BOOKCOMP, Inc. — John Wiley & Sons / Page 694 / 2nd Proofs / Heat Transfer Handbook / Bejan 694 BOILING 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [694], (60) Lines: 2046 to 2081 ——— 2.34213pt PgVar ——— Normal Page * PgEnds: Eject [694], (60) the wall is too hot to be rewetted by the liquid, and a continuous stable, if chaotic, vapor film is formed between the wall and the continuous liquid core. For horizontal and inclined tubes, dryout typically initiates on the upper perimeter of the tube while the lower perimeter remains wet, and may also occur only on one side of a vertical tube heated nonuniformly by, say, a radiant heat source. Post-dryout heat transfer is characterized by the following modes: • Wall-to-vapor heat transfer: turbulent (or laminar) convection to the continuous vapor phase • Wall-to-droplet heat transfer: evaporation of droplets that impinge on the hot wall • Vapor-to-droplet heat transfer: convection from the bulk superheated vapor to the saturated liquid in the droplets, including any droplets passing through the thermal boundary layer on the wall that do not actually contact the wall • Radiation heat transfer from wall-to-droplets/vapor/upstream wall: net radiation flux dependent on the view factor, emissive properties, transparency of the vapor, and respective temperatures. 9.11.4 Inverted Annular Flow Heat Transfer This regime is also referred to as forced-convective film boiling. From observations of film boiling inside a vertical tube, Dougall and Rohsenow (1963) observed that the flow consisted of a central liquid core surrounded by a thin annular film of vapor on the heated wall when occurring at low vapor quality and low flow rates. The interface was not smooth but wavy. Because of the density difference between the two phases, the vapor was assumed to be traveling at a much higher velocity than the liquid core. Depending on the conditions imposed on vertical upward flow, the liquid core was observed to flow upward, remain more or less stationary, or even flow downward. Entrained vapor bubbles were also observed in the liquid core. The simplest inverted annular flow to analyze is heat transfer through a laminar vapor film. For a vertical flat surface, this is similar to the Nusselt solution for falling film condensation on a vertical flat plate. The local heat transfer coefficient α(z) at a distance z from the point of onset of film boiling is α(z) = C λ 3 G ρ G (ρ L − ρ G )gh LG zµ G ∆T 1/4 (9.149) where the wall superheat is ∆T = T w − T sat and the value of C depends on the boundary conditions: C = 0.707 for zero interfacial stress and C = 0.5 for zero interfacial velocity, for example. For turbulent flow in the vapor film, the heat transfer coefficient is inversely dependent on the distance z according to Wallis and Collier (1968): α(z)z λ G = 0.056Re 0.2 G (Pr G · Gr G ) 1/3 (9.150) BOOKCOMP, Inc. — John Wiley & Sons / Page 695 / 2nd Proofs / Heat Transfer Handbook / Bejan POST-DRYOUT HEAT TRANSFER 695 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [695], (61) Lines: 2081 to 2134 ——— 2.72023pt PgVar ——— Normal Page PgEnds: T E X [695], (61) where the vapor Reynolds number Re G is that of the vapor fraction flowing alone in the tube, Pr G is the vapor Prandtl number, and Gr G is the vapor Grashof number: Gr G = z 3 gρ G (ρ L − ρ G ) µ 2 G (9.151) Other important effects on inverted annular flow heat transfer are the flow structure at the interface (waves, periodic disturbances, instabilities), subcooling of the liquid core, thermal radiation, and so on. 9.11.5 Mist Flow Heat Transfer A heat transfer model for the mist flow regime should ideally include the heat transfer mechanisms mentioned earlier and nonequilibrium effects on the local temperature and vapor quality. However, most methods include only one or several of these. For single-phase turbulent convection from the wall to the continuous vapor phase, Dougall and Rohsenow (1963) have used the Dittus–Boelter correlation: Nu G = αd i λ G = 0.023Re 0.8 GH · Pr 0.4 G (9.152) where the velocity was assumed to be the homogeneous velocity u H : u H = ˙m ρ H =˙m χ ρ G + 1 − χ ρ L (9.153) so that the Reynolds number of the homogeneous vapor is Re GH = ˙md i µ G χ + ρ G ρ L (1 − χ) (9.154) They used the equilibrium vapor quality χ e in this expression with all properties evaluated at the saturation temperature. Hence, nonequilibrium effects and other heat transfer modes are neglected, so this method should only be used as a first approximation. Groeneveld (1973) added another multiplying factor Y to this approach, where Y = 1 − 0.1 ρ L ρ G − 1 (1 − χ) 0.4 (9.155) Nu G = 0.00327 ˙md i µ G χ + ρ G ρ L (1 − χ) 0.901 · Pr 1.32 G · Y −1.50 (9.156) The equilibrium vapor quality χ e and saturation properties are used. His database covers flows in vertical and horizontal tubes and in vertical annuli for the following conditions: BOOKCOMP, Inc. — John Wiley & Sons / Page 696 / 2nd Proofs / Heat Transfer Handbook / Bejan 696 BOILING 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [696], (62) Lines: 2134 to 2184 ——— 3.1792pt PgVar ——— Normal Page * PgEnds: Eject [696], (62) • 2.5 mm <d i < 25 mm • 34 bar <p<215 bar • 700 kg/m 2 · s < ˙m<5300 kg/m 2 · s • 0.1 < χ < 0.9 • 120 kW/m 2 <q<2100 kW/m 2 Use of his correlation beyond the range above is not recommended. Groeneveld and Delorme (1976) subsequently proposed a new correlation that accounts for non- equilibrium effects, whose simplified version is as follows. First the parameter ψ is obtained from ψ = 0.13864Pr 0.203 G · Re 0.2 GH,e qd i c pG,e λ L h LG −0.0923 1.307 − 1.083χ e + 0.846χ 2 e (9.157) which is valid for 0 ≤ ψ ≤ π/2. (Note: When ψ < 0, its value is set to 0.0; when ψ > π/2, it is set to π/2.) Their homogeneous Reynolds number Re GH,e based on the equilibrium vapor quality is Re GH,e = ˙md i µ G χ e + ρ G ρ L 1 − χ e (9.158) For values of χ e greater than unity (i.e., when the enthalpy added to the fluid places its equilibrium state in the superheated vapor region), χ e is set equal to 1.0 in the expres- sions above. To determine the values of T G,a and χ a , an energy balance is used where h G,a is the actual vapor enthalpy and h L,sat is the enthalpy of the saturated liquid, while χ e is the equilibrium vapor quality and h LG is the latent heat of evaporation. The actual vapor quality is obtained from χ a = h LG χ e h G,a − h L,sat (9.159) and the change in enthalpy is h G,a − h L,sat = h LG + T G,a T sat c pG dT G (9.160) The difference between the actual vapor enthalpy h G,a and the equilibrium vapor enthalpy h G,e is h G,a − h G,e h LG = exp(−tan ψ) (9.161) For 0 ≤ χ e ≤ 1, the equilibrium vapor enthalpy h G,e is that of the saturated vapor, that is, BOOKCOMP, Inc. — John Wiley & Sons / Page 697 / 2nd Proofs / Heat Transfer Handbook / Bejan POST-DRYOUT HEAT TRANSFER 697 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [697], (63) Lines: 2184 to 2238 ——— 4.21811pt PgVar ——— Normal Page PgEnds: T E X [697], (63) h G,e = h G,sat (9.162) For χ e > 1, the equilibrium vapor enthalpy h G,e is calculated as h G,e = h G,sat + (χ e − 1)h LG (9.163) Finally, the heat transfer coefficient, defined as α = q/(T w −T G,a ), is obtained from αd i λ G,f = qd i (T w − T G,a )λ G,f = 0.008348 ˙md i µ G,f χ a + ρ G ρ L (1 − χ a ) 0.8774 · Pr 0.6112 G,f (9.164) where the subscript “G,f ” in these expressions indicates that the vapor properties should be evaluated at the film temperature T G,f = T w + T G,a 2 (9.165) This iterative method predicts the values of α,T G,a , and χ a when given those of ˙m, χ e , and q. The method includes the effect of departure from equilibrium but still ignores the contributions of wall-to-droplet, vapor-to-droplet, and radiation heat transfer. This method is more accurate than that of Groeneveld (1973) and has a similar application range. A more complete model has been proposed by Ganic and Rohsenow (1977). In their model the total heat flux in mist flow was assumed to be the sum of wall-to- vapor convection q G , wall-to-droplet evaporation q L , and radiation q rad , so that q = q G + q L + q r (9.166) The wall-to-vapor convection contribution was obtained by introducing the actual vapor velocity into the McAdams turbulent flow correlation as q G = 0.0023 λ L d i ˙mχd i εµ G 0.8 · Pr 0.4 G (T w − T sat ) (9.167) using the void fraction ε (e.g., see Section 9.9 for an expression to calculate the void fraction), while the physical properties are evaluated at the saturation temperature. The total radiant heat flux from the wall to droplets and from the wall to vapor is q rad = F wL σ SB T 4 w − T 4 sat + F wG σ SB T 4 w − T 4 sat (9.168) where F wL and F wG are the respective view factors, σ SB is the Stephan–Boltzmann constant (σ SB = 5.67×10 −8 W/m 2 ·K 4 ) and blackbody radiation isassumed.F wG = 0 for a transparent vapor. The radiant heat flux is in fact negligible except at very large wall temperatures. BOOKCOMP, Inc. — John Wiley & Sons / Page 698 / 2nd Proofs / Heat Transfer Handbook / Bejan 698 BOILING 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [698], (64) Lines: 2238 to 2290 ——— 2.44522pt PgVar ——— Long Page PgEnds: T E X [698], (64) Although ignoring nonequilibrium effects, they predicted the heat flux due to impinging droplets on the wall as q L = u d (1 − ε)ρ L h LG f cd exp 1 − T w T sat 2 (9.169) where the droplet deposition velocity u d is u d = 0.15 ˙mχ ρ L ε f G 2 (9.170) f cd is the cumulative deposition factor, and f G is the single-phase friction factor calculated at the effective vapor Reynolds number (i.e., ˙mχ e d i /εµ G ). The value of f cd is a complicated function of droplet size. The importance of q L relative to the total heat flux is significant at low to medium vapor qualities, where a large fraction of liquid is present in the flow. For heat transfer from the superheated vapor to a single, isolated entrained liquid droplet, Ganic and Rohsenow (1977) predicted the convective heat transfer coefficient from the vapor to the droplet, α D , in terms of a droplet Nusselt number as Nu D = 2 + 0.6Re 1/2 D · Pr 1/3 G (9.171) where Nu D = α D D λ G (9.172) Re D = ρ G D(u G − u D ) µ G (9.173) D is the droplet diameter, u G the vapor velocity, u D the droplet velocity, and the Prandtl number Pr G is based on vapor properties: Pr G = µ G c pG λ G (9.174) The factor of 2 on the right-hand side of eq. (9.171) is that resulting for pure conduc- tion to the droplet, and the second term accounts for convection. The heat transfer rate to the droplet is Q = πD 2 α D (T G,a − T D ) (9.175) where T G,a is the superheated vapor temperature and T D is the droplet temperature. T D is assumed to be the saturation temperature, but a method for estimating the value of T G,a is required. Methods to model mist flow heat transfer for internal flows numerically have pro- gressed rapidly in recent years. For example, Andreani and Yadigaroglu (1997) have BOOKCOMP, Inc. — John Wiley & Sons / Page 699 / 2nd Proofs / Heat Transfer Handbook / Bejan BOILING OF MIXTURES 699 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [699], (65) Lines: 2290 to 2305 ——— -0.073pt PgVar ——— Long Page PgEnds: T E X [699], (65) developed a three-dimensional Eulerian–Lagrangian model of dispersed flow boiling that includes a mechanistic description of the formation of the droplet spectrum. 9.12 BOILING OF MIXTURES Evaporation of pure fluids is typical of systems that operate on a closed cycle, such as water in a power plant or a refrigerant in an air-conditioning system. Instead, evaporation of mixtures is an important heat transfer process in the petrochemical processing industries, in the production of polymers, occurs in refrigeration systems when a miscible oil enters the refrigerant charge in the compressor, and so on. Thus, in this section, the basic principles of mixture boiling are presented. For a more complete discussion of this topic, refer to Thome and Shock (1984). 9.12.1 Vapor–Liquid Equilibria and Properties Some knowledge of the principles of vapor–liquid equilibria is required to understand the basics of mixture boiling. Phase equilibrium of a binary mixture sytem is typically presented on a phase diagram such as the one depicted in Fig. 9.20 for a mixture that does not exhibit an azeotrope. This diagram shows the bubble point and dew point temperature curves at constant pressure, where the vertical axis is temperature and the horizontal axis gives the mole fraction of the two components in both the liquid and vapor phases. The component with the lower boiling point temperature at the particular pressure (i.e., in this case the one to the right at a mole fraction of 1.0) is referred to as the more volatile or lighter component; the other fluid is referred to as the less volatile or heavier component. For a mixture with the mole fraction x in the liquid phase, its equilibrium mole fraction in the vapor phase is y. The bubble point temperatures T bub are given by Figure 9.20 Phase equilibrium diagram of a binary mixture. BOOKCOMP, Inc. — John Wiley & Sons / Page 700 / 2nd Proofs / Heat Transfer Handbook / Bejan 700 BOILING 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [700], (66) Lines: 2305 to 2321 ——— 3.39606pt PgVar ——— Normal Page * PgEnds: Eject [700], (66) the bottom curve as a function of x, and the dew point temperatures T dew are given by the upper curve as a function of y. The bubble point temperature represents the temperature at which a subcooled mixture of the liquid will first form vapor when heating the fluid. Similarly, the dew point temperature is the temperature at which a superheated vapor will first form liquid upon being cooled. The difference in the liquid and vapor mole fractions is caused by the different partial pressures exerted by each fluid, and (y − x) is the driving force for mass transfer to the bubble during boiling. The temperature difference between the two curves at any vertical line at a liquid mole fraction x is referred to as the boiling range or temperature glide of the mixture, ∆T bp . The physical properties of mixtures often do not follow a linear interpolation between the pure component properties, whether using a mixing law based on mass fraction or on mole fraction. For instance, the liquid viscosity of a binary mixture may be higher or lower than that of its two components at the same temperature. Thus, it is important to use appropriate methods for the prediction of mixture properties for use in thermal design. A comprehensive treatment is available in Reid et al. (1987). 9.12.2 Nucleate Boiling of Mixtures The basic relationship between the mixture boiling heat transfer coefficient α mixt with respect to the ideal pure fluid boiling heat transfer coefficient α id is α mixt α id = F c = ∆T id ∆T id + dT bp (9.176) The ideal boiling coefficient is that which would be obtained by inserting the mixture physical properties into a nucleate pool boiling correlation in Section 9.5, so this can also be referred to as the boiling coefficient of the equivalent pure fluid. For a heat flux of q, the wall superheat for boiling of the equivalent pure fluid is ∆T id . For a zeotropic mixture, mass transfer of the more volatile component to the bubble interface and evaporation into the bubble to provide its larger equilibrium mass fraction in the vapor phase has the effect of forming a mass diffusion layer around the bubble. Hence, the local mass fraction of the more volatile component is lower at the bubble interface, and thus the bubble point temperature of the mixture at the bubble interface is higher than in the bulk liquid. This rise in bubble point temperature dT bp diminishes the superheat available for evaporation and hence slows down the bubble growth rate. The value of dT bp ranges from a minimum value of zero for a pure fluid or an azeotrope up to the maximum possible value, which is the boiling range (or temperature glide) of a zeotropic mixture. The value of dT bp is controlled by the combined heat and mass transfer diffusion process. A mixture in which the liquid and vapor mole fractions are the same is referred to as an azeotrope. Schl ¨ under (1983) proposed a simple solution predicting dT bp for a bubble growing in a uniformly superheated fluid. That method was extended by Thome (1989) to multicomponent mixtures in terms of the boiling range ∆T bp , and his analytically derived mass transfer factor F c for nucleate pool boiling of mixtures is BOOKCOMP, Inc. — John Wiley & Sons / Page 701 / 2nd Proofs / Heat Transfer Handbook / Bejan BOILING OF MIXTURES 701 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [701], (67) Lines: 2321 to 2344 ——— 0.07602pt PgVar ——— Normal Page PgEnds: T E X [701], (67) F c = 1 + α id q ∆T bp 1 − exp −q ρ L h LG β L −1 (9.177) For zeotropic mixtures, F c < 1.0 since ∆T bp > 0, but F c equals 1.0 for pure fluids and azeotropes since for these fluids ∆T bp = 0. The nucleate boiling heat transfer coefficient for zeotropic mixtures is thus obtained by including F c in, for example, the Cooper correlation to give α nb = 55p 0.12 r (−log 10 p r ) −0.55 M −0.5 q 0.67 F c (9.178) where q is the heat flux and p r and M are those of the liquid mixture. The ideal heat transfer coefficient α id is first determined with eq. (9.178) by setting ∆T bp to 0.0 such that F c = 1.0. This method is valid for boiling ranges up to 30 K and hence covers many of the zeotropic refrigerant blends and hydrocarbon mixtures of industrial interest. In these expressions, the heat flux q is in W/m 2 , the liquid density ρ L is in kg/m 3 , the latent heat h LG is in J/kg, and the mass transfer coefficient β L equals a fixed value of 0.0003 m/s. 9.12.3 Flow Boiling of Mixtures Evaporation of mixtures inside vertical and horizontal tubes is typical of numerous industrial processes. More recently, with the retirement of the older refrigerants and their replacements in some cases by three-component zeotropic mixtures, for example R-407C, evaporation of mixtures has now become common to the design of air- conditioning systems. Mixtures have three important effects on thermal design. First, as a mixture evaporates along a tube, its local bubble point temperature rises as the more volatile component preferentially evaporates into the vapor phase. Hence the change in enthalpy also includes sensible heating of the liquid and vapor up this temperature gradient in addition to the latent heat of vaporization. The vapor produced has a mole fraction of y, while that of the liquid has a mole fraction of x. Hence, it is the enthalpy change between these two states that is used to calculate the latent heat change during flow boiling. Consequently, an enthalpy curve is required to do the energy balance between the evaporating fluid and the heating fluid in a heat exchanger. The second effect is that of the mass transfer on nucleate pool boiling contribution to the flow boiling heat transfer coefficient. This can be introduced into heat transfer models that have explicit nucleate boiling and convective boiling contributions, such as most of those discussed in Sections 9.8 and 9.9. This can be accomplished by multiplying the nucleate boiling contribution in those methods by the mixture boiling correction factor F c , discussed in Section 9.12.2. The third effect is the gas-phase heat transfer resistance. The most widely used approach for predicting in-tube condensation of miscible mixtures where all com- ponents are condensable is commonly referred to as the Silver–Bell–Ghaly method. This method accounts for the need to cool the vapor phase when condensing a mix- ture along its dew point temperature curve in addition to removal of the latent heat. BOOKCOMP, Inc. — John Wiley & Sons / Page 702 / 2nd Proofs / Heat Transfer Handbook / Bejan 702 BOILING 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [702], (68) Lines: 2344 to 2371 ——— -2.53786pt PgVar ——— Long Page PgEnds: T E X [702], (68) Similarly, the vapor phase must be heated up when a mixture proceeds up the bubble point curve during evaporation. The effective flow boiling heat transfer coefficient α eff for evaporation of a mixture is calculated by proration as 1 α eff = 1 α tp (χ) + Z G α G (9.179) The flow boiling heat transfer coefficient α tp (χ) is obtained with one of the in-tube correlations cited previously for pure fluids but using the local physical properties of the mixture and including the effect of F c on the nucleate boiling coefficient. The other heat transfer coefficient is that of the vapor α G , which is calculated with the Dittus–Boelter turbulent flow correlation using the vapor fraction of the flow in calculating the vapor Reynolds number. The parameter Z G is the ratio of the sensible heating of the vapor to the total heating rate, which can be written as Z G = χc pG dT bp dh (9.180) In this expression χ is the local vapor quality, c pG is the specific heat of the vapor, and dT bp /dh is the slope of the bubble point curve with respect to the enthalpy of the mixture as it evaporates (i.e., the slope of the enthalpy curve). This approach is based on two important assumptions in determining the value of α G : (1) Mass transfer has no effect; and (2) the value of α G is determined assuming that the vapor occupies the entire cross section of the tube. Since the error in ignoring the first assumption becomes significant for mixtures with large boiling ranges, the method above is reliable only for mixtures with small to medium-sized boiling ranges (perhaps up to about 15 K). The second assumption, on the other hand, tends to be conservative since the interfacial waves in annular flows tend to enhance the vapor-phase heat transfer coefficient above that obtained with the Dittus–Boelter correlation. 9.12.4 Evaporation of Refrigerant–Oil Mixtures Introduction of a miscible lubricating oil in a refrigerant often has a detrimental effect on nucleate pool boiling heat transfer, similar to that described for zeotropic mixtures discussed in Section 9.12.2. A refrigerant–oil mixture is, in fact, a very wide-boiling- range mixture with values of ∆T bp of up to 300 K or more. Other effects are also important here, such as the three-order-of-magnitude difference between the oil’s dynamic viscosity and that of the refrigerant liquid. For flow boiling of refrigerant–oil mixtures, similar to zeotropic mixtures, it is necessary to calculate the bubble point temperature of the mixture as a function of the local oil mass fraction and to apply the enthalpy profile approach to determine the change of enthalpy of the mixture. Simple algebraic methods were proposed by Thome (1995b) for both these purposes. For flow boiling of refrigerant–oil mixtures, experimental data sometimes dem- onstrate an increase in the local heat transfer coefficient at low to medium vapor qualities, but typically, oil has only a detrimental effect, causing substantially reduced heat transfer coefficients at high vapor qualities, where the local oil mass fraction BOOKCOMP, Inc. — John Wiley & Sons / Page 703 / 2nd Proofs / Heat Transfer Handbook / Bejan BOILING OF MIXTURES 703 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [703], (69) Lines: 2371 to 2392 ——— 1.79807pt PgVar ——— Long Page PgEnds: T E X [703], (69) rises rapidly. For plain tubes, Z ¨ urcher et al. (1998) conducted refrigerant–oil evapo- ration tests with local oil mass fractions up to 50 wt % oil and liquid viscosities up to 0.035 N ·s/m 2 (35 cP in common engineering units) with R-134a and R-407C. They showed that the Kattan–Thome–Favrat method described in Section 9.9 gave reason- able accuracy for these increasingly viscous mixtures using only the liquid viscosity of the mixture in the appropriate equations. They utilized the well-known Arrhenius logarithmic mixing law for viscosities of liquid mixtures, rearranged in the form µ ref−oil µ ref = µ oil µ ref w (9.181) The local viscosity of the refrigerant–oil mixture, µ ref−oil , thus calculated is used directly for the liquid viscosity µ L in the boiling model and flow pattern map calcula- tions described in Section 9.9, while refrigerant properties are used for all others. The refrigerant–oil viscosity, which changes by several orders of magnitude with respect to that of the pure refrigerant, completely dominates the much smaller changes expe- rienced by other physical properties. The oil and refrigerant viscosities, µ ref and µ oil , are those at the respective local bubble point temperature of the mixture. The local oil mass fraction, w, in terms of the nominal inlet oil mass fraction w inlet circulating in the system, is w = w inlet 1 − χ (9.182) where χ is the local vapor quality, including the mass of the oil in the liquid phase. Note, however, that the expression above is undefined when χ = 1 and that a local vapor quality greater than (1 − w inlet ) cannot be achieved since the oil is nonvolatile and remains totally in the liquid phase. Figure 9.21 illustrates the effect of oil on the 0 102030405060708090100 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Plain tube G300 Vapor quality (%) Heat transfer coefficient (W/m . K) 2 HFC 134a, Tsat = 4.4°C, = 10,000 W/mq 2 0% 0.50% 1% 3% 5% Figure 9.21 Simulation of Kattan–Thome–Favrat model for R-134a/oil mixtures. . one side of a vertical tube heated nonuniformly by, say, a radiant heat source. Post-dryout heat transfer is characterized by the following modes: • Wall-to-vapor heat transfer: turbulent (or laminar). continuous vapor phase • Wall-to-droplet heat transfer: evaporation of droplets that impinge on the hot wall • Vapor-to-droplet heat transfer: convection from the bulk superheated vapor to the saturated. Gr G ) 1/3 (9.150) BOOKCOMP, Inc. — John Wiley & Sons / Page 695 / 2nd Proofs / Heat Transfer Handbook / Bejan POST-DRYOUT HEAT TRANSFER 695 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [695],