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Characterization of Boiling Heat Transfer ina Cryogenic System

Eveline Chao, Matthew Helgeson,

Moha Kulkarni, Priyanka Vaddi

06-363: Transport Process Lab, Team 3Carnegie Mellon University

Pittsburgh, PA 15213

May 9, 2003

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Abstract

The objective of this experiment was to determine the overall boiling heat transfer coefficient, h,

for a system including a phase change. Smooth aluminum and stainless steel cylinders were

submerged in liquid nitrogen to study boiling heat transfer at cryogenic temperatures. For free

convection, values of h were determined to range from 20 to 70 W/m2*K. Using empirical

correlations, determined h values for nucleate boiling ranged from 2500 to 10,000 W/m2*K for

stainless steel and from 10,000 to 30,000 W/m2*K for aluminum. Using the Hsu and Westwater

correlation, h for film boiling was determined to range from 100 to 250 W/m2*K for stainless

steel and from 400 to 700 W/m2*K for aluminum. An experimental boiling curve was produced

using these values that mirrored results found in literature, confirming the theoretical basis for

analysis.

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Introduction

Boiling heat transfer occurs when thermal energy is transferred from a boiling liquid to an object

immersed in that liquid. When a fluid undergoes a phase change from liquid to gas, preferential

formation of gas on a surface can cause potentially large convective heat transfers between the

fluid and the object.

Boiling heat transfer is of great interest in industrial practice, as large heat flux can occur in a

relatively small space. Cryogenic processes including refrigeration, food preservation, and

cryogenic freezing are all carried out by some sort of boiling heat transfer.

Even though cryogenic heat transfer is utilized in many processes, the phenomenon is fairly ill-

explained by current theory. The objective of this experiment was to quantitatively describe

boiling heat transfer at cryogenic temperatures, such that conclusions about the nature of

qualitative observations could be confirmed.

Background and Theory

In general, heat transfer with phase change is more complex than normal convective heat transfer

due to effects such as latent heat of vaporization, surface tension of the gas being formed, and

other complications due to the nature of a two-phase system. Due to the nature of liquid-vapor

phase transitions, boiling heat transfer can be described as a series of boiling regimes that occur

based upon system conditions. Figure 1 below1is a schematic describing the various regimes of

boiling heat transfer obtained from experimental heat transfer data gathered by placing a heated

horizontal wire in a pool of boiling water at its saturation temperature:

1Hands, page 158

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Figure 1: Heat transfer for platinum wire in boiling nitrogen. The general shape of the heat flux

curve is applicable to most systems.

where Tw and Tsatare the temperatures of the wire and saturated fluid, respectively, and q/A

represents the heat flux to the wire from the fluid given by the equation

vmq = (1)

where q is the heat flux, m is the mass flow of vapor, and v is the latent heat of vaporization of

the fluid.

Free Convection

Below the superheating of 5 K, free convection, which is characterized by boiling of fluid in the

bulk, occurs2. Since this boiling does not significantly occur at the surface, heat transfer occurs

by the usual natural convection seen in most systems.

All boiling heat transfer correlations for Nu, the Nusselt number, follow the form

( )PrRe,=Nu (2)

2W3R, page 341

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where Re is the Reynolds number and Pr, the Prandtl number, is tabulated for most materials.

The Nusselt number for the boiling bubbles is defined as:

Lsat

b

bkTT

DAq

Nu

)(

)/(

(3)

where kLis the conductivity, Db is the diameter of bubbles being formed, and other parameters

have their usual definitions. The Reynolds number Rebis defined as:

L

bbb

GD

Re (4)

where Gbis the mass velocity of the vapor breaking away from the object, and Lis the viscosity

of the liquid.

Calculations for free convection can be performed assuming a lumped parameter analysis for

simplification. This can be used when internal resistance is negligible, i.e the Biot Number, Bi,

is less than 0.1:

k

hLBi= (5)

where k is the thermal conductivity of the object, h is the heat transfer coefficient, and L is the

relevant length scale. For vertical cylinders, h can be found by:

( )[ ] 9/416/94/1

Pr/492.01

670.068.0

+

+= L

L

RaNu (6)

where RaL, the Rayleigh number, is the product PrGr . The Grashoff number, Gr, is defined as:

TCLGr = 3 (7)

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where C is tabulated for most materials, and T is the temperature difference between the object

and fluid.

The heat transfer coefficient can be determined from (2) using

k

hDNuL = (8)

Nucleate Boiling

Once the temperature difference is sufficient enough, nucleate boiling is observed, in which

small bubbles of gas form preferentially on the surface of the object. At sufficient temperature

differences, this phenomenon begins to outweigh transfer by free convection.

Perrys handbook3gives the following correlation for the nucleate boiling arising from empirical

observations:

+

+

=

102.117.07.0

1048.1ccc

cP

P

P

P

P

P

A

qPbh (9)

where b is the nucleate boiling coefficient, Pcis the critical pressure of the vapor, and P is the

absolute pressure of the system.

Film Boiling

As superheat temperature increases, heat transfer reaches a transition region in which boiling

occurs in an ill-defined manner. This transition region has not been the subject of much study,

and therefore no correlations exist to predict its behavior.

Past the transition region, film boiling occurs. Here, a thin film of gas forms around the object,

with various portions of the film being released with time exposing the surface of the object.

This unstable film acts as an insulating resistance to heat transfer, as the object is constantly

3Perrys

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shielded from the boiling liquid, and therefore reduces the heat flux along with the heat transfer

coefficient.

Similarly to free convection, analytical calculations for film boiling can be made using equations

following the form of equations (6), (7), and (8). Hsu and Westwater have developed a

correlation for film boiling of the form4:

( )6.0

3

1

3

2

Re0020.0 =

LvLv

v

kgh

(10)

where h is the film boiling coefficient, g is acceleration due to gravity, L and vare the densitiesof liquid and gas, respectively, and the other values take their usual meanings. Re for film

boiling can also be given by:

vD

m

=

4Re (11)

where m is the mass flow rate of gas boiled off, and other values take their usual meanings.

Experimental

Four cylinders with a diameter of 1 5/8 were utilized in this experiment. Two were composed

of stainless steel, and two of aluminum. Each cylinder was initially capped at the bottom, with a

T-Thermocouple in the center, sheathed by stainless steel, and insulated with ceramic. These

thermocouples were connected to an electrical relay by one of six leads. A LabView program

monitored the voltages of the thermocouples and outputted the temperature of each cylinder over

time.

4W3R, page 344

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Figure 2: Setup of thermocouple cylinder.

The cylinders were placed in a warm water bath and maintained at a constant temperature. A

two liter graduated cylinder was filled with liquid nitrogen. Once a cylinder in the bath reached

constant temperature, it was submerged in the liquid nitrogen. The level of the cylinder in the

liquid nitrogen was adjusted over time to ensure complete immersion. This procedure was

repeated with each cylinder over multiple trials. To attain consistency and reduce possible

errors, the same thermocouple lead was used for the final trial of each cylinder.

Results

Figure 3 (Appendix AI.1) below shows a typical plot of the cylinder temperature over time. As

shown by the graph, the temperature stays relatively constant for a short period of time, and then

begins to drop steadily in an exponential decay fashion. Then, at a time of approximately 300

seconds, the temperature shows a sharp discontinuity in slope, and then proceeds to decay until itreaches a stable temperature.

0 100 200 300 400200

100

0

time (s)

Temperature(C)

Figure 3: Heat transfer data for stainless steel cylinder. The first hash markrepresents the time at which the cylinder was submerged. The second hash mark

represents a transition in boiling..

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This data was then interpolated using MathCAD in order to obtain the derivative of temperature

versus time. Examining equation (3) we see that this derivative is proportional to the heat

transfer coefficient around the cylinder. With this in mind, the derivative of temperature versus

time was plotted against the temperature difference between the cylinder and liquid nitrogen.

Experimental observations showed that when a cylinder was placed in the liquid nitrogen, the

boiling went through several qualitative phases. Boiling first occurred in violent layers around

the cylinder, then reducing to large bubbles forming on the surface. With this in mind, it was

determined that heat transfer over experimentation occurred by film boiling for a majority of

time, and nucleate boiling for the remainder at the end of each trial.

First, heat transfer coefficients in the free convection regime were calculated, as free convection

occurs at all times. The temperature difference and Gr were calculated at various times, and h

was calculated using equation (6) over the course of the experiment. The results of the analysis

for free convection are given in Figure 4 (Appendix AI.2) below as a function of the wall

superheat temperature.

0 50 100 150 2000

50

100

Stainless Steel

Aluminum

Wall superheat (K)

h(W/m^2*

K)

Figure 4: Free convection heat transfer coefficients.The curves for steel

and aluminum are equivalent at all superheat temperatures.

Once these hs were calculated, they were substituted back into equation (1), resulting in Biot

numbers for steel and aluminum ranging from 0.1 to 0.3 and from 0.005 to 0.016, respectively.

It is important to note that the curves look identical for both metals as expected, since h is

independent of cylinder material for this analysis.

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The empirical correlation of equation (9) was then used to calculate h in the nucleate boiling

regime, assumed to begin after a time corresponding to the slope discontinuity discussed above.

The heat transferred to the cylinder was assumed to be completely due to evaporation of gas,

such that equation (1) could be used to calculate q. The heat transfer coefficient was calculated

in a similar fashion to that for free convection, with h calculated over a range of superheat

temperatures (see Appendix AI.2 for extensive results). The results for nucleate boiling analysis

are given in Table 1 below.

Film boiling was assumed to take place from the point when the cylinder was initially submerged

until the system reached a superheat of approximately 20 K, where the minimum heat flux in

Figure 1 occurs. The Hsu and Westwater correlation of equation (10) was used in a similar

fashion to the nucleate boiling analysis to find h (also see Appendix AI.2); once again assuming

equation (1) could be used to calculate q. The general results of analysis for h are given in Table

1 below.

Table 1: Results of analysis for boiling heat transfer

Boiling phase h (W/m^2*K) for Stainless Steel h (W/m^2*K) for Aluminum

Free convection 20-70 20-70Nucleate boiling 2500-10,000 10,000-30,000

Film boiling 100-250 400-700

Once h values were calculated for the various regimes of boiling, heat flux was calculated versus

wall superheat to obtain an experimental boiling curve (Appendix AI.2) like that of Figure 1.

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1 10 100 1 .1030

5 .104

1 .105

Wall superheat (K)

Heatflux(W/m

^2)

Figure 5: Experimental boiling curve for stainless steel. The first and second

portions of the curve represent nucleate and film boiling, respectively. The hash marksrepresent those of Figure 3.

Discussion

Comparing Figures 1 and 5, both curves are similar in both general shape and heat flux

magnitude, except for the transition region (not shown in Figure 5). The transition region is not

shown because transition boiling has not yet been empirically or analytically characterized. The

noise in the experimental curve stems from the fact that the temperature reading is taken atdiscrete intervals, and is therefore subject to random local disturbances in the thermocouple.

However, these disturbances were minimized by the ceramic insulation around the

thermocouple, and the general shape of the curve is retained.

The first hash in Figure 3 corresponds to the second hash line in Figure 5, and vice versa, as

cylinders began with high wall temperatures and cooled progressively. Noting the position of

these lines on the experimental boiling curve shows that the transition is not from film boiling to

nucleate boiling as originally predicted, but rather as a transition from stable film boiling to the

unstable transition region shown in Figure 1. The transition from unstable boiling to nucleate

most likely does not appear on figure 3 because the cooling is too rapid in this region to observe

this transition.

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Another area of note is the difference in experimentally determined ranges of h for the different

metals for nucleate and film boiling. Looking at Table 1, values of h for aluminum can be as

much as four times those of stainless steel at similar superheats. This may seem to point out

error in the analysis, as calculations for free convection resulted in identical values. However,

experimentation has determined that boiling transfer is inherently a function not only of fluid

properties, but a strong function of object properties such as material and history5. Also, h

values calculated for free convection resulted in Bi of as high as 0.3, outside of the normally

acceptable range for this analysis. Considering that these values of h were several orders of

magnitude smaller than those for nucleate boiling, though, they would have a negligible effect on

the appropriate region of the boiling curve.

During experimentation, end caps on the cylinders fell off after being subjected to several

immersions in liquid nitrogen. This may have affected results, as these end caps serve to reduce

end effects. The increase in heat transfer through the bottom of the cylinders would result in a

lower reading of temperature. Any effects this may have caused would be uniform throughout

experimentation, and simply shift the boiling curve left. The end effects produced, however,

would be minimal, since the aspect ratio for the cylinders of 3.9 is sufficient to neglect end

effects. Thermocouple insulation would also serve to reduce end effects.

Conclusions

Heat transfer coefficients in various regimes were determined with some level of confidence, as

their behavior mirrored documented characterizations well6. Considering the large size of heat

transfer coefficients and heat fluxes experimentally obtained in cryogenic boiling, the basis for

inherent advantages in boiling heat transfer as opposed to convective transfer can be reaffirmed.

The relative magnitudes of h for various boiling regimes suggest that nucleate boiling obtains

higher heat flux than other boiling types, as theorized previously.

5Hands, page 1596Besterfield, page 31

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It is apparent from the results given above that boiling curves for cryogenic fluids such as liquid

nitrogen can be experimentally reproduced at a cursory level. Qualitatively, the results of this

experiment confirm the theoretical basis for boiling heat transfer in regards to the presence of

various stages of boiling. The degree with which the quantitative results of analysis emulate the

qualitative observations made in theory regarding boiling heat transfer suggests that the models

used for analysis are well-suited to cryogenic heat transfer.

Recommendations for Future Research

Specific to this particular experiment, some improvements could be made to the design in order

to make results more useful and robust. If an enclosed chamber is built with this experiment in

mind, many aspects of the experiment such as flow rate measurements, cylinder positioning, and

fluid conditions could be better controlled. For experimental accuracy, end effects could be

reduced if end caps could be assured to remain attached over the course of experimentation.

Also, if a higher resolution could be obtained for the temperature measurement, experimentation

may be able to show the transition from unstable boiling to nucleate not currently observed.

As seen in this experiment, there is a definite need for characterization of the transition boiling

region, as its behavior impacts heat transfer greatly at moderate superheat temperatures.

Research leading to general correlations for boiling heat transfer would prove most useful in an

industrial setting, and serve to better quantify cryogenic boiling heat transfer.

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References

Besterfield, Crane, Kaw, University of South Florida,Parametric Finite Element Modeling and

Full-Scale Testing of Trunnion-Hub-Girder Assemblies for Bascule Bridges, Journal

of American Society of Mechanical Engineers, 2001.

CRC Handbook of Chemistry and Physics, 82nd

ed. New York: McGraw-Hill Book Company,

2001.

Hands, B.A. Cryogenic Engineering, London: Academic Press Inc., 1986

Holman, J.P. Heat Transfer, 6thed. New York: McGraw-Hill Book Company, 1986.

Perry, Green, Maloney, Perrys Chemical Engineers Handbook, 7th

ed. New York: McGraw-

Hill Book Company, 1997.

Welty, Wicks, Wilson, Rorer, Fundamentals of Momentum, Heat, and Mass Transfer,

4th

ed. New York: John Wiley and Sons, Inc., 2001.

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Abbreviations and NomenclatureSYMBOL/VARIABLE DEFINITION UNITS

Lowercase

b Constant in Nucleate-boiling coefficientequation

dimensionless

g Gravitational acceleration constant m

s2

h Convective heat transfer coefficient W

m2*K

k Thermal conductivity of cylinder Wm

2*K

kL Thermal conductivity of liqud Wm

2*K

m Mass kg

q Heat flux Js

t Time s

Uppercase

A Area of heat transfer m2

Bi Biot number dimensionlessC Material constant m

-3

Cp Specific heat capacity J .kg*K

Db Bubble diameter m

D Outer diameter of cylinder m

Gb Mass velocity of vapor kgm

3*s

Gr Grashoff number dimensionless

L Length m

Nu Nusselt Number dimensionless

Nub Bubble Nusselt number dimensionless

NuL Liquid Nusselt number dimensionlessP Pressure of the system Pa

Pc Critical pressure Pa

PrL Liquid Prandtl number dimensionless

RaL Liquid Rayleigh number dimensionless

Re Reynolds number dimensionless

Reb Bubble Reynolds number dimensionless

T Temperature of cylinder K

Tsat Saturated vapor temperature K

V Volume of cylinder m3

Greek

Temperature difference Kv Latent heat of vaporization J

g*molL Viscosity of liquid kgm

2*s

v Viscosity of vapor kgm

2*s

Pi dimensionlessL Density of liquid g

cm3

v Density of vapor g*cm-3

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