard regionof fluidized beds, AIChE J., 29(5), 712–716.Dou, S., Herb, B., Tuzla, K., and Chen, J.C. 1992. Dynamic variation of solid concentration and heattransfer coefficient at wall of circulating fluidized bed, in Fluidization VII, Eds. Potter and Nicklin,Engineering Foundation, 793–802.Fraley, L.D., Lin, Y.Y., Hsiao, K.H., and Solbakken, A.
1983. ASME Paper 83-HT-92, National HeatTransfer Conference, Seattle.Grace, J.R. 1985. Heat transfer in circulating fluidized beds, Circulating Fluidized Bed Technology I,Peramon Press, New York, 63–81.Jacob, A. and Osberg, G.L. 1957. Effect of gas thermal conductivity on local heat transfer in a fluidizedbed, Can. J. Chem. Eng., 35(6), 5–9.Kunii, D. and Levenspiel, O.
1991. Fluidization Engineering, 2nd ed., Butterworth-Heinemann, Boston.Leva, M. and Grummer, M. 1952. A correlation of solids turnovers in fluidized systems, Chem. Eng.Prog., 48(6), 307–313.Martin, H. 1984. Chem. Eng. Process, 18, 157–223.Mickley, H.S. and Fairbanks, D.F. 1955. Mechanism of heat transfer to fluidized beds, AIChE J., 1(3),374–384.Molerus, O. and Scheinzer, J. 1989.
Prediction of gas convective part of the heat transfer to fluidizedbeds, in Fluidization IV, Engineering Foundation, New York, 685–693.Ozkaynak, T.F. and Chen, J.C. 1980. Emulsion phase residence time and its use in heat transfer modelsin fluidized bed, AIChE J., 26(4), 544–550.Vreedenberg, H.A. 1958. Heat transfer between a fluidized bed and a horizontal tube, Chem. Eng.
Sci.,9(1), 52–60.Wen, C.Y. and Yu, Y.H. 1966. A generalized method for predicting the minimum fluidization velocity,AIChE J., 12(2), 610–612Wen, C.Y. and MIller, E.N. 1961. Ind. Eng. Chem., 53, 51–53.© 1999 by CRC Press LLC4-104Section 4Melting and FreezingNoam LiorIntroduction and OverviewMelting and freezing occur naturally (Lunardini, 1981) as with environmental ice in the atmosphere(hail, icing on aircraft), on water bodies and ground regions at the Earth surface, and in the molten Earthcore (Figure 4.4.13).
They are also a part of many technological processes, such as preservation offoodstuffs (ASHRAE, 1990, 1993), refrigeration and air-conditioning (ASHRAE, 1990, 1993), snowand ice making for skiing and skating (ASHRAE, 1990), organ preservation and cryosurgery (Rubinskyand Eto, 1990), manufacturing (such as casting, molding of plastics, coating, welding, high-energy beamcutting and forming, crystal growth, electrodischarge machining, electrodeposition) (Flemings, 1974;Cheng and Seki, 1991; Tanasawa and Lior, 1992), and thermal energy storage using solid–liquid phasechanging materials (deWinter, 1990).(a)(b)FIGURE 4.4.13 Melting and freezing in nature.
(a) A melting icicle. (b) Frozen lava in Hawaii.© 1999 by CRC Press LLC4-105Heat and Mass TransferIn simple thermodynamic systems (i.e., without external fields, surface tension, etc.) of a pure material,melting or freezing occurs at certain combinations of temperature and pressure. Since pressure typicallyhas a relatively smaller influence, only the fusion (freezing or melting) temperature is often used toidentify this phase transition.
Fusion becomes strongly dependent on the concentration when the materialcontains more than a single species. Furthermore, melting and freezing are also sensitive to externaleffects, such as electric and magnetic fields, in more-complex thermodynamic systems.The equilibrium thermodynamic system parameters during phase transition can be calculated fromthe knowledge that the partial molar Gibbs free energies or chemical potentials of each component inthe two phases must be equal. One important result of using this principle for simple single-componentsystems is the Clapeyron equation relating the temperature (T) and pressure (P) during the phasetransition, such thathdP= sldT TDv(4.4.28)where hsl is the enthalpy change from phase A to phase B (=hB – hA, the latent heat of fusion withappropriate sign) and Dn is the specific volume difference between phases A and B (= nB – nA).Considering for example that phase A is a solid and B a liquid (hsl is then positive), examination ofEquation (4.4.28) shows that increasing the pressure will result in an increase in the melting temperatureif Dn > 0 (i.e., when the specific volume of the liquid is higher than that of the solid, which is a propertyof tin, for example), but will result in a decrease of the melting temperature when Dn < 0 (for water,for example).In some materials, called glassy, the phase change between the liquid and solid occurs with a gradualtransition of the physical properties, from those of one phase to those of the other.
When the liquidphase flows during the process, the flow is strongly affected because the viscosity increases greatly asthe liquid changes to solid. Other materials, such as pure metals and ice, and eutectic alloys, have adefinite line of demarcation between the liquid and the solid, the transition being abrupt. This situationis easier to analyze and is therefore more thoroughly addressed in the literature.Gradual transition is most distinctly observed in mixtures. Consider the equilibrium phase diagramfor a binary mixture (or alloy) composed of species a and b, shown in Figure 4.4.14. c is the concentrationof species b in the mixture, l denotes the liquid, s the solid, sa a solid with a lattice structure of speciesa in its solid phase but containing some molecules of species b in that lattice, and sb a solid with a latticestructure of species b in its solid phase but containing some molecules of species a in that lattice.“Liquidus” denotes the boundary above which the mixture is just liquid, and “solidus” is the boundaryseparating the final solid mixture of species a and b from the solid–liquid mixture zones and from theother zones of solid sa and solid sb.For illustration, assume that a liquid mixture is at point 1, characterized by concentration c1 andtemperature T1 (Figure 4.4.14), and is cooled (descending along the dashed line) while maintaining theconcentration constant.
When the temperature drops below the liquidus line, solidification starts, creatinga mixture of liquid and of solid sa. Such a two-phase mixture is called the mushy zone. At point 2 inthat zone, the solid phase (sa) portion contains a concentration c 2,sa of component b, and the liquidphase portion contains a concentration c2,l of component b.
The ratio of the mass of the solid sa to thatof the liquid is determined by the lever rule, and is (c2,l – c2)/(c2 – c 2,sa ) at point 2. Further coolingto below the solidus line, say to point 3, results in a solid mixture (or alloy) of sa and sb, containingconcentrations c 3,sA and c 3,sB of species b, respectively. The ratio of the mass of the solid sa to that ofsb is again determined by the lever rule, and is ( c 3,sb – c3)/(c3 – c 3,sa ) at point 3.A unique situation occurs if the initial concentration of the liquid is ce: upon constant-concentrationcooling, the liquid forms the solid mixture sa + sb having the same concentration and without the formationof a two-phase zone. ce is called the eutectic concentration, and the resulting solid mixture (or alloy)is called a eutectic.© 1999 by CRC Press LLC4-106Section 4FIGURE 4.4.14 A liquid–solid phase diagram of a binary mixture.The presence of a two-phase mixture zone with temperature-dependent concentration and phaseproportion obviously complicates heat transfer analysis, and requires the simultaneous solution of boththe heat and mass transfer equations.
Furthermore, the liquid usually does not solidify on a simple planarsurface. Crystals of the solid phase are formed at some preferred locations in the liquid, or on coldersolid surfaces immersed in the liquid, and as freezing progesses the crystals grow in the form of intricatelyshaped fingers, called dendrites. This complicates the geometry significantly and makes mathematicalmodeling of the process very difficult.
An introduction to such problems and further references areavailable in Hayashi and Kunimine (1992) and Poulikakos (1994).Flow of the liquid phase often has an important role in the inception of, and during, melting andfreezing (see Incropera and Viskanta, 1992). The flow may be forced, such as in the freezing of a liquidflowing through or across a cooled pipe, and/or may be due to natural convection that arises wheneverthere are density gradients in the liquid, here generated by temperature and possibly concentrationgradients. It is noteworthy that the change in phase usually affects the original flow, such as when theliquid flowing in a cooled pipe gradually freezes and the frozen solid thus reduces the flow passage, orwhen the evolving dendritic structure gradually changes the geometry of the solid surfaces that are incontact with the liquid. Under such circumstances, strong coupling may exist between the heat transferand fluid mechanics, and also with mass transfer when more than a single species is present.
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