Heat Transfer Handbook part 67 ppt

BOOKCOMP, Inc. — John Wiley & Sons / Page 654 / 2nd Proofs / Heat Transfer Handbook / Bejan 654 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 [654], (20) Lines: 637 to 691 ——— 0.81018pt PgVar ——— Normal Page PgEnds: T E X [654], (20) Nu = α nb λ L  σ g(ρ L − ρ G )  1/2 (9.42) using the bubble departure diameter [which is the bracketed term in eq. (9.42)] as the characteristic length, and α nb is the nucleate pool boiling heat transfer coefficient. He defined the Reynolds number using the superficial velocity of the liquid as Re = q h LG ρ L  σ g(ρ L − ρ G )  1/2 ρ L µ L (9.43) where Pr L is the liquid Prandt number. For the lead constant C 1 , he introduced the empirical constant C sf to account for the particular liquid–surface combination, so that Nu = 1 C sf Re 1−n · Pr −m (9.44) which he presented in the form c pL ∆T h LG = C sf  q µ L h LG  σ g(ρ L − ρ G )  1/2  n [ Pr ] m+1 (9.45) Thus, this gives ∆T ∝ q n and α nb is obtainable from its definition (i.e., α nb = q/∆T where ∆T = T w − T sat and T w is the wall temperature). The exponents are m = 0.7 and n = 0.33 (thus equivalent to q ∝ ∆T 3 ), except for water, where m = 0. Physical properties are evaluated at the saturation temperature of the fluid. Rohsenow provided a list of values of C sf for various surface–fluid combinations that has been extended by Vachon et al. (1967) in Table 9.2. Because this method requires a surface–fluid factor, it is inconvenient to use for general thermal design. TABLE 9.2 Values of C sf for Rohsenow Correlation Liquid–Surface Combination C sf n-Pentane on polished copper 0.0154 n-Pentane on polished nickel 0.0127 Water on polished copper 0.0128 Carbon tetrachloride on polished copper 0.0070 Water on lapped copper 0.0147 n-Pentane on lapped copper 0.0049 n-Pentane on emery polished copper 0.0074 Water on scored copper 0.0068 Water on ground and polished stainless steel 0.0800 Water on PTFE pitted stainless steel 0.0058 Water on chemically etched stainless steel 0.0133 Water on mechanically polished stainless steel 0.0132 BOOKCOMP, Inc. — John Wiley & Sons / Page 655 / 2nd Proofs / Heat Transfer Handbook / Bejan POOL BOILING HEAT TRANSFER 655 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 [655], (21) Lines: 691 to 740 ——— 4.08205pt PgVar ——— Normal Page PgEnds: T E X [655], (21) Reduced Pressure Correlation of Mostinski Mostinski (1963) applied the principle of corresponding states to the correlation of nucleate pool boiling data, arriving at a reduced pressure formulation without a surface–fluid parameter or fluid physical properties. His dimensional reduced pressure correlation is α nb = 0.00417q 0.7 p 0.69 crit F P (9.46) where α nb is the nucleate pool boiling coefficient in W/m 2 · K, q the heat flux in W/m 2 , and p crit the critical pressure of the fluid in kN/m 2 (i.e., in kPa). Pressure effects on nucleate boiling are correlated using the factor F P , determined from the expression F P = 1.8p 0.17 r + 4p 1.2 r + 10Pr 10 (9.47) where p r is the reduced pressure, defined as p r = p/p crit . This correlation gives reasonable results for a wide range of fluids and reduced pressures. Physical Property Type of Correlation of Stephan and Abdelsalam Stephan and Abdelsalam (1980) developed individual correlations for four classes of fluids (water, organics, refrigerants, and cryogens), utilizing a statistical multi- ple regression technique. These correlations used the physical properties of the fluid (evaluated at the saturation temperature) and are hence said to be physical property– based correlations. Their correlation applicable to organic fluids is α nb d o λ L = 0.0546   ρ G ρ L  1/2 qd o λ L T sat  0.67  h LG d 2 o a 2 L  0.248  ρ L − ρ G ρ L  −4.33 (9.48) The term at the left is a Nusselt number and the bubble departure diameter d o (meters) is calculated with a Fritz type of equation: d o = 0.0146β  2σ g(ρ L − ρ G )  1/2 (9.49) Note that the contact angle β is assigned a fixed value of 35° in this expression, irrespective of the fluid, such that the lead constant becomes 0.511. In the expressions above, T sat is the saturation temperature of the fluid in Kelvin and a L is the liquid thermal diffusivity in m 2 /s. Reduced Pressure Correlation of Cooper with Surface Roughness Cooper (1984) proposed the following reduced pressure expression for the nucleate pool boiling heat transfer coefficient: α nb = 55p 0.12−0.4343 lnR p r (−log 10 p r ) −0.55 M −0.5 q 0.67 (9.50) Note that this is a dimensional correlation in which α nb is in W/m 2 · K, the heat flux q is in W/m 2 , and M is the molecular weight and R p the mean surface roughness BOOKCOMP, Inc. — John Wiley & Sons / Page 656 / 2nd Proofs / Heat Transfer Handbook / Bejan 656 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 [656], (22) Lines: 740 to 835 ——— 8.88406pt PgVar ——— Normal Page * PgEnds: PageBreak [656], (22) in micrometers (R p is set to 1.0 µm for undefined surfaces). Increasing the surface roughness has the effect of increasing the nucleate boiling heat transfer coefficient. Since R p may be affected by fouling or oxidation of the surface, it is common to use his standard value of 1.0 µm for R p . Although he recommends multiplying α nb by a factor of 1.7 for horizontal copper cylinders, the equation more accurately predicts boiling of the new generation of refrigerants on copper tubes without applying this factor, and that is the approach recommended here. The correlation covers a database of reduced pressures from 0.001 to 0.9 and molecular weights from 2 to 200 and is highly recommended for general use. Fluid-Specific Correlation of Gorenflo Gorenflo (1993) proposed a reduced pressure type of correlation that utilizes a fluid-specific heat transfer coefficient α 0 , defined for each fluid at the fixed reference conditions of p r0 = 0.1,R p0 = 0.4 µm, and q 0 = 20,000 W/m 2 . His values for α 0 are given in Table 9.3 for various fluids. The general expression for the nucleate boiling heat transfer coefficient α nb at other conditions is α nb = α 0 F PF (q/q 0 ) n (R p /R p0 ) 0.133 (9.51) where the pressure correction factor F PF is F PF = 1.2p 0.27 r + 2.5p r + p r 1 − p r (9.52) and p r is the reduced pressure. The exponent n on the heat flux ratio is also a function of reduced pressure: n = 0.9 − 0.3p 0.3 r (9.53) The value of n decreases with increasing reduced pressure, typical of experimental data. Surface roughness is included in the last term of eq. (9.51), where R p is in micrometers (set to 0.4 µm when unknown). The method above is for all fluids listed except water and helium. For water, the corresponding equations are F PF = 1.73p 0.27 r +  6.1 + 0.68 1 − p r  p 2 r (9.54) n = 0.9 − 0.3p 0.15 r (9.55) This method is applicable for 0.0005 ≤ p r ≤ 0.95 using the values of α 0 in the list. For other fluids, experimental values can be input at the standard reference conditions cited in the table, or another correlation can be used to estimate α 0 . This method is accurate over a very wide range of heat flux and pressure and is probably the most reliable of those presented. However, this approach is not extendable to boiling of mixtures, which is of interest in numerous industrial processes. BOOKCOMP, Inc. — John Wiley & Sons / Page 657 / 2nd Proofs / Heat Transfer Handbook / Bejan POOL BOILING HEAT TRANSFER 657 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 [657], (23) Lines: 835 to 835 ——— 3.33952pt PgVar ——— Normal Page PgEnds: T E X [657], (23) TABLE 9.3 Values of α 0 in W/m 2 · Katp r0 = 0.1,q 0 = 20,000 W/m 2 , and R p0 = 0.4 µm, with p crit in bar Fluid p crit M α 0 Methane 46.0 16.04 7,000 Ethane 48.8 30.07 4,500 Propane 42.4 44.10 4,000 n-Butane 38.0 58.12 3,600 n-Pentane 33.7 72.15 3,400 i-Pentane 33.3 72.15 2,500 n-Hexane 29.7 86.18 3,300 n-Heptane 27.3 100.2 3,200 Benzene 48.9 78.11 2,750 Toluene 41.1 92.14 2,650 Diphenyl 38.5 154.2 2,100 Ethanol 63.8 46.07 4,400 n-Propanol 51.7 60.10 3,800 i-Propanol 47.6 60.10 3,000 n-Butanol 49.6 74.12 2,600 i-Butanol 43.0 74.12 4,500 Acetone 47.0 58.08 3,950 R-11 44.0 137.4 2,800 R-12 41.6 120.9 4,000 R-13 38.6 104.5 3,900 R-13B1 39.8 148.9 3,500 R-22 49.9 86.47 3,900 R-23 48.7 70.02 4,400 R-113 34.1 187.4 2,650 R-114 32.6 170.9 2,800 R-115 31.3 154.5 4,200 R-123 36.7 152.9 2,600 R-134a 40.6 102.0 4,500 R-152a 45.2 66.05 4,000 R-226 30.6 186.5 3,700 R-227 29.3 170.0 3,800 RC318 28.0 200.0 4,200 R-502 40.8 111.6 3,300 Chloromethane 66.8 50.49 4,400 Tetrafluoromethane 37.4 88.00 4,750 Hydrogen (on Cu) 12.97 2.02 24,000 Neon (on Cu) 26.5 20.18 20,000 Nitrogen (on Cu) 34.0 28.02 10,000 Nitrogen (on Pt) 34.0 28.02 7,000 Argon (on Cu) 49.0 39.95 8,200 Argon (on Pt) 49.0 39.95 6,700 Oxygen (on Cu) 50.5 32.00 9,500 Oxygen (on Pt) 50.5 32.00 7,200 Water 220.6 18.02 5,600 Ammonia 113.0 17.03 7,000 Carbon dioxide a 73.8 44.01 5,100 Sulfur hexafluoride 37.6 146.1 3,700 a At triple point. BOOKCOMP, Inc. — John Wiley & Sons / Page 658 / 2nd Proofs / Heat Transfer Handbook / Bejan 658 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 [658], (24) Lines: 835 to 880 ——— 2.64111pt PgVar ——— Normal Page * PgEnds: Eject [658], (24) 9.5.3 Departure from Nucleate Pool Boiling (or Critical Heat Flux) The maximum attainable heat flux in the nucleate boiling regime is the DNB or CHF point shown in Section 9.2. The maximum in the nucleate boiling curve heat flux is reached when a hydrodynamic instability destabilizes the vapor jets rising from the heater surface. Zuber (1959) was first to demonstrate that this process is governed by the Taylor and Helmholtz instabilities. His model was refined by Lienhard and Dhir (1973a) for an infinite flat heated surface facing upward and has been extended to other geometries. Taylor instability governs the collapse of an infinite, horizontal planar interface of liquid above a vapor or gas, and the Taylor wavelength is that which predominates at the interface during the collapse. Applied to the DNB phenomenon, vapor jets are formed above a large, flat horizontal heater surface as illustrated in Fig. 9.8. For jets in a rotated square array as shown, their in-line spacing between jets is the two-dimensional Taylor wavelength λ d2 , but since λ d2 = √ 2λ d1 , the characteristic dimension can be considered to be λ d1 , which is equal to λ d1  (ρ L − ρ G )g σ  1/2 = 2π √ 3 (9.56) The Helmholtz instability is that which causes a planar liquid interface to go unstable when a vapor or gas flowing parallel to the interface reaches some critical velocity. Presently, it is the rising vapor jet that creates the instability. The critical velocity of the vapor u G is u G =  2πσ ρ G λ H (9.57) where λ H is the Helmholtz wavelength of a disturbance in the jet wall. Setting λ d1 = λ H and performing an energy balance, the expression for q DNB is obtained: q DNB = ρ G h LG  2πσ ρ G 1 2π √ 3  g(ρ L − ρ G ) σ π 16 (9.58) or q DNB = 0.149ρ 1/2 G h LG 4  g(ρ L − ρ G )σ (9.59) This expression is valid for flat infinite heaters facing upward, providing good agree- ment with experimental results for large flat heaters with vertical sidewalls to prevent lateral liquid flow as long as the diameters or widths of the heaters are larger than 3λ d1 . Using dimensional analysis, Kutateladze (1948) had already arrived at nearly the same result: q DNB = Cρ 1/2 G h LG 4  g(ρ L − ρ G )σ (9.60) BOOKCOMP, Inc. — John Wiley & Sons / Page 659 / 2nd Proofs / Heat Transfer Handbook / Bejan POOL BOILING HEAT TRANSFER 659 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 [659], (25) Lines: 880 to 892 ——— 2.288pt PgVar ——— Normal Page * PgEnds: Eject [659], (25) Figure 9.8 Vapor jets on a horizontal heater at DNB showing the Taylor wavelengths. where he found the empirical factor C to be 0.131 based on a comparison to experi- mental data. Zuber’s original analysis yielded a nearly identical value of C = π/24 = 0.1309, while the Lienhard and Dhir solution gives C = 0.149, which is 15% higher. Lienhard and Dhir (1973a,b) extended this theory to finite surfaces using the expression q DNB q DNB,Z = fn(L  ) (9.61) BOOKCOMP, Inc. — John Wiley & Sons / Page 660 / 2nd Proofs / Heat Transfer Handbook / Bejan 660 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 [660], (26) Lines: 892 to 935 ——— 0.14067pt PgVar ——— Normal Page * PgEnds: Eject [660], (26) TABLE 9.4 q DNB Ratios for Finite Bodies Geometry q DNB q DNB,Z Dimension Range Infinite flat plate 1.14 Width or diameter L  ≥ 2.7 Small flat heater 1.14A heater /λ 2 d1 Width or diameter 0.07 ≤ L  ≤ 0.2 Horizontal cylinder 0.89 +2.27e −3.44 √ R  Radius RR  ≥ 0.15 Large horizontal cylinder 0.90 Radius RR  ≥ 1.2 Small horizontal cylinder 0.94/(R  ) 1/4 Radius R 0.15 ≤ R  ≤ 1.2 Large sphere 0.84 Radius R 4.26 ≤ R  Small sphere 1.734/(R  ) 1/2 Radius RR  ≤ 4.26 Small horizontal ribbon oriented vertically a 1.18/(H  ) 1/4 Height of side H 0.15 ≤ H  ≤ 2.96 Small horizontal ribbon oriented vertically b 1.4/(H  ) 1/4 Height of side H 0.15 ≤ H  ≤ 5.86 Any large finite body  0.9 Length L About L  ≥ 4 Small slender cylinder of any cross section 1.4/(P  ) 1/4 Transverse perimeter P 0.15 ≤ P  ≤ 5.86 Small bluff body Constant/(L  ) 1/2 Length L About L  ≥ 4 Source: Adapted from Lienhard (1981). a Heated on both sides. b One side insulated. where q DNB /q DNB,Z is a constant or a geometrical expression with a characteristic dimension of the particular surface, and eq. (9.60) with C = π/24 gives the value of q DNB,Z . The dimensionless length scale is L  = 2π √ 3 L λ d1 (9.62) where λ d1 is given by eq. (9.56) and L may be a length L, a perimeter P , a height H , or a radius R, which give the values of L  ,P  ,H  , and R  , respectively, according to the type of geometry listed in Table 9.4. The methods are accurate to within about 20% for a wide range of fluids. 9.5.4 Film Boiling and Transition Boiling Film boiling bears a strong similarity to falling film condensation, where the rising va- por film is analogous to the falling liquid film. Recognizing this fact, Bromley (1950) used the Nusselt equation for film condensation on horizontal cylinders to predict film boiling on the same geometry. He did this simply by changing the thermal con- ductivity and the kinematic viscosity from liquid to vapor properties and introducing an empirical lead constant of 0.62 rather than 0.728. Thus, for a cylinder of diameter D, the film boiling heat transfer coefficient α fb is BOOKCOMP, Inc. — John Wiley & Sons / Page 661 / 2nd Proofs / Heat Transfer Handbook / Bejan POOL BOILING HEAT TRANSFER 661 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 [661], (27) Lines: 935 to 980 ——— 6.08429pt PgVar ——— Normal Page PgEnds: T E X [661], (27) α fb = 0.62  ρ G (ρ L − ρ G )gh  LG λ 3 G Dµ G (T w − T sat )  1/4 (9.63) The vapor properties are evaluated at the film temperature (T sat + ∆T/2), the liq- uid properties at the saturation temperature T sat , and the latent heat is corrected for sensible heating effects of the vapor as h  LG = h LG  1 + 0.34  c pG ∆T h LG  (9.64) Berenson (1960) proposed a film boiling model for film boiling on cylinders, incor- porating the Taylor hydrodynamic wave instability theory into the Bromley model, arriving at α fb = 0.425  ρ G (ρ L − ρ G )gh  LG λ 3 G µ G (T w − T sat )  σ/g(ρ L − ρ G )  1/2  1/4 (9.65) where the physical properties are evaluated as above but 0.5 is used in eq. (9.64) rather than 0.34. For film boiling on spheres, Lienhard (1981) has similarly shown that α fb = 0.67  ρ G (ρ L − ρ G )gh  LG λ 3 G Dµ G (T w − T sat )  1/4 (9.66) At large superheats, thermal radiation may be important, depending on the emissivity of the heated surface, ε w . Bromley (1950) proposed combining the contributions of film boiling and thermal radiation on cylinders when α rad < α fb as follows: α total = α fb + 3 4 α rad (9.67) where the radiation heat transfer coefficient α rad from the heater to the surrounding liquid or vessel is α rad = q rad T w − T sat = ε w σ SB (T 4 w − T 4 sat ) T w − T sat (9.68) and σ SB is the Stephan–Boltzmann constant (σ SB = 5.67×10 −8 W/m 2 · K 4 ). Apply- ing this analogy to vertical plates is less tenable because in film boiling the liquid– vapor interface becomes Helmholtz unstable near the leading edge. Leonard et al. (1976) showed that replacing the diameter D in eq. (9.63) with the one-dimensional Taylor instability wavelength λ d1 given by eq. (9.56) gives satisfactory results for film boiling on relatively tall vertical plates. The minimum heat flux at which film boiling can be maintained is again controlled by the Taylor instability of the interface (i.e., point MFB in Section 9.2). Zuber (1959) supposed that the minimum is reached when the vapor generation rate becomes too BOOKCOMP, Inc. — John Wiley & Sons / Page 662 / 2nd Proofs / Heat Transfer Handbook / Bejan 662 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 [662], (28) Lines: 980 to 1009 ——— -3.32997pt PgVar ——— Long Page PgEnds: T E X [662], (28) small to sustain Taylor wave action on the free interface for stable generation of bubbles. For a horizontal cylinder, q MFB is then q MFB = Cρ G h LG 4  σg(ρ L − ρ G ) (ρ L + ρ G ) 2 (9.69) where C is an arbitrary empirical constant, which Berenson (1960) identified exper- imentally to be equal to 0.09. Transition boiling occurs between the heat fluxes at the DNB and MFB points on surfaces in which the surface temperature is the independent variable. For example, the transition boiling portion of the pool boiling curve may be obtained by quenching a hot sphere. If the Biot number of the sphere is small, an energy balance on the sensible heat removed from the body can be used to determine the transient surface heat flux during that portion of the cooling process. Thus, measuring the temperatures of the sphere and the liquid, the transition heat transfer coefficient can be obtained. However, tests show that the transition boiling curve obtained by cooling may differ significantly from that obtained by heating. The heat transfer process in the transition regime can be thought of as a combi- nation of nucleate and film boiling, occurring either side by side or one after another in rapid succession at the same location on the heater surface. The endpoints of this regime are given by the values of q DNB and q MFB . Very approximate values of the transition boiling heat transfer coefficient can be obtained by linear interpolation be- tween their respective values at q DNB and q MFB . For more details on transition boiling, refer to Witte and Lienhard (1982) or Dhir and Liaw (1987). 9.6 INTRODUCTION TO FLOW BOILING For evaporation under forced-flow conditions, heat transfer includes both a convective contribution and a nucleate boiling contribution, whose relative importance depends on the specific conditions. The process of flow boiling is most commonly used inside vertical tubes, in horizontal tubes, in annuli, and on the outside of horizontal tube bundles. The local flow boiling heat transfer coefficient is primarily a function of vapor quality, mass velocity, heat flux, flow channel geometry and orientation, two- phase flow pattern, and fluid properties. Because the flow boiling coefficient is a function of vapor quality, these calculations are typically done locally in thermal design methods. Flow boiling is the most typical of industrial applications; pool boiling is sometimes applied to cooling of electronic parts. In the next five sections we present a review of two-phase flow patterns (Section 9.7), flow boiling inside vertical tubes (Section 9.8), flow boiling in horizontal tubes (Section 9.9), boiling on tube bundles (Section 9.10) and post-dryout heat transfer inside tubes (Section 9.11). 9.7 TWO-PHASE FLOW PATTERNS Flow boiling heat transfer is closely related to the two-phase flow structure of the evaporating fluid. Commonly observed flow structures are defined as two-phase flow BOOKCOMP, Inc. — John Wiley & Sons / Page 663 / 2nd Proofs / Heat Transfer Handbook / Bejan TWO-PHASE FLOW PATTERNS 663 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 [663], (29) Lines: 1009 to 1026 ——— 0.897pt PgVar ——— Long Page PgEnds: T E X [663], (29) patterns that have particular identifying characteristics. Analogous to criteria for delineating laminar flow from turbulent flow in single-phase flow, two-phase flow pattern maps are used to predict the transition from one type of two-phase flow pattern to another and hence to identify which flow pattern is occurring at the particular local conditions under consideration. In this section, first the flow patterns themselves are described for internal tube flows, then a flow pattern map and its flow regime transition equations are presented for horizontal tubes. For a more comprehensive treatment of two-phase flow transitions, refer to Barnea and Taitel (1986). 9.7.1 Flow Patterns in Vertical and Horizontal Tubes Flow patterns encountered in co-current upflow of gas and liquid in a vertical tube are shown in Fig. 9.9. The commonly identifiable flow patterns are: • Bubbly flow. In this regime, the gas is dispersed in the form of discrete bubbles in the continuous liquid phase. The shapes and sizes of the bubbles may vary widely, but they are notably smaller than the pipe diameter. • Slug flow. Increasing the gas fraction, bubbles collide and coalesce to form larger bubbles similar in size to the pipe diameter. These have a characteristic hemi- spherical nose with a blunt tail end, similar to a bullet, and are referred to as Taylor bubbles. Successive bubbles are separated by a liquid slug, which may include smaller entrained bubbles. These bullet-shaped bubbles have a thin film of liquid between them and the channel walls, which may flow downward due to the force of gravity, even though the net flow of liquid is upward. • Churn flow. Further increasing the velocity, the flow becomes unstable and the liquid travels up and down in an oscillatory fashion, although the net flow is Figure 9.9 Flow patterns in vertical upflow. . diameter D, the film boiling heat transfer coefficient α fb is BOOKCOMP, Inc. — John Wiley & Sons / Page 661 / 2nd Proofs / Heat Transfer Handbook / Bejan POOL BOILING HEAT TRANSFER 661 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 [661],. processes. BOOKCOMP, Inc. — John Wiley & Sons / Page 657 / 2nd Proofs / Heat Transfer Handbook / Bejan POOL BOILING HEAT TRANSFER 657 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 [657],. (9.60) BOOKCOMP, Inc. — John Wiley & Sons / Page 659 / 2nd Proofs / Heat Transfer Handbook / Bejan POOL BOILING HEAT TRANSFER 659 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 [659],