2 Heat flux, q/A, Btu/(hr)(ft )

이 윤 우

서울대학교 응용화학부

Heat and Mass Transfer

25

Boiling and Condensation

-Phase changes: Boiling & Condensation -Phase change gives high heat flux

5 Nuclear reactor design 5 Rocket technology

Boiling gives high heat flux q

_boil

~ 50,000,000 Btu/(h)(ft

²

)

Large quantities of

heat are produced in

small space

-Phase changes: Boiling & Condensation -Phase change gives high heat flux

Condenser design

Condensation gives high heat flux h

condensation

~ 20,000 Btu/(h)(ft

²

)(

^o

F)

Large quantities of

heat are removed in small space

Boiling

In quenching of very hot metals in liquids,

the heat transfer rate often increases as the

temperature difference between the metal

and liquid decreases.

No Liquid drop bounce No Liquid drop bounce

Drop wet the surface Drop wet the surface

Very very Very

The explanation for both the paradoxical quenching behavior and the Leidenfrost phenomenon lies in the fact that

V

boiling heat transfer occurs by several difference mechanisms and that

V

the mechanism is often more important in determining heat flux than the temperature-difference driving force.

Bubble Departure Behavior During Film Boiling

Among the various heat transfer mechanisms, boiling

is perhaps the most complex.

Hong, You, Ammerman and Chan

Heat flux, q/A, Btu/(hr)(ft )2

Shiro Nukiyama, “Maximum and minimum values of heat transmitted from metal to boiling Water under atmospheric pressure”, J. Soc. Mech. Eng. Japan, 37(206):367-374 (1934)

t_w-t_sat, ^oF

Heated platinum wire electrically Water at 100^oC

CHF(Critical Heat Flux)

Bubble condenses before reaching the free liquid surface

Natural convection

t_w-t_sat, ^oF

1.0 10 100 1,000 10,000

Heat flux, q/A, Btu/(hr)(ft )

Nucleate boiling

Transition zone

Film boiling

Nucleate boiling bubbles

Nucleate boiling bubbles rise to interface

Partial nucleate boiling and unstable film

stable film boiling

Radiation coming into play

The film collapse and reformation vapor film provides a considerable resistance to heat transfer

Vapor film forms around the wire and portions of the film break off and rise More sites

Bubble column

A

B

C

D

Superheating

impurity

150^oC 150^oC

Superheating Superheating

clean glassware, pure liquid Violent ebullition of vapor

Superheating in excess of 100^oF can be obtained if care is taken to use pure liquids and clean glassware. However, this state of supersaturation can be quickly ended, and violent ebullition of vapor occurs if impurities are added to the system.

heater

1mm

116-127^oC

100^oC

Thin zone: most of temperature drop usually occurs less than 1mm from the heater

Why the presence of superheat in boiling systems?

Superheating

How to explain for presence of superheat

P

_g

P

_l

2r

p r p

r r

p r

p

l g

l g

σ

σ π π

π

2

2 )

( )

(

^{2 2}

=

−

+

=

t_sat, P_sat ordinarily used by engineers apply to equilibrium at a flat interface between vapor and liquid. However, if a force balance is written at the equator of a spherical vapor bubble of radius r, P_g >P_l.

bubble

Effect of the surface force, which tends to contact the bubble

For small bubble, ΔP is very high:

Temperature of liquid must be much higher than the flat-surface saturation temperature

to from the vapor nucleus

How to explain for presence of superheat

If nuclei with large radii of curvature are available, the required excess pressure will be smaller and boiling will commence at a low superheat.

A perfect pure liquid in contact with a flat heated surface would, in theory, require an infinite amount of superheat.

A liquid is not, however, a continuum, and clusters of molecules could serve as nuclei. Furthermore, the conditions of perfect purity and flatness are unobtainable, so that the highest superheats recorded are of the order of 100 to 200^oF (55 to 110^oC).

However, it is likely that boiling does not require the presence of foreign matter, but can be initiate on the heating surface.

p r

p

_g

−

_l

= 2 σ

Heat Transfer Coefficient for n-hexane boiling

on a flat plate polished with three grades of emerypaper

t_s-t_sl, ^oF

10 100

100 1,000

Boiling coefficient, h, Btu/(hr)(ft2 )(o F)

Emery paper (金剛砂) 4-0

0

2 (roughest)

3,000 금강사로 연마 처리한

가장 미끈한 표면 금강사로 연마 처리한

가장 거친 표면

Surface roughness affects boiling

Boiling Boiling stop Boiling resumes

Pits on the heater surface serve as sources of bubble Stable gas pocket

pit Round-

bottomed

Angular- bottomed

Surface roughness affects boiling

Pits on the heater surface serve as sources of bubble Stable gas pocket

-The liquid-vapor interface will bulge downward into the pit. The surface forces act with the pressure in the vapor space to balance the liquid pressure.

-The liquid advances only until the radius of curvature of the interface is small enough so that ΔP (P_l-P_g) is equal to 2σ/r and a stable gas pocket remain.

p r p

r r

p r

p

g l

g l

σ

σ π π

π

2

2 )

( )

(

^{2 2}

−

=

−

=

Negative (-) radius of curvature of the interface

Heat Transfer Coefficient for boiling

-Experiments have shown that the heat transfer coefficient is proportional to some power of the concentration of bubble site ranging from 0.25 to 0.46.

-The number of sites on a heater surface increases with an increase of superheat. The number of sites depends on the roughness of the surface and the physical properties of the boiling fluid.

-The accurate prediction of boiling coefficients may be possible when these two mechanisms are understood.

Bubble behavior

0.01s

Growth time for the bubble at a nucleation site

0.01-0.06s

Following departure of the bubble from the site, there is a delay time of 0.01 to 0.06s before new bubble appears and repeats growth cycle.

The formation, growth, and release of bubbles is an extremely rapid sequence of events.

J.B. Roll, AIChE J., 10:530 (1964)

Boiling

Boiling stop Boiling resumes

Boiling

Boiling Boiling

F.D. Moore and R.B. Mesler, AIChE J., 7:620 (1961)

Fluctuating surface Temperature: Moore and Mesler showed that the surface temperature beneath a bubble site was lower than the surrounding surface temperature. They suggested that vaporization of a thin layer of liquid between the growing bubble and the heating surface caused removal of heat from the surface, thus lowing the surface temperature at that site.

Continue production

of bubble

Erratic production

of bubble

Correlations of nuclear boiling heat transfer coefficients

Rohsenow and Forster-Zuber

c

a b

Nu = Re Pr

[m/s]

bubble growing

the of interface the

of velocity radial

the u

Zuber and

Forster

] /bubble bubble[m

a of volume the

:

] m area[site/

unit per

sites active

of number the

:

site]

[bubble/s/

site, a

at formation bubble

of frequency the

:

] / [ Re

3

2

=

=

=

b b

b b

V n f

s m fnV

u

Rohsenow u D

μ ρ

u=Characteristic velocity

u x r_b=constant Re_b=constant ≠ function of time

Correlations of nuclear boiling heat transfer coefficients

Westwater

h = constant ⋅ σ

n

The effect of surface tension

(25-4)

( ) ^t

ⁿ

h = constant Δ

n = 2.5 for many commercial surfaces n = 1.4 for copper tube

n = 25 for flat surface polished with coarse emery paper

Δ ^{t =} t

heater surface –

t

saturated liquid

-2.5 < n < 1.275

The effect of degree of superheat

(25-4)

Correlations of nuclear boiling heat transfer coefficients

(

_{s sat}

)

b

l b b b

c b

t t

A h q

k D Nu h

a Nu

−

=

=

= Re Pr

D_b : max. bubble diameter at the free surface.

t_s-t_sat : temp. difference between surface and sat’d liquid temp.

k_l : thermal conductivity of liquid.

angle contact

bubble :

tension surface

:

for water) 0.0148

( constant :

) (

/ 2

velocity mass

average :

number) Reynolds

(bubble Re

β σ

ρ ρ

σ β

μ

=

−

=

=

d

v l

d b

b l

b b b

C

g C

D G

G D

Maximum Heat Flux

At steady state, the mass rate of the vapor rising from the surface

= The mass rate of liquid proceeding toward the surface the boiling rate



, rate of liquid influx



^,

the area of available for liquid flow



, the liquid velocity must increase very sharply.

A limiting condition is reached because the drag exerted by each phase on the other prevents indefinite increases in velocity. At this limiting condition, the liquid flow toward the heated surface cannot increase and the surface becomes largely blanketed with vapor.

Electrical heater (constant heat flux): t_s rises quickly becoming film boiling Steam-heated tube (constant temp.): becoming transition zone

the boiling rate



the boiling rate 

} Heater surface completely blankets with vapor (Film) } Heat transfer by conduction, convection and radiation.

} t_high : radiation dominant (high heat flux)

Film boiling is important in rocket technology when liquefied gases such as H₂ and O₂ are used to cool the rocket engine. Extremely high superheats occur in these systems, causing heat to be transferred by film boiling.

Stable film boiling (Ⅴ)

On the surface of horizontal tubes and vertical plates Bromley eq. :

Film boiling (Ⅵ)

( ) ( )

( )

14

0

2

0 . 4

62 .

0 ⎥ ⎥

⎦

⎤

⎢ ⎢

⎣

⎡

−

Δ +

= −

sat s

p fg

l

t t

D

t C

h g h k

υ

υ υ

υ

μ ρ ρ

ρ υ

t coefficien transfer

heat radiant

: h

t coefficien :

h

t coefficien transfer

heat total

: h

r c

2 / 1

r c

c

h

h h h

h ⎟ +

⎠

⎜ ⎞

⎝

= ⎛

Heat transfer with boiling

natural convective

boiling

forced convective

boiling

• 가시화 기법

• 정압 측정법

• 압력강하 측정법

• X선 감쇠법

• 전기전도도 측정법

1/2-inch-diameter copper tube.

Only the right half of the copper tube has been coated.

• Phase-Change Heat Exchangers

• Electronics Cooling (Electrically Non-Conducting Composition)

• Refrigeration Evaporators

• Chemical Processing

Spayed alumina

•minimum impact to existing hardware

•low wall superheats at boiling incipience

•high heat transfer coefficients in nucleate boiling

•increased critical heat flux

for a multi-chip module package

for various coolants and modes of convection

some fluorocarbon coolants and water

with a fluorocarbon liquid

Each module assembly consisted of 8 printed circuit boards on which were mounted arrays of single chip carriers. A total flow rate of 70 gpm was used to cool 14 stacks containing 24 module assemblies each. The power dissipated by a module assembly was reported to be 600 to 700 watts.

Condensation

Film condensation Dropwise condensation

Higher heat transfer coefficient !

vapor

D. West group, Int. J. Heat and Mass Transfer, 8, 419 (1965)

0 10 20 30

20x10⁴ 15x10⁴

10x10⁴

5x10⁴

0

Dropwise condensation

Film condensation

Δt, ^oF

Heat flux, Btu/(hr)(ft

2

)

To generate the low surface energy, hydrophobic surface required to promote dropwise condensation, the surfaces are treated using a plasma coating process.

promoting dropwise condensation (DWC) of organo-silicon polymer films deposited by plasma enhanced chemical vapor deposition (PECVD) on steam condenser tube materials

액적응축에 관하여는 막응축의 경우에 비해 큰 열전달 성능이 기대되어 많은 연구가 이루어졌으나, 실제로 이를 구현하는 데에는 큰 어려움이 있는 관계로, 아직도 실용화가 되지 않고 있다.

액적응축을 구현하려면 열교환 표면의 wettability를 조절할 수 있어야 하는데, 현실적으로 이를 구현할 만한 신뢰성 있는 방법이 알려져 있지 않다.

즉, 표면의 wettability를 방지하는 여러 가지 방법들이 제안되고는 있 으나, 사용 기간이 오래 지나거나 벽면의 과냉도가 커지는 경우에는 액

적응축이 막응축으로 변화해 가므로 실제 응축장치는 열전달 성능이 낮

은 막응축을 기준으로 설계되고 있다.

막응축에 관해서는 1916년에 Nusselt에 의해서 제안된 모델이 기본이 되어 현재까지 꾸준히 개선되고 사용되어 오고 있다.

즉, 당초의 Nusselt의 모델에서는 층류 액막, 일정한 물성치, 전 도 만에 의한 열전달 등의 가정들과 함께, 액막내의 과냉도 및 운 동량 변화 무시, 그리고 액막과 기체 경계면에서의 전단력 무시 등 여러 가지 가정들을 전제하고 있다.

그러나, 좀더 실제적이고 넓은 범위에서 적용이 가능하도록 위의 가정을 제거하고 모델을 개선하는 과정을 거쳐 오고 있다

x y

Assumption: (Laminar flow, Re_L<2000)

1. The flow of liquid is entirely viscous.

2. There is negligible drag at the v-l interface 3. The contribution of inertia forces to the

downward flow of liquid is negligible.

Γ

=

= Γ

= Γ

=

D u

x

u x

b e

b e L

π ρ

μ μ

ρ

rate flow

mass

perimeter) tube

of unit per

rate flow

(mass

4 Re 4

x

_e

u

_b

tube

D

u

_y

(x)

D>>x_e: cylindrical system can be described by rectangular coordinate Steady state incompressible & Newtonian, Laminar (Re_L < 2000)

kinematics : u_y=u_y(x), u_x=u_z=0 : continuity is satisfied.

v gy

p P

z comp P

z

y P x P

u y

comp P y

x comp P

x

y

∇

− +

=

∂

− ∂

=

−

∂ = + ∂

∂

− ∂

=

−

∂

− ∂

=

−

μ ρ

μ

3 1 0

:

) ( 0

: 0 :

2 2

0

From continuity

⎟ ⎟

⎠

⎞

⎜ ⎜

⎝

⎛

∂ + ∂

∂ + ∂

∂ + ∂

∂

− ∂

∂ = + ∂

∂ + ∂

∂ + ∂

∂

∂

2 2 2

2 2

2

z u y

u x

u y

p Y g

u g z u

u u y

u u x

u

_x

u

^y _y ^y _z ^y _x ^y _c ^c

ν

^{y y y}

ρ θ

⎟⎟ ⎠

⎜⎜ ⎞

⎝

⎛ −

=

=

=

=

=

=

−

=

−

∂ =

∂

2

0 ,

0 ,

0 :

) / (

2 2

2

x x g x

u

dx x du

x at

u x

at BCs

g g g Y

g x

u

e y

y e

y

c y

ν

ν μ

ρ

_(25-9)

(25-11)

3 3

3 0

3 3

3 3

⎟⎟ ⎠

⎜⎜ ⎞

⎝

= ⎛ Γ

= Γ

=

⋅

= Γ

=

=

= ∫

x g gx

x u Dg

x D D

w

x g x

dx u

u

e e

e b

e e e

y b

ρ ν ν

ρ

ν ρ ρπ

π π

ν

(25-13)

( ) ( )

( ) ( )

( ) ( )

dy d k t x

dy t d t

t x

h k

dy d Ddy

dw dA

dw

t t

dA

dw t

t dA h dq

x h k

x t Ddy t

k t

t Ddy h

dq

e s

sv y

s sv

s sv

y

e y

e s sv

s sv

y

= Γ Γ −

= −

=

= Γ

=

= −

= −

=

= −

−

=

λ λ

π

λ λ π π

ion vaporizat of

heat latent

:

(25-16) (25-15)

(25-18)

(25-20) dy located at a distance y from the top of the tube.

All heat of condensation released at the v-l interface is conducted horizontally to the tube surface

Γ π

= D w

conduction convection

( ) ( )

( )

( )

4 / 3 1

3 / 3 1

3 / 3 1

3 / 1 3 / 1 3

/ 1

942 . 0

925 .

0 925

. 0

,

0 ,

0

3 3

⎟⎟ ⎠

⎜⎜ ⎞

⎝

⎛

= −

⎟⎟ ⎠

⎜⎜ ⎞

⎝

⎛

= −

⎟⎟ ⎠

⎜⎜ ⎞

⎝

⎛

= Γ

Γ

= Γ

=

= Γ

=

Γ

⎟⎟ Γ

⎠

⎜⎜ ⎞

⎝

⎛

= Γ Γ Γ

⎟⎟ ⎠

⎜⎜ ⎞

⎝

= ⎛ Γ Γ Γ

=

= Γ

=

−

=

−

=

s sv

m

s sv

m L

m

L

L m L

m L

m e

m L m

L s

sv L

s sv

m

t t

L

g h k

t t

L h

g k

g h k

L y

at

y at

g d k

L d h

k L h d g

k L h dy x

L h A

h t w

t w

t t

A h q

ν

λ ρ

ν

λ ρ ν

ρ

ρ ν ρ

ν

λ

λ λ

(25-21, 22)

Supercritical Fluid Process Lab

(25-23)

(25-28)

(25-29)

L A

w

_L

= Γ

_L

/

(25-22)  (25-20)

3

3 3

3 ⎟⎟

⎠

⎜⎜ ⎞

⎝

⎛ ρ

Γ

= ν ν

= ρ

Γ gx x g

e e

Integration gives the mean heat-transfer coefficient for the entire laminar region

λ

= −

Γ _m ( _{sv s})

L

t t L h

Solving h_m

( )

2000 Re

Turbulent for

Re 0077

. 0

2000 Re

Laminar for

Re 47

. 1 942

. 0

L 4

. 0 3

/ 1

3 2

L 3

/ 1 3

/ 1

3 2

>

⎟⎟ =

⎠

⎜⎜ ⎞

⎝

⎛

<

⎟⎟ =

⎠

⎜⎜ ⎞

⎝

⎛

⎟⎟ ⎠

⎜⎜ ⎞

⎝

⎛

= −

−

L m

L m

s sv

m

g h k

g h k

t t

L

g h k

ν ν

ν

λ ρ

(25-31) (25-30)

μ

= 4 Γ Re

_L

If the tube is sufficiently long, the film thickness increases and the flow becomes turbulent.

Empirical correlation is given as Eq. (25-31) which can be applied to the entire tube, i.e., Both the laminar and turbulent portion.

10² 10³ 10⁴ 10⁵ 1.0

0.1

3 / 1 3

2

⎟⎟⎠

⎜⎜ ⎞

⎝

⎛ g h_m k

ν

Ripples on the surface of the condensation film give a certain amount of mixing.

Recommended=1.2 h_m

Theoretical Eq (25-29)

μ

= 4Γ^L Re

Eq (25-30)

W.H. McAdams, “Heat Transmission”, 3^rd ed., p335, McGraw-Hill, NY

2000 Re

0077 .

0 ^0.4

3 / 1 3

2 ⎟⎟ = >

⎠

⎞

⎜⎜

⎝

⎛ ν

ReL

Turbulent

L for

m k g h

2000 Re

47 .

1 ^1/3

3 / 1 3

2 ⎟⎟ = <

⎠

⎞

⎜⎜

⎝

⎛ ν ₋

ReL

Laminar

L for

m k g h

Eq (25-31)

( )

( )( )( ) ( )( )( )

side each

for rate the

length of

foot per

tube the

on formation condensate

of rate total

x radius

hydaulic _e

: 2 / :

2 2

4 4 Re 4

Re 20 . 1 725

. 0

3 / 1 3

/ 1 3

2

4 / 3 1

L L

L b L

b L

m

s sv m

u u

g h k

t t

D g h k

Γ Γ

μ

= Γ Γ

= μ μ

= ρ μ

= ρ

⎟ =

⎟

⎠

⎞

⎜⎜

⎝

⎛ ν

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

− ν

λ

= ρ

−

(25-32)

(25-33)

Highest h (thinnest film)

Lowest h (thick film)

Nusselt’s derivation

Hydraulic radius=Thickness of the film at any point Vapor may cause

ripples to occur Ö higher than (25-32)

Effect of N tubes in a vertical row

( )

4 / 3 1

725 .

0 )

( ⎟⎟

⎠

⎜⎜ ⎞

⎝

⎛

= −

s sv

N

m

ND t t

g h k

ν

λ

ρ

(25-37)

Vertical row

Re

_L < 2000

The mean heat transfer coefficients on successive tubes diminish at Re_L <2100.

There will always be a certain amount of turbulence on any tube below the top, because of the condensate dripping from the tube above. This has the effect of increasing (h_m)_N.

Condensation of superheated vapor

De-superheating + Removal of latent heat

Temperature

Pressure

Vapor Liquid

Solid _{t(oC) P* (bar)}

50 0.12

100 1.0

180 10.0

234 30.0

Resistance is negligible

’

Superheat vapo

ed r Saturated

vapor

Condensation of superheated vapor Sensible heat + Removal of latent heat

Resistance is not negligible

Total condenser must contain provision for continuous or periodic venting; Otherwise the non-condensable gases will

accumulate

and the capacity of the condenser will diminish to zero.

25-1(a)

25-4