BOOKCOMP, Inc. — John Wiley & Sons / Page 704 / 2nd Proofs / Heat Transfer Handbook / Bejan 704 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 [704], (70) Lines: 2392 to 2412 ——— -2.0pt PgVar ——— Normal Page PgEnds: T E X [704], (70) local flow boiling heat transfer coefficient, which is most pronounced at high vapor qualities and at high local oil mass fractions. 9.13 ENHANCED BOILING In the foregoing sections we have addressed boiling when it occurs on plain surfaces, either outside or inside tubes. Boiling on specially formed microsurfaces, to enhance nucleate boiling or convective boiling or both, is referred to as enhanced boiling and these surfaces as enhanced boiling surfaces. Typically, enhanced surfaces on the out- side of tubes are for the purpose of enhancing nucleate boiling, whereas those on the inside are for enhancing forced-convective boiling. The exception is the porous lay- ered surfaces that enhance nucleate boiling whether applied inside or outside a tube. In this section, first enhancement of nucleate boiling is discussed and then enhance- ment of forced-convective boiling. Both types of enhanced surfaces are used widely in industry, particularly in the refrigeration and air-conditioning industries. Refer to Bergles (1996), Thome (1990), and Webb (1994) for comprehensive treatments of this subject. 9.13.1 Enhancement of Nucleate Pool Boiling Boiling on plain, smooth surfaces is a weak function of the roughness of the sur- face, which increases nucleate pool boiling heat transfer coefficient with increas- ing roughness. This is only marginal, on the order of up to 30%, and may also be temporary if the surface becomes fouled. For substantial and sustainable enhance- ment, numerous geometries have been proposed and patented over the years. The earliest commercially successful enhancement was the integral low finned tube (i.e., a continuous helical fin that is formed on the outside of an otherwise plain tube), which is still used for appropriate applications. Applying a porous metallic coating on the surface of a tube is another important historical development, giving up to 15 times the heat transfer coefficient of a plain tube. In recent years, attention has fo- cused on mechanically deformed low finned tubes, whose fins are notched, bent, and compressed to form reentrant channels, essentially mechanically emulating a porous coating. Enhanced nucleate boiling surfaces provide significant performance advantages over those of a plain tube. For instance, the enhancement ratio of their coefficient relative to that of a comparable plain tube ranges from about 2 to 4 for low finned tubes and up to about 10 or more times for porous-coated tubes and mechanically deformed low finned tubes. Evaporation occurs both on the external surface of an enhanced boiling surface and inside its reentrant passageways. Hence, there are four possible paths by which heat can leave such a surface (Fig. 9.22): 1. As latent heat in the vapor formed within the reentrant passageways 2. As latent heat in bubbles growing on the exterior and on those emerging from the pores BOOKCOMP, Inc. — John Wiley & Sons / Page 705 / 2nd Proofs / Heat Transfer Handbook / Bejan ENHANCED BOILING 705 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 [705], (71) Lines: 2412 to 2447 ——— -0.103pt PgVar ——— Normal Page PgEnds: T E X [705], (71) 3. As sensible heat to the liquid “pumped” through the reentrant passageways 4. As sensible heat to the liquid in the external thermal boundary layer The factors contributing to the substantial increase in thermal performance of enhanced surfaces can be summarized as follows: • Nucleation superheat. Enhanced surfaces have an abundant supply of reentrant nucleation (except for low finned tubes) and hence initiate boiling at very low wall superheats with respect to plain surfaces. • Wetted surface area. Low finned tubes have from 2 to 3.5 times the surface area of a similar-sized plain tube, while complex enhancements have area ratios from 4 to 10 times that of a plain surface. • Thin-film evaporation. Reentrant channels favor the formation of thin evaporat- ing liquid films on the inner walls of the passageways. • Capillary evaporation. In a porous coating, the myriad of liquid menisci can evaporate as heat is conducted into the liquid behind them. • Internal convection. Liquid is pumped through the narrow channels by capillary forces and by growth and departure of bubbles. The small hydraulic diameters and entrance region effects yield very large laminar heat transfer coefficients for the liquid flow. • External convection. The larger number of active boiling sites accentuates the external convection mechanisms (i.e., bubble agitation and thermal boundary layer stripping). These mechanisms can be compared to those occurring on a plain surface in Section 9.5.1. The thermal effectiveness of these factors depends on the type of 2 3 4 1 5 Liquid Vapor Vapor Vapor Liquid Liquid Liquid Particles 1. Thin-film evaporation 2. External evaporation 3. Convection in passageways 4. External convection 5. Capillary evaporation Figure 9.22 Heat transfer paths for boiling on a porous-coated surface. BOOKCOMP, Inc. — John Wiley & Sons / Page 706 / 2nd Proofs / Heat Transfer Handbook / Bejan 706 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 [706], (72) Lines: 2447 to 2460 ——— 14.097pt PgVar ——— Normal Page PgEnds: T E X [706], (72) Figure 9.23 Low finned tube (left) and Turbo-Bii tube (right). enhanced surface geometry and its characteristic dimensions. As an example, Fig. 9.23 depicts photographs of the surfaces of a low finned tube and a Turbo-Bii tube (trademark of Wolverine Tube Inc.). 9.13.2 Enhancement of Internal Convective Boiling Numerous geometries exist for enhancing in-tube evaporation: porous coatings, cor- rugations, ribs, star inserts, twisted tapes, and microfins, to name just a few. The two most important geometries are the porous coating (commercially available as High Flux from UOP, Inc.) and the microfin (manufactured by numerous companies). The High Flux porous coating is used in large refrigeration systems working with propane or ethylene as the working fluids and also in vertical thermosyphon reboilers in the petrochemical industry for evaporation of nonfouling fluids, typically mixtures. Its nucleate boiling performance is so high that typically the convective contribution for forced-convective boiling becomes negligible in comparison. Hence, nucleate pool boiling data can be used for these design applications. Microfin tubes are characterized by numerous small internal fins 0.1 to 0.4 mm in height that can be either longitudinal or helical and either two-dimensional (i.e., plain microfins) or three-dimensional (i.e., crosscut or notched microfins). Figure 9.24 de- picts a typical geometry. The fins have a height-to-width at base ratio of about 1.0, and their fin profiles tend to be trapezoidal, triangular, or rectangular, depending on the particular tooling of the manufacturer. Most microfin tubes are seemless (manufac- tured by drawing a plain tube over an externally grooved mandrel), but manufacturers now also produce these tubes from strip by first rolling the enhancement geometry onto one side of the strip and then forming a longitudinally seamed tube from the strip. Microfin tubes are most commonly available in copper in diameters from about 5 to 16 mm outside diameter. Several versions are available in high alloys with 14 to 22-mm internal diameters (stainless steels and titanium) and also in carbon steel and aluminum (for ammonia systems). Nearly all microfin tubes tested in university labs have been used in their original production form; in some industrial applications of microfin tubes, such as air-conditioning coils with external aluminum fins, they are BOOKCOMP, Inc. — John Wiley & Sons / Page 707 / 2nd Proofs / Heat Transfer Handbook / Bejan ENHANCED BOILING 707 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 [707], (73) Lines: 2460 to 2473 ——— 0.166pt PgVar ——— Normal Page PgEnds: T E X [707], (73) Figure 9.24 Microfin tube. expanded mechanically into the coils, and hence their fin heights are reduced by a small margin and their internal diameters increased. In-tube evaporation inside microfin tubes has become an important research topic because of their widespread application in direct-expansion evaporators in recent years. These are all horizontal units, and hence all the published test data for microfin tubes presented here will be for that orientation. Microfin tubes typically provide heat transfer augmentation on the order of 1.5 up to 4 times that of a plain tube operating at the same conditions. This significant enhancement relative to plain tubes, with only a small adverse augmentation of their two-phase pressure drops, has been attributed to the following heat transfer enhancement mechanisms: • Extended surface area effect. Internal wetted surface area ratios for microfin tubes relative to their equivalent plain bore tubes range from about 1.3 to 1.9, depending on the number of fins and on their shape, height, and helix angle (typ- ically, the area ratio represents the lower bound on the heat transfer enhancement level). • Enhanced convective heat transfer. Microfins augment the convective heat trans- fer process across the annular liquid film, similar to internal ribs used for single- phase flow inside tubes, and this increases the two-phase convection contribution to annular flow boiling. • Flow pattern effect. The helical microfins tend to convert what would otherwise be a stratified-wavy flow in plain tubes into the more thermally effective annular flow regime, meaning that all the internal tube wall perimeter is wetted and active rather than only the lower wetted fraction in plain tubes; this represents the principal reason for their very large augmentation ratios at low mass velocities. • Nucleate boiling heat transfer. The microfins may favor the activation of nucle- ation sites by partially shielding the potential cavities from the flow; nucleate boiling will also occur on the total wetted extended surface area. BOOKCOMP, Inc. — John Wiley & Sons / Page 708 / 2nd Proofs / Heat Transfer Handbook / Bejan 708 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 [708], (74) Lines: 2473 to 2652 ——— -1.7936pt PgVar ——— Normal Page PgEnds: T E X [708], (74) • Swirl effects. Swirl imparted to the annular liquid film by helical microfins may retard the onset of dryout to higher vapor qualities; swirl of the continuous vapor phase in mist flow and annular flow with partial dryout will augment vapor-phase heat transfer to the dry wall, similar to a single-phase turbulent flow inside an internally ribbed tube; swirl will also drive entrained droplets to the tube wall. • Grigorig film thinning effects. The convex contours at the tips of microfins will tend to thin the evaporating liquid film on the fins, similar to that which occurs for film condensation on external low finned tubes, increasing the evaporating heat transfer coefficients on the microfins significantly. In recent years, numerous methods have been proposed for predicting the flow boiling heat transfer coefficients in microfin tubes. Refer to Webb (1999) and Thome (1999) for a summary of these methods. NOMENCLATURE Roman Letter Symbols a drag constant, dimensionless empirical constant, dimensionless a L liquid thermal diffusivity, m 2 /s A cross-sectional area, m 2 bubble growth parameter, m/s A G cross-sectional area of vapor, m 2 A Gd dimensionless cross-sectional area of vapor, dimensionless A L cross-sectional area of liquid, dimensionless A Ld dimensionless cross-sectional area of liquid, m 2 b empirical exponent, dimensionless B bubble growth parameter, m/s 1/2 c empirical exponent, dimensionless c pL liquid specific heat, J/kg ·K C empirical constant, dimensionless inverted annular flow constant, dimensionless C D drag coefficient, dimensionless C 0 boiling constant, dimensionless C sf surface factor, dimensionless C 1 lead constant, dimensionless d b bubble base diameter, m d i tube diameter, m d i,0 reference tube diameter, m d o bubble departure diameter, m d oF bubble departure diameter of Fritz, m D outside tube diameter, m droplet diameter, m e empirical constant, dimensionless BOOKCOMP, Inc. — John Wiley & Sons / Page 709 / 2nd Proofs / Heat Transfer Handbook / Bejan NOMENCLATURE 709 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 [709], (75) Lines: 2652 to 2652 ——— 0.0059pt PgVar ——— Normal Page PgEnds: T E X [709], (75) E convection enhancement factor, dimensionless E 2 stratified flow correction factor, dimensionless f bubble departure frequency, s −1 empirical constant, dimensionless Fanning friction factor, dimensionless friction factor, dimensionless f cd cumulative deposition factor, dimensionless f G vapor-phase friction factor, dimensionless F drag force, N two-phase multiplier, dimensionless constant of Shah, dimensionless F 1 (q) nondimensional exponent, dimensionless F 1 (q) nondimensional exponent, dimensionless F b buoyancy force, N bundle boiling factor, dimensionless F c mixture boiling correction factor, dimensionless F D drag force, N F i inertia force, N F(M) residual correction factor, dimensionless F nb nucleate boiling correction factor, dimensionless F p excess pressure force, N reduced pressure factor, dimensionless F pf pressure correction factor, dimensionless F PF pressure correction factor, dimensionless F tp two-phase multiplier, dimensionless F wG radiative view factor from wall to vapor, dimensionless F wL radiative view factor from wall to liquid droplets, dimensionless F σ surface tension force, N g acceleration of gravity, m/s 2 empirical exponent, dimensionless h liquid height, m h G,a actual vapor enthalpy, J/kg h G,e equilibrium vapor enthalpy, J/kg h G,sat enthalpy of saturated vapor, J/kg h Ld dimensionless liquid height, dimensionless h LG latent heat of vaporization, J/kg h L,sat enthalpy of saturated liquid, J/kg H characteristic height, m H dimensionless height, dimensionless L characteristic length, m L dimensionless length, dimensionless m mass, kg exponent, dimensionless ˙m total mass velocity of liquid and vapor, kg/s ·m 2 BOOKCOMP, Inc. — John Wiley & Sons / Page 710 / 2nd Proofs / Heat Transfer Handbook / Bejan 710 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 [710], (76) Lines: 2652 to 2652 ——— 0.0059pt PgVar ——— Normal Page PgEnds: T E X [710], (76) ˙m bubbly bubbly flow transition mass velocity, kg/s ·m 2 ˙m high value of wavy (new) flow mass velocity transition at χ, kg/s · m 2 ˙m low value of stratified low mass velocity transition at χ, kg/s ·m 2 ˙m min minimum mist flow transition mass velocity, kg/s · m 2 ˙m mist mist flow transition mass velocity, kg/s · m 2 ˙m strat stratified flow transition mass velocity, kg/s · m 2 ˙m wavy wavy flow transition mass velocity, kg/s ·m 2 ˙m wavy(new) new wavy flow transition mass velocity, kg/s ·m 2 M molecular weight, kg/mol n exponent, dimensionless nf nucleate boiling exponent, dimensionless N dimensionless parameter, dimensionless p pressure, N/m 2 ∆p pressure difference, N/m 2 ∆p sat saturation pressure difference, N/m 2 p a partial pressure of air, N/m 2 p crit critical pressure, N/m 2 p G vapor pressure, N/m 2 p L liquid pressure, N/m 2 p r reduced pressure, dimensionless p sat saturation pressure, Pa p ∞ vapor pressure at planar interface, N/m 2 P characteristic perimeter, m P characteristic perimeter, m P G vapor perimeter, m P Gd dimensionless vapor perimeter, dimensionless P i length of liquid–vapor interface, m P id interface length, dimensionless P L wetted perimeter, m P Ld liquid perimeter, dimensionless P v dry perimeter, m q heat flux, W/m 2 q DNB heat flux at DNB, W/m 2 q DNB,z heat flux at DNB according to Zuber, W/m 2 q G heat flux resulting from wall-to-droplet evaporation, W/m 2 q L heat flux resulting from droplet evaporation, W/m 2 q MFB heat flux at MFB, W/m 2 q ONB heat flux at onset of nucleate boiling, W/m 2 q rad radiation heat flux, W/m 2 q 0 reference heat flux, W/m 2 r b bubble base radius, m r i internal radius of tube, m r max maximum nucleation radius, m r min minimum nucleation radius, m BOOKCOMP, Inc. — John Wiley & Sons / Page 711 / 2nd Proofs / Heat Transfer Handbook / Bejan NOMENCLATURE 711 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 [711], (77) Lines: 2652 to 2652 ——— 0.96321pt PgVar ——— Normal Page PgEnds: T E X [711], (77) r nuc nucleation radius, m R bubble radius, m characteristic radius, m R radius, dimensionless R + bubble radius, dimensionless ¯ R ideal gas constant, J/mol ·K R p mean surface roughness, µm R p0 reference mean surface roughness, µm R p,0 reference mean surface roughness, µm S nucleation suppression factor, dimensionless S 2 stratified flow correction factor, dimensionless t bubble growth time, s t + bubble growth time, dimensionless t g bubble growth time, s t w bubble waiting time, s T absolute temperature, K T bub bubble point temperature, K T crit critical temperature, K T D droplet temperature, K T dew dew point temperature, K T G vapor temperature, K T G,a actual bulk vapor temperature, K T G,f film temperature of vapor, K T L subcooled liquid temperature, K T sat saturation temperature, K or °C T w wall temperature, K or °C T ∞ bulk liquid temperature, K or °C ∆T wall superheat, K ∆T bp boiling range or temperature glide of mixture, K ∆T id ideal wall superheat, K ∆T nuc nucleation superheat, K ∆T sat wall superheat, K u velocity, m/s u d droplet deposition velocity, m/s u G vapor velocity, m/s u H velocity for homogeneous flow, m/s v G vapor specific volume, m 3 /kg v L liquid specific volume, m 3 /kg w local mass fraction of oil, kg/kg w inlet inlet mass fraction of oil before expansion valve, kg/kg x mole fraction of liquid, dimensionless X tt Martinelli parameter, dimensionless y mole fraction of vapor, dimensionless Y multiplying factor, dimensionless z axis along tube, m BOOKCOMP, Inc. — John Wiley & Sons / Page 712 / 2nd Proofs / Heat Transfer Handbook / Bejan 712 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 [712], (78) Lines: 2652 to 2714 ——— 0.20764pt PgVar ——— Short Page PgEnds: T E X [712], (78) z a length from inlet where liquid is actually completely evaporated, m z DO length from inlet where dryout occurs, m z e length from inlet under equilibrium conditions, m Z G mixture boiling parameter, dimensionless Greek Letter Symbols α mist flow heat transfer coefficient, W/m 2 · K α b bundle boiling heat transfer coefficient, W/m 2 · K α cb convective boiling heat transfer coefficient, W/m 2 · K α D convective boiling heat transfer coefficient from vapor to droplet, W/m 2 · K α eff effective mixture flow boiling heat transfer coefficient, W/m 2 · K α fb film boiling heat transfer coefficient, W/m 2 · K α FZ Forster–Zuber nucleate boiling heat transfer coefficient, W/m 2 · K α G vapor heat transfer coefficient, W/m 2 · K α id ideal pure fluid boiling heat transfer coefficient, W/m 2 · K α L liquid only heat transfer coefficient, W/m 2 · K α mixt mixture boiling heat transfer coefficient, W/m 2 · K α nb nucleate boiling heat transfer coefficient, W/m 2 · K α nb,0 reference nucleate boiling heat transfer coefficient for flow boiling, W/m 2 · K α nc natural convection heat transfer coefficient, W/m 2 · K α rad radiation heat transfer coefficient, W/m 2 · K α st single-tube nucleate boiling heat transfer coefficient, W/m 2 ·K α total total heat transfer coefficient, W/m 2 · K α tp two-phase flow boiling heat transfer coefficient, W/m 2 · K α vapor vapor-phase heat transfer coefficient on dry wall, W/m 2 · K α wet wet wall heat transfer coefficient, W/m 2 · K α 0 reference nucleate boiling heat transfer coefficient, W/m 2 · K α(z) local heat transfer coefficient at position z, W/m 2 · K β contact angle, rad β apparent contact angle, rad β L mass transfer coefficient, m/s δ thickness of annular liquid layer, m boundary layer thickness, m ε void fraction, dimensionless θ dry dry angle around top perimeter of tube, rad θ max dry angle at χ max ,rad θ strat stratified angle around bottom perimeter of tube, rad κ ratio of droplet heat flux to total heat flux, dimensionless λ thermal conductivity, W/m 2 · K BOOKCOMP, Inc. — John Wiley & Sons / Page 713 / 2nd Proofs / Heat Transfer Handbook / Bejan NOMENCLATURE 713 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 [713], (79) Lines: 2714 to 2747 ——— -2.86235pt PgVar ——— Short Page * PgEnds: PageBreak [713], (79) λ d1 one-dimensional Taylor wavelength, m λ d2 two-dimensional Taylor wavelength, m λ H Helmholtz wavelength, m µ dynamic viscosity, N · s/m 2 µ oil dynamic viscosity of oil, N · s/m 2 µ ref dynamic viscosity of refrigerant, N · s/m 2 µ ref−oil dynamic viscosity of refrigerant-oil mixture, N · s/m 2 ξ Ph friction factor, ξ w emissivity of the wall, dimensionless ρ density, kg/m 3 σ surface tension, N/m σ SB Stephan–Boltzmann constant, W/m 2 · K 4 φ heterogeneous nucleation factor, dimensionless χ vapor quality, kg/kg χ a actual local vapor quality, dimensionless χ DO vapor quality at dryout, dimensionless χ e local equilibrium vapor quality, dimensionless χ max vapor quality at intersection of mist and wavy flow transition curves, kg/kg ψ mist flow parameter, dimensionless Dimensionless Numbers Bo boiling number Fr L Froude number of liquid phase Gr G Grashof number of vapor Ja Jakob number Nu Nusselt number Pr Prandtl number Re Reynolds number Re bub bubble Reynolds number Re G Reynolds number of vapor phase Re GH Reynolds number for vapor in homogeneous flow Re L Reynolds number of liquid phase Re tp two-phase Reynolds number We Weber number Subscripts e equilibrium f film G vapor H homogeneous L liquid . mist flow heat transfer coefficient, W/m 2 · K α b bundle boiling heat transfer coefficient, W/m 2 · K α cb convective boiling heat transfer coefficient, W/m 2 · K α D convective boiling heat transfer. boiling heat transfer coefficient, W/m 2 · K α fb film boiling heat transfer coefficient, W/m 2 · K α FZ Forster–Zuber nucleate boiling heat transfer coefficient, W/m 2 · K α G vapor heat transfer. boiling heat transfer coefficient, W/m 2 · K α L liquid only heat transfer coefficient, W/m 2 · K α mixt mixture boiling heat transfer coefficient, W/m 2 · K α nb nucleate boiling heat transfer