BOILING

HEAT TRANSFER

Pendahuluan

• Pool Boiling (Pendidihan kolam) adalahpendidihan pada sejumlah volume fluida diam.

• Di industri, hampir semua proses industrimerupakan model pendidihan mengalir (flow boiling mode).

• Peralatan Pool boiling lebih sederhana dan lebihmurah untuk skala laboratorium.

• Pool Boiling memberikan studi yang lebihjelas/dekat terhadap fenomena nukleat, yang sangat penting dalam sistem pendidihan nukleat.

• Pendidihan terjadi ketika fluida bersentuhan denganpermukaan panas yang temperaturnya mencapaitemperatur saturasi fluida.

• Ada dua jenis pendidihana. Pool Boiling, fluida diam.

a. Subcooled Boiling

b. Saturated Boiling

b. Flow Boiling, bila fluida mengalir melalui saluran/permukaanpanas

Boiling

Nukiyama Experiment

4

Pool Boiling

According to Nukiyama’s experiment, pool boiling is classified (regimes) to:

• Natural Convection Boiling Regime

• Nucleat Boiling Regime

• Transition Boiling Regime

• Film Boiling Regime

6

• Boiling regimes differ considerably in their character.

• Different heat transfer relations need to be used for different boiling regimes.

• In the natural convection boiling regime heat transfer rates can be accurately determined using natural convection relations.

Heat Transfer Correlations in Pool Boiling

• No general theoretical relations for heat transfer in the nucleate boiling regime is available.

• Experimental based correlations are used.

• The rate of heat transfer strongly depends on the nature of nucleation and the type and the condition of the heated surface.

Nucleate Boiling

Pendidihan kolam/bejana

• A adalah titik onset temperatur, dimana mulai terjadinya nukleat boiling.

• B temperatur transisi, dimana mulai terjadinya pendidihan nukleat berkembang penuh (fully developed)

• C adalah titik puncak, dimana dihasilkan fluks kalor maksimum

• D adalah titik dimana dihasilkan fluks kalor minimum. (Leidenfrost point)

• E adalah titik dimana mulai terjadinya burnout

9

Natural Convection Boiling(to Point A on the Boiling Curve)

• Gelembung tidak terbentuk pada permukaan panas hingga cairan terpanaskanmencapai temperatur di atas temperatur saturasinya (kira kita 2 to 6°C untukwater)

• Cairan berada dalam keadaan superheat (Keadaan metastable).• Pergerakan cairan dalam keadaan mode pendidihan ini diatur dengan “arus“

konveksi alami.

Natural Convection

Surface temperature rased by controling the heater.

Heat Flux is calculated based on themperature changes at heated block.

Convection calculated by:

�� = ����

Where:

C = 0,1 - 1,

For Laminar: m = ¼

For Turbulen: m = 1/3

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• The bubbles form at an increasing rate at an increasing number of nucleation sites as we move along the boiling curve toward point C.

Nucleate Boiling (between Points A and C)

• Region A–B ─ isolated bubbles.

• Region B–C ─ numerous continuous columns of vapor in the liquid.

Point A is referred to as the onset of nucleateboiling (ONB).

12

• In region A–B the stirring and agitation caused by the entrainment of the liquid to the heater surface is primarily responsible for the increased heat transfer coefficient.

• In region A–B the large heat fluxes obtainable in this region are caused by the combined effect of liquid entrainment and evaporation.

• For the entire nucleate boiling range, the heat transfer coefficient ranges from about 2000 to 30,000 W/m2·K.

• After point B the heat flux increases at a lower rate with increasing Texcess, and reaches a maximum at point C.

• The heat flux at this point is called the critical (ormaximum) heat flux, and is of prime engineering importance.

• Kesetimbangan dalam keadaan uap nukleat (vapour nucleat),

• Beda tekanan menurut Clausius-Clapeyron:

• Asumsi bahwa volume spesifik cairan diabaikan terhadap spesifik volume uap,

• diperoleh:

rprpr fg 222

rpp fg

2

satfg

fg

Tv

h

T

p

sat

fgg

satg

fg

T

h

TT

pp

satgfgg

sat

TTh

Tr

2

Radius gelembung, bergantung pada beda temperatur superheat, interaksi permukaan dan fluida, dan karakteristik fluida.Pada temperatur tinggi, kelompok gelembung mikro terbentuk, disebut dengan nukleasi homogen (homogeneous nucleation).

Boiling Nucleation

• Nukleasi dipengaruhi oleh kekasaran permukaan dansifat uap dari fluida (Jacob and Fritz,1931)

Effect of Surface finish on Boiling Curve.(Berenson, 1962)

Critical Cavity Radius

• Winterton (1977) dan Cornwell (1982), menunjukkan pengaruh sudut kontak (contact angle), .

• Gelembung terbentuk oleh adanya kavitasi, dan bergantung pada ukuran kavitasi.

• Kavitasi kritis (Critical/Smalest cavity) dimana gelembung akan terbentuk:

• Air pada 1 atm, Tsat=7oC, and rc = 4 m

• Bahan organik dan kriogenik rc = 0,1 rc air.

satfgg

satc

Th

Tr

2

• Efek udara yang terperangkap dlm kavitasi:

• The superheated temperature of surface for nucleation

rppp fag

2

a

fgg

satsat p

rh

TT

2

Bubble Growth

• It is generally assumed there is a superheated layer on the surface between bubble nucleation sites where natural convection occurs.

• Bubble growth is caused by the vapour pressure exceeding that balance by surface tension

• Vapour formed by rapid vapourisation of a microlayer left on surface and by saturated liquid evaporating at bubble surface

• Hydrodynamic analysis based on Rayleigh equation shown that bubble radius (R) is proportional to time:

• By limitation of thermal diffusion through the liquid layer surrounding the bubble, the bubble radius growth become slower.

• Where, C = a constant = (according to Plesset and Zwick, 1954), is thermal diffusivity of liquid, and Ja is Jacob Number difined as:

tR

t2CJa R

3

Tc a

sat

fgg

liquid

hJ

• In general equation, the bubble growth presence of superheated layer (proposes by Mikic, Rohsenow and Griffith 1970), R+ and t+ is Dimensionless radius:

• Where the dimensionless variable:

• It shown that: – for t+ << 1,

– and for t+ >> 1,

113

2 2/32/3 ttR

Rb

aR t

b

at

fsat

gfgsat

T

hTa

7

212Jab

tR tR

Bubble size at departure

• Fritz (1935), gives the equation of bubble size when it release from the surface:

• Where: Cd = 0,02 and = contact angle (usually symbolized )

• The waiting period of bubble from created and released, is commonly measure where:

• According to Jacob (1949) f and Db are related, and Zuber (1959) developed the expression:

• Ivey (1976) has shown that , where: n = 2 for bubble dynamically controled growth, and n = ½ when thermally controlled.

gf

dbg

CD

2

periodgrowth period waiting

1

f

2/1

259.0

f

gf

b

gfD

ConstantbnDf

Nucleat boiling mechanisms

Hsu and Graham (1976) identify 4 mechanism of nucleat boiling

• Evaporation: rapid vapourization behind the receding liquid during initial initial bubble growth.

• Enhanced turbulent convection: typically for 1.5 – 2.0 Db , Convection directly affected by the stream of departing bubble. Heat transfer rate is high.

• Turbulent Convection: no bubble formation, heat transfer is induced mainly by the bubble stirring action

• Transient conduction: when the bubble depart, it takes times to re-establish. During this period, heat transfered by transient conduction.

Nucleat Boiling Correlation

Correlation based on Perceived mechanism

• Convective relationship

• Instablility Wavelength difined as:

• With experimental determination, Rohsenow introducing:

• Where Csf depends on the surface-fluid interaction and has values between 0.0025 – 0.015

baCNu PrRe

2/1

gfgL

7.1

3/12/1

Pr f

gffgf

sf

fg

satf

gh

qC

h

Tc

23

Nucleat boiling of water on cooper surface

• Mikic and Rohsenow (1969) developed the bulk convection model. The surface divided into natural convection region yielding heat flux qnc and boiling induced region yields heat flux qbc:

• Transient conduction into liquid given by:

• Average heat flux over the area is:

• And the average heat flux over the total area due to boiling is:

• Regarding to the proportional influence mechanism, then the model become:

ncbctotal qqq

5.0

t

TTkq

satsf

c

5.0

5.0/1

0

, 2 fTTck

qdtfq sats

f

f

c

satbf

cbbc

TnDfck

nqDq

25.05.02

,2

2

mencbctotal qqqq

At Other way, Cooper (1984) expressed

Where : = roughness of surface, M is the molecular weight, q is heat flux

Correlation based on physical property

• The Borishanski-Mostinski equation, heat transfer coeff:

• Here

• Pr is difined as “reduce pressure”

• Constant A is found experimentally at Pr = 0.0294, if A is not available, use :

)(7.0 pfAq

102.117.0 1048.1)( rrr ppppf crit

rp

pp

69.01011.0 critpA

67.05.055.0log2.012.0 log55 qMpp rr

Nucleat Boiling in Tilt Surface

Nucleat boiling on Tubes

Enhance Nucleate Boiling

• Nucleat boiling heat transfer coefficient is higher than that most other heat transfer processes.

• Enhancement of nucleat boiling heat transfer coefficient can be :– Altering liquid properties (such as surface tension) with

additives

– Inducing bubble flow boiling as in tube bundles

– Encouraging foaming of liquid and hence thin film boiling

– Altering the geometri.

Boiling curve for various geometries in R113 at 1 atm (Cornwell, 1982)

Enhancement by structured surfaces (Yilmaz at.al, 1980)

Enhancement by finned tube in R113 at 1 atm (Scoones, 1986)

Critical Boiling

• Critical heat flux (CHF) is a condition which nucleate boiling on a surface reaches the maximum vapour production rate (maximum heat flux).

• From the point of CHF, increase of superheat temperature leads to transition region,

• Increase of heat flux leads to rapid rise of surface temperatur and film boiling. The rise of temperature may lead to the surface melting (and the critical point refered to as burnout)

• For critical boiling on a horizontal surface, the vapour layer largerly support the liquid layer above.

• The system is unstable and the spacing of the coloum is determined by hydrodynamic instability criteria (known as Taylor instability wavelength), given by:

• C = 2/16 for horizontal plate

• Considering the vapour flow (Zuber, 1958),

• And the heat flux is :

• Where K = 1.14 for a flat plate, 0.904 for a horizontal cylinder, and 0.84 for a sphere

2/1

gC

gf

c

4/1

,24

ghq gfgfgzcrit

Kq

q

zcrit

crit ,

36

Peak Heat Flux• The maximum (or critical) heat flux (CHF) in nucleate pool boiling:

Ccr is a constant whose value depends on the heater geometry, but generally is about 0.15.

• The CHF is independent of the fluid–heating surface combination, as well as the viscosity, thermal conductivity, and the specific heat of the liquid.

• The CHF increases with pressure up to about one-third of the critical pressure, and then starts to decrease and becomes zero at the critical pressure.

• The CHF is proportional to hfg, and large maximum heat fluxes can be obtained using fluids with a large enthalpy of vaporization, such as water.

Post-Critical Boiling

• On film boiling, there is vapour layer between surface and liquid. Heat transfer coefficient reduces.

• Heat passage through the thin insulating layer is limited by conduction and radiation.

• This condition divided into: transition boiling (where the thin layer partialy occurs) and film boiling

38

Transition Boiling (between Points C and D)

• When Texcess is increased past point C, the heat flux decreases.

• This is because a large fraction of the heater surface is covered by a vapor film, which acts as an insulation.

• In the transition boiling regime, both nucleate and film boiling partially occur.

• Operation in the transition boiling regime, which is also called the unstable film boiling regime, is avoided in practice.

• For water, transition boiling occurs over the excess temperature range from about 30°C to about 120°C.

39

• Beyond point D the heater surface is completely covered by a continuous stable vapor film.

• Point D, where the heat flux reaches a minimum is called the Leidenfrost point.

• The presence of a vapor film between the heater surface and the liquid is responsible for the low heat transfer rates in the film boiling region.

• The heat transfer rate increases with increasing excess temperature due to radiation to the liquid.

Film Boiling (beyond Point D

40

Burnout Phenomenon

• A typical boiling process does not follow the boiling curve beyond point C.

• When the power applied to the heated surface exceeded the value at point C even slightly, the surface temperature increased suddenly to point E.

• When the power is reduced gradually starting from point Ethe cooling curve follows Fig. 10–8 with a sudden drop in excess temperature when point D is reached.

41

Any attempt to increase the heat flux beyond qmax will cause the operation point on the boiling curve to jump suddenly from point C to point E.

However, surface temperature that corresponds to point E is beyond the melting point of most heater materials, and burnout occurs.

Therefore, point C on the boiling curve is also called the burnout point, and the heat flux at this point the burnout heat flux.

Most boiling heat transfer equipment in practice operate slightly below qmax to avoid any disastrous burnout.

• Berenson (1961) proposed the equation to calculate the heat transfer coefficient at film boiling:

• Where instability wavelength is:

• And corrected enthalpy of vapourization:

• For laminar film boiling,

4/13'

425.0

csatg

gfggfg

cT

kgh

2/1

gf

cg

fg

satg

fgfgh

Tchh 4.01'

4/13'

62.0

DT

kgh

satg

gfggfg

c

• When the surface temperature is high and radiation is dominant, Bromley (1950) proposed:

• Where:

• If Ts >> Tf, then

rctotal 75.0

4/13'

425.0

csatg

gfggfg

cT

kgh

fs

fs

SBrTT

TT 44

3sSBr T

4/1

2min 09.0

gf

gf

gfg

ghq

Leidenfrost Point

• Leidenfrost point, is the lowest point at boiling curve, lie-down on transition-film boiling.

• It is important when quenching process and rapid cooling by liquid as may required in nuclear reaction under LOCA (loss of cooling accident)

• The heat flux at this point is:

45

Minimum Heat Flux

• Minimum heat flux, which occurs at the Leidenfrost point, is of practical interest since it represents the lower limit for the heat flux in the film boiling regime.

• Zuber derived the following expression for the minimum heat flux for a large horizontal plate

• This relation above can be in error by 50% or more.

Transition boiling regime

46

Film Boiling

• At high surface temperatures (typically above 300°C), heat transfer across the vapor film by radiationbecomes significant and needs to be considered.

The heat flux for film boiling on a horizontal cylinder or sphere of diameter D is given by

47

Enhancement of Heat Transfer in Pool Boiling

• The rate of heat transfer in the nucleate boiling regime strongly depends on the number of active nucleation sites on the surface, and the rate of bubble formation at each site.

• Therefore, modification that enhances nucleation on the heating surface will also enhance heat transfer in nucleate boiling.

• Irregularities on the heating surface, including roughness and dirt, serve as additional nucleation sites during boiling.

• The effect of surface roughness is observed to decay with time.

48

• Surfaces that provide enhanced heat transfer in nucleate boiling permanently are being manufactured and are available in the market.

• Heat transfer can be enhanced by a factor of up to 10 during nucleate boiling, and the critical heat flux by a factor of 3.

• The use of finned surfaces is also known to enhance nucleate boiling heat transfer and the maximum heat flux.

• Boiling heat transfer can also be enhanced by other techniques such as mechanical agitation and surface vibration.

• These techniques are not practical, however, because of the complications involved.

EXAMPLE : Pool Boiling of Water

As the example:

• Consider the saturated pool boiling of water on a cooper tube of ¼ inch (19.1 mm) diameter at 1 atmosphere.

• The properties in the equation are 1.013 bar and 100 oC.

a. Natural convection for laminar flow on a horizontal cylinder (Cornwel, 1977):

25.053.0 RaNu

T

T

k

cTDgRa

ff

ff

3

33

233

23

10989

10681.010279.0

95822.40191.01071.081.9

225.1

25.125.033

25.0

kW/m .5960

1098953.00191.0

10681.0

53.0

T

T

TRaD

kTNu

D

kq

ff

Nucleat Boiling

B. The Rohsenow Equation

7.1

3/12/1

3

7.1

3/12/1

73.195781.9

059.0

255710279.0015.0

2557

22.4

Pr

qT

gh

qC

h

Tcf

gffgf

sf

fg

f

30263.0 Tq

Nucleat Boiling

C. The Borishanski-Mostinski equation:

For Water

Thus:

q/T = 4.21 x q0.7 x 0.726

q = 41.6 T3.33 W/m2 = 0.0416 T3.33 kW/m2

D. The Cooper equation with assumed roughness as 1 m

For Pr = 0.00457 andM = 18 (H2O Molecular Weight) yields

E. For horizontal Copper tubes, Cooper has recomended the value multiplied by 1.7 Then

)(7.0 pfAq

726.01048.1)( 102.117.0 rrr ppppf00457.07.221

1013.1rp

67.05.055.0log2.012.0 log55 qMpp rr

30771.0 Tq

3131.0 Tq

Critical Heat Flux

F. For cylinder:

2

4/1

4/1

kW/m 1000

81.9957059.0596.0225724

904.0

24904.0

crit

gfgfgcrit

q

ghq

G. Post Critical Boiling:

H. Leidenfrost

25.0

4/1

3

33

4/13'

72.0

0191.010018.0

10040.0225781.9957385.062.0

62.0

T

T

DT

kgh

c

satg

gfggfg

c

2min

4/1

2min

4/1

2min

kW/m 0.19

958

95781.9059.0596.0225709.0

09.0

q

q

ghq

gf

gf

gfg

75.072.0 TTq cc

4/13'

62.0

DT

kgh

satg

gfggfg

c

fg

g

fgfgh

Tchh 68.01' 2889

2257

500 x 86.168.012257'

fgh

Resume:

a) Corwel

b) Rohsenow

c) Borishanski-Mostinski

d) Cooper, equation 23

e) Cooper for horizontal tubes

f) CHF

g) Bromley

h) Leidenfrost Point

225.1 kW/m .5960 Tq

kW/m 0263.0 23Tq

kW/m 04160 2333.T .q

23 kW/m 0771.0 Tq

23 kW/m 131.0 Tq

2kW/m 1000critq

275.0 kW/m 72.0 Tqc

2min kW/m 0.19q

FLOW BOILING

57

FLOW BOILING

• In flow boiling, the fluid is forced to move by an external source such as a pump as it undergoes a phase-change process.

• It exhibits the combined effects of convection and pool boiling.

• External flow boiling over a plate or cylinder is similar to pool boiling, but the added motion increases both the nucleate boiling heat flux and the maximum heat flux considerably.

• The higher the velocity, the higher the nucleate boiling heat flux and the critical heat flux.

• Internal flow boiling, commonly referred to as two-phase flow, is much more complicated in nature because there is no free surface for the vapor to escape, and thus both the liquid and the vapor are forced to flow together.

Pendidihan aliran paksa

• Mirip dengan pendidihan kolam.

• Dengan meningkatnya laju aliran fluida, kurva pendidihan berada di atas (semakin meningkat fluks kalornya).

• Pada A’B’ disebut pendidihan nukleat partial (bubble terbentuk terpisah pisah pada permukaan.

• Pada B’C’, (fully develop Nucleat Boiling) tidak dipengaruhi kecepatan.

59

• The two-phase flow in a tube exhibits different flow boiling regimes, depending on the relative amounts of the liquid and the vapor phases.

• Note that the tube contains a liquid before the bubbly flow regime and a vapor after the mist-flow regime.

• Heat transfer in those two cases can be determined using the appropriate relations for single-phase convection heattransfer.

60

• Slug flow

– Bubbles coalesce into slugs of vapor.

– Moderate mass qualities

• Annular flow

– Core of the flow consists of vapor only, and liquid adjacent to the walls.

– Very high heat transfer coefficients

• Mist flow

– A sharp decrease in the heat transfer coefficient

• Vapor single-phase flow

– The liquid phase is completely evaporated and vapor is superheated.

• Liquid single-phase flow

In the inlet region the liquid is subcooled and heat transfer to the liquid is by forced convection (assuming no subcooled boiling).

• Bubbly flow

Individual bubbles

Low mass qualities

Nucleat Boiling on Vertical Tube

Nucleat Boiling on Horizontal Tube

Boiling Mixture

Extensive property of pure substance can be expressed as M:

For Binary solution, then can be write:

At Constant temperature:

Molal properties can be :

Where z1 and z2 are mole fraction of each component.

So it shoulds be:

Phase Diagram of binary mixture

Temperature – concentration Diagram

Berlaku:

Molar

Maka :

Pressure-concentration Diagram

Temperature-pressure Diagram

Phase change at constant pressure

Binary mixture heated from A to D.

• AB : temperature rise

• BC’ : phase change partialy

• C’D : temperature increase

Between B and C’, Vapor phase has concentration of y1b and liquid phase x1c.

At temperature Tc’, all liquid change into vapor.

Azeotrope

Liquid and vapor composition of mixture like pure fluid.

Boiling of mixture

• Nucleation od sites on the surface is influenced by liquid properties which can be very sensitive to composition.

• The surface tension and hence liquid/solid contact angle is altered and this effects the air trapping mechanism and the available site density on the surface.

• It is found the advancing contact angle for mixture is lower than for a pure fluid, hence greater penetration of liquid into the cavities.

• The available cavities with trapped air tend to be smaller, and the required Tsat is larger.

• The onset nucleate boiling is therefore delayed.

Binary Correlation

Let say TI is the mean of saturation temperature difference for the component:

Stephan and Corners' (1969) relation of mixture temperature difference between surface and the bubble point Tm

Where:

And p = pressure (in Bar), Ao is the empirical constant, depend of the mixture

ABAI x

BAI xx 1

xyAI

EIm

1

pAA o 12.088.0

pAA o 12.088.0

Referensi:

• Slide show: Mehmet Kanoglu, University of Gaziantep

• Heat and Mass Transfer: Fundamentals &Applications, Fourth Edition, Yunus A. Cengel, AfshinJ. Ghajar, McGraw-Hill, 2011.

• Catatan tanpa judul/cover.

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