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BOILING

Nazaruddin Sinaga

Efficiency and Energy Conservation Laboratory

Diponegoro University

General Considerations General Considerations

•Boiling is associated with transformation of liquid to vapor at a solid/liquid

interface due to convection heat transfer from the solid.

•Agitation of fluid by vapor bubbles provides for large convection coefficients

and hence large heat fluxes at low-to-moderate surface-to-fluid temperature

differences.

•Special form of Newton’s law of cooling:

( )

s s sat e

q h T T h T

= − =

➢

saturation temperatur of liquide

sat

T→

➢

( )

excess temperature

e s sat

T T T

− →

General Considerations (cont.)

•Special Cases

➢Pool Boiling:

Liquid motion is due to natural convection and bubble-induced mixing.

➢Saturated Boiling:

Liquid temperature is slightly larger than saturation temperature.

➢Forced Convection Boiling:

Fluid motion is induced by external means, as well as by bubble-induced mixing.

➢Subcooled Boiling:

Liquid temperature is less than saturation temperature.

Boiling Curve The Boiling Curve

Reveals range of conditions associated with saturated pool boiling on a

plot.

se

qT

−

➢Little vapor formation.

➢Liquid motion is due principally to single-phase natural convection.

•Free Convection Boiling

( )

5

e

TC

•Onset of Nucleate Boiling -

( )

5

e

ONB T C

Water at Atmospheric Pressure

Boiling Curve (cont.)

•Nucleate Boiling

( )

5 30

e

TC

➢Isolated Vapor Bubbles

( )

5 10

e

TC

–Liquid motion is strongly influenced by nucleation

of bubbles at the surface.

–

and increase sharply with increasing .

se

h q T

–Heat transfer is principally due to contact of liquid

with the surface (single-phase convection) and not

to vaporization.

➢Jets and Columns

( )

10 30

e

TC

–Increasing number of nucleation sites causes

bubble interactions and coalescence into

jets and slugs.

–Liquid/surface contact is impaired.

–continues to increase with while h begins to decrease.

s

q

e

T

Boiling Curve (cont.)

•Critical Heat Flux -CHF,

( )

max 30

e

q T C

➢Maximum attainable heat flux in nucleate boiling.

➢

2

max 1MW/m for water at atmospheric pressure.q

•Potential Burnout for Power-Controlled Heating

➢An increase in beyond causes the surface to be blanketed by vapor,

and the surface temperature can spontaneously achieve a value that potentially

exceeds its melting point

s

q

max

q

( )

1000 .

s

TC

➢If the surface survives the temperature shock, conditions are characterized

by film boiling.

•Film Boiling

➢Heat transfer is by conduction and

radiation across the vapor blanket.

➢A reduction in follows the cooling

curve continuously to the Leidenfrost

point corresponding to the minimum

heat flux for film boiling.

s

q

min

q

Boiling Curve (cont.)

➢A reduction in below causes an abrupt reduction in surface

temperature to the nucleate boiling regime.

s

q

min

q

•Transition Boiling for Temperature-Controlled Heating

➢Characterized by a continuous decay of with increasing

( )

max min

from to

s

q q q

.

e

T

➢Surface conditions oscillate between nucleate and film boiling, but portion

of surface experiencing film boiling increases with

.

e

T

➢Also termed unstable or partial film boiling.

Correleations Pool Boiling Correlations

•Nucleate Boiling

➢Rohsenow Correlation

( )

,

3

1/ 2 ,Pr

pl

lv

l fg n

s f f

e

gl

scT

qg

hCh

−

=

,, Surface/Fluid Combination (Table 10.1)

sf

Cn→

•Critical Heat Flux

( )

1/ 4

max 2

0.149 lv

fg v v

g

qh

−

=

Correleations

•Film Boiling

The cumulative (and coupled effects) of convection and radiation across

the vapor layer

4/3

4/3 1/3

conv rad

h h h h+

( )

( )

1/ 4

3

l v fg

conv

D

v v v s sat

g h D

hD

Nu C

k k T T

−

==

−

Geometry

Cylinder(Hor.) 0.62

C

Sphere 0.67

( )

,

0.80

fg fg p v s sat

h h c T T

= + −

( )

44

s sat

rad

s sat

TT

hTT

−

=−

If ,

0.75

conv rad

conv rad

hh

h h h

+

Problem: Electronic Chip Cooling

Problem 10.23: Chip thermal conditions associated with cooling by

immersion in a fluorocarbon.

KNOWN: Thickness and thermal conductivity of a silicon chip. Properties of saturated

fluorocarbon liquid

FIND: (a) Temperature at bottom surface of chip for a prescribed heat flux and for a flux that is

90% of CHF, (b) Effect of heat flux on chip surface temperatures; maximum allowable heat flux

for a surface temperature of 80°C.

Problem: Electronic Chip Cooling (cont)

ASSUMPTIONS: (1) Steady-state conditions, (2) Uniform heat flux and adiabatic sides, hence

one-dimensional conduction in chip, (3) Constant properties, (4) Nucleate boiling in liquid.

PROPERTIES: Saturated fluorocarbon (given):

p,

c

= 1100 J/kgK, hfg = 84,400 J/kg,

=

1619.2 kg/m3, v = 13.4 kg/m3, = 8.1 10-3 kg/s2,

= 440 10-6 kg/ms,

Pr

= 9.01.

ANALYSIS: (a) Energy balances at the top and bottom surfaces yield

( )

o cond s o s

q q k T T L

= = −

=

s

q

; where Ts and

s

q

are related by the Rohsenow correlation,

( )

1/3 1/6

n

s,f fg s

s sat p, fg v

C h Pr q

TT c h g

−=

−

Hence, for

s

q

= 5 104 W/m2,

( )

1/3

1.7 42

s sat 6

0.005 84,400J kg 9.01 5 10 W m

TT 1100J kg K 440 10 kg m s 84,400J kg

−

−=

( )

1/6

32

23

8.1 10 kg s 15.9 C

9.807m s 1619.2 13.4 kg m

−

=

−

( )

s

T 15.9 57 C 72.9 C= + =

Problem: Electronic Chip Cooling (cont)

From the rate equation,

42

o

os s

qL 5 10 W m 0.0025m

T T 72.9 C 73.8 C

k 135W m K

= + = + =

For a heat flux which is 90% of the critical heat flux (C1 = 0.9),

( )

()

1/ 4

3 2 2 3

2

3

8.1 10 kg s 9.807m s 1619.2 13.4 kg m

13.4kg m

−

−

From the results of the previous calculation and the Rohsenow correlation, it follows that

()

( )

1/3 1/3

42

eo

T 15.9 C q 5 10 W m 15.9 C 13.9 5 22.4 C

= = =

Hence, Ts = 79.4C and

42

o13.9 10 W m 0.0025m

T 79.4 C 82 C

135W m K

= + =

( )

1/ 4

v3

o max fg v 2

v

g

q 0.9q 0.9 0.149h 0.9 0.149 84,400J kg 13.4kg m

−

= = =

4 2 4 2

o

q 0.9 15.5 10 W m 13.9 10 W m

= =

Problem: Electronic Chip Cooling (cont)

(b) Parametric calculations for 0.2 C1 0.9 yield the following variations of

so

T and T with q .

o

30000 60000 90000 120000 150000

Chip heat flux, qo''(W/m^2)

70

72

74

76

78

80

82

Temperature (C)

To

Ts

The chip surface temperatures, as well as the difference between temperatures, increase with

increasing heat flux. The maximum chip temperature is associated with the bottom surface, and

To = 80C corresponds to

42

o,max

q 11.3 10 W m

=

<

which is 73% of CHF (

max

q

= 15.5 104 W/m2).

COMMENTS: Many of today’s VLSI chip designs involve heat fluxes well in excess of 15

W/cm2, in which case pool boiling in a fluorocarbon would not be an appropriate means of heat

dissipation.

Problem: Quenching of Aluminum Sphere

Problem 10.26: Initial heat transfer coefficient for immersion of an

aluminum sphere in a saturated water bath at atmospheric

pressure and its temperature after immersion for 30 seconds.

KNOWN: A sphere (aluminum alloy 2024) with a uniform temperature of 500C and

emissivity of 0.25 is suddenly immersed in a saturated water bath maintained at atmospheric

pressure.

FIND: (a) The total heat transfer coefficient for the initial condition; fraction of the total

coefficient contributed by radiation; and (b) Estimate the temperature of the sphere 30 s after

it has been immersed in the bath.

SCHEMATIC

Saturated water

T = 100 C

sat o

Problem: Quenching of Aluminum Sphere

(cont.)

ASSUMPTIONS: (1) Water is at atmospheric pressure and uniform temperature, Tsat, and

(2) Lumped capacitance method is valid.

PROPERTIES:

( )

6

f,i fg v p,v

3 7 2 3

v v v

Vapor Blanket T 573K : h 1.41 x 10 J/kg, k 0.0767 W/m K, c 5889 J/kg K,

Pr 1.617, 46.0kg/m , 4.33x 10 m /s, 712 kg/m .

l

−

= = = =

= = = =

Aluminum Alloy:

s

s3p, s

2700 kg/m , 875 J/kg K, k 186W/m K.c

= = =

ANALYSIS: (a) For the initial condition with Ts = 500C, film boiling will occur and the

coefficients due to convection and radiation are estimated using Eqs. 10.9 and 10.11,

respectively,

( )

( )

D

1/ 4

3

v fg

conv

v v v s sat

g h D

hD

Nu C

k k T T

−

==

−

()

44

s sat

rad s sat

TT

hTT

−

=−

(1)

(2)

where C = 0.67 for spheres and = 5.67 10-8 W/m2K4. The corrected latent heat is

( )

fg fg p,v s sat

h h 0.8 c T T

= + −

(3)

Problem: Quenching of Aluminum Sphere

(cont.)

Using the foregoing relations, the following results are obtained.

()()()

D2 2 2

cnv rad

Nu h W / m K h W / m K h W / m K

226 867 12.0 876

where s and cs are properties of the sphere. Numerically integrating Eq. (5) and evaluating

h

as a function of Ts, the following result is obtained for the sphere temperature after 30s.

( )

s

T 30s 333 C.=

The total heat transfer coefficient is given by Eq. 10.10a as

4/3 4/3 1/3

conv rad

h h h h= +

(4)

(b) For the lumped-capacitance method, from Section 5.3, the energy balance is

( )

s

s s sat s s dT

hA T T Vc dt

− − =

(5)

(2) Radiation makes a negligible contribution to the heat rate throughout the process.

COMMENTS: (1) The Biot number associated with the aluminum alloy sphere cooling process for

the initial condition is Bi = 0.09. Hence, the lumped-capacitance method is valid.