유체역학및열전달Chapter 13. Heat transfer to fluids with Phase Change

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유체역학 및 열전달

Chapter 13. Heat transfer to fluids with Phase Change

부산대학교 화공생명공학부

현 규 (Kyu Hyun)

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부산대학교 현규

Heat transfer with phase change

l Condense on a cold surface

유체역학 및 열전달 2

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Heat transfer from Condensing Vapors

(4)

부산대학교 현규

Heat transfer with phase change

(5)

Coefficient for film-type condensation (1)

• In film-type condensation, the condensate film starts to form at the top of the tube

• The thickness of the film increases rapidly near the top of the tube and then more and more slowly in the remaining length

• The heat is assumed to flow through the condensate film solely by conduction

• The local coefficient is given by (heat flux가 같음)

d

f x

h = k

\ - Vertical tubes

d

x

diameter tube

D

D =

< (10^-³ ~10^-²) ,

d

d k T dA

T dq dA h

dq

x

= D D

= ,

• 응축으로 생성되는 막(film) 자체는 두껍지 않다.

y

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부산대학교 현규

Coefficient for film-type condensation (2)

• Layer flow with free surface (Gravity driven)

• Film Thickness

• The local heat-transfer coefficient

3 1

2

3

^/

÷÷ ø ö çç è

= æ

g b

m r d m ^&

d

b m &

=

G

Mass rate per unit length (condensate loading)

3 1

2

3 ^/

÷÷ ø ö çç

è

æ G

=

\ _f g

f

r

d m f 는 film을 의미함

3 2 1

3

/

÷ ÷ ø ö ç ç

è æ

= G

\

f f f

x

k g

h m

r

(13.3)

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Coefficient for film-type condensation (3)

• Vapor condense at outside of tubes

• The local heat transfer coefficient (일반적인 정의)

d

dL D T

m d dA

T h dq

o o o

o

x

p

l

= D

= D &

dL

condensate of

rate flow local

m

on vaporizati of

heat

=

&

l

Do

m

p

&

= G

dL T

h d

o

x

D

= G

\ l

-파이프를 타고 흘러내리므로 단위 길이당 흘러내리는 질량유속은 원주의 길이를 local flow rate로 나누는 값이 된다.

(13.5)

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부산대학교 현규

Coefficient for film-type condensation (4)

• The average coefficient for the entire tube

o T

b T

o o

T o

o T

T L

L D T

m T

A h q

D

= G

= D

= D l

p l ^&

tube of

bottom at

loading condensate

length tube

total L

on condensati of

rate total

m

transfer heat

of rate total

q

b T T T

= G

=

&

dL k

d T g

f f f o

G

÷ ÷ ø ö ç ç

è

= æ G D

\ l

r

m

¹ ³

2

3

^/

-여기서 중요한 두 가지.

1. 단위길이당 흘러내리는 총 질량유속이 tube 마지막 부분(bottom of tube)에서 흘러내리는 유속과 같다는 것이다.

2. ΔT_o 는 필름의 평균 온도와 바깥쪽 vapor의 평균 온도 차이를 나타내는 것으로서, local heat transfer에서와 같은 값을

나타낸다. â 따라서 앞의 (13.3)과 (13.5)에서 ΔT_o

를 계산할 수 있다.

L

T

이 식을 위의 식에 대입하면 (13.6)

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Coefficient for film-type condensation (5)

• The average coefficient for the entire tube

• Reynolds number를 이용해서 정의하면 G

÷ G

÷ ø ö çç

è G æ

= d

g dL L

h k

f f T

f b

3 1 3 2 1

3 ^/

/

m r

L

T ^{위 식을 0부터 L}^T^{까지 적분하면}

ò

÷÷

ø ö çç

è G æ

= G G

G_b L_T

f f T

f

b g dL

L d k

h

0 3 2 1

0

3 1

3

/ /

m r

4 2 1

3 3 2 1

943 3 0

3

4 ^/ ^/

. ÷÷

ø ö çç

è æ

= D

÷÷ ø ö çç

è æ

= G

\

f o

f f f

b f f

L T

g h k

g or h k

m l r

m r

3 1 3

3 1 1

3 2 2

47 4 1

47

1 ^/

/ /

Re .

. ^-

-

÷ =

÷ ø ö çç

è

= æ G

÷÷ ø ö çç

è æ

f b f

f f

g h k

r m m

f b

m

= 4G Re

(13.6)을 이용

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부산대학교 현규

Coefficient for film-type condensation (6)

• For Laminar flow

• For the wavy laminar and turbulent regions : the empirical equation

3 1 3

1

2 2

47

1

^/

/

Re

.

^-

÷ =

÷ ø ö ç ç

è

= æ

¢ k g

u h N

f f

f

r

m

-Characteristic length, but this length is not the same as film thickness

2 1 3 1 8 0 6

44 0 3

1

2 2

10 82

5

^. ^. ^/

. /

) Pr Re

.

(Re

^-

+ ´

^-

÷ =

÷ ø ö ç ç

è

= æ

¢ k g

u h N

f f

f

r

m

-Small ripples cause eddies which improve the heat transfer near the liquid surface

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Heat transfer to Boiling Liquids (비등 액체로의 열전달)

(포화액체의 풀 비등)

(12)

부산대학교 현규

Heat transfer to Boiling Liquids

l Line A-B

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Natural Convection to air from a hot, horizontal pipe (1)

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부산대학교 현규

Natural Convection to air from a hot, horizontal pipe (2)

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Heat transfer to Boiling Liquids

-Natural Convection

l Line A-B

- Pure convection

- Heat transferred by superheated liquid rising to the liquid-vapor interface where evaporation takes place

-Onset of boiling (Point B)

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부산대학교 현규

Superheating

- Superheating is an exception to this simple rule; a liquid is sometimes

observed not to boil even though its vapor pressure does exceed the ambient pressure. The cause is an additional force, the surface tension, which

suppresses the growth of bubbles.

- or by heating it in a sealed vessel with a headspace, where the liquid water is in equilibrium with vapor at the saturated vapor pressure.

- Water is said to "boil" when bubbles of water vapor grow without bound, bursting at the surface.

- For a vapor bubble to expand, the temperature must be high enough that the vapor pressure exceeds the ambient pressure (the

atmospheric pressure, primarily).

Below that temperature, a water vapor bubble will shrink and vanish

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Heat transfer to Boiling Liquids

-Natural Convection

l Line A-B

- Pure convection

- Heat transferred by superheated liquid rising to the liquid-vapor interface where evaporation takes place

-Onset of boiling (Point B)

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부산대학교 현규

Heat transfer to Boiling Liquids

-Individual Bubble regime

l Line B-C

- As the temperature drop is raised more sites become active,

- improving the agitation of the liquid - increasing the heat flux and the heat-

transfer coefficient

-Regime of slugs and Bubbles

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Nucleate boiling – linear scale graph

-Individual Bubble regime -Regime of slugs and Bubbles -핵비등에서 높은 열전달 속도는 주로 기포의 동적작용에 의해 액체에서

생기는 난류의

결과이다.

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부산대학교 현규

Heat transfer to Boiling Liquids

-Transition film boiling

l Line C-D

- So many bubbles are present

- They tend to coalesce and cover portions of the heating surface

- 절연성 증기층 (Layer of insulating vapor)

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Heat transfer to Boiling Liquids

-Stable film boiling

l Line D-E

- The hot surface becomes covered with a quiescent film of vapor, through which heat is transferred by conduction or radiation (after E point)

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부산대학교 현규

Heat transfer to Boiling Liquids

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Heat transfer to Boiling Liquids

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부산대학교 현규

Heat transfer to Boiling Liquids

-열전달 면적이 크다

유체역학및열전달Chapter 13. Heat transfer to fluids with Phase Change