`

Experimental study of natural frost formation on a

horizontal cylinder

M. Yaghoubi* H. Khoshnazar

Engineering School, Shiraz University

Shiraz, Iran

Abstract

In this study frost formation on a horizontal cylinder at free convection condition has been

experimentally investigated. The cold surface temperature of cylinder varied from -4 to -8 Co , the

humidity ratio of ambient is changed from 6.4 to 8.9 DAkgg and ambient temperature controlled

between 15 and 22 Co. The thickness of frost over cylinder and heat flux from the cold surface is

measured for average of eight hours. Smoke test is carried to illustrate cold plume how around cylinder

with the present of frost on the cylinder. Results showed that frost on the top surface of the horizontal

cylinder layer is thicker than the bottom layer. Heat flux at the beginning of frost formation is high and

then reduced to a constant value. Measured quantities were compared with results given by a simple

model based on similarity between heat and mass transfer and a correlation is developed to predict frost

thickness with respect to time for all the ranges of measurement.

Keywords: Frost deposition, Free convection, Horizontal cylinder.

10th AIAA/ASME Joint Thermophysics and Heat Transfer Conference28 June - 1 July 2010, Chicago, Illinois

AIAA 2010-4659

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Nomenclature

Specific heat capacity( 11 KkgJ ) Cp

Cylinder diameter ( m) D

Mass diffusivity of water vapor in air ( 12Sm ) vD

Fourier number ( 2tDDv ) Fo

Heat transfer coefficient( 12 KmW ) h

Mass transfer coefficient( 2mskg ) mh

Conductivity( 11 msW ) k

Lewis number Le

Mass flux ( 21 mskg ) .

m

Nusselt number Nu

Pressure( pa ) P

Heat flux(2mW ) 'q

Total energy transfered(W ) Q

Cylinder radius, ( m ) r

Rayleigh number Ra

Relative humidity( % ) RH

Frost thickness ( m ) fS

Dimensionless frost thickness ( DS f ) *

fS

Time ( s ) t

Temperature ( K ) T

Dimensionless temperature *T

Absolute humidity(1

DAkgkg ) w

Greeks

Density( 3mkg )

Estephan- Boltzmann( 428107.5 KmW )

Subscript

Air a

Average av

Conduction cond

Convection conv

Diffuse diff

Effective ef

frost surface fs

Latent lat

Water triple point tp

Wall w

1. Introduction

Frost begins to form when humid air comes into contact with a cold surface that is

kept below water freezing temperature. This process affects heat transfer rate

particularly in air-conditioners, refrigerators and heat pumps. In most cases, frost

formation is undesirable because it contributes to the heat transfer resistance and

pressure drop. Analyzing frost formation is not easy because it is a complicated

transient phenomenon in which a variety of heat and mass transfer mechanism occur

simultaneously. Recent articles [Ostine and Andersoon, 1991; lee and Ro, 2002; lee

and Ro, 2001; Cheng and Wu, 2003; Na and Webb, 2004; Salmanopur et al. 2008]

shows that frost formation during forced convection of humid air has been studied

extensively, while on the other hand, only a limited number of investigations deal

with heat-mass transfer during natural convection on a surface at subfreezing

temperatures. Barron and Han (1965) studied heat and mass transfer to a cryosurface

in free convection. Kennedy and Goodman (1974), studied frost formation on a

vertical surface in free convection condition. They found that humidity effect on frost

thickness growth is very small. Cremers and Mehra(1982) studied frost formation on

vertical cylinders in free convection and gave correlation for frost thickness. Transient

natural convection heat and mass transfer during refrigeration of air by horizontal

tubes is studied by Riedy (1983). They showed that the heat transfer coefficient

increases at the begging and reduces to a constant value. Chen and Oosthuizen (1994)

studied frost formation on a horizontal tube and shown that the effect of cylinder

surface temperature is more than ambient temperature and humidity on the frost

thickness. Fossa and Tanda (2002) studied free convection frost formation on a

vertical plate. Wu et.al(2007) studied early stage of frost formation on a horizontal

plate and showed that the surface temperature is the primary factor affecting the frost

crystal shape and relative humidity has less effect on the frost crystal shape. To the

authors' knowledge, there are few experimental study deals with natural convection

heat and mass transfer around horizontal cylinders. The present paper reports the

results of an experimental study of frost formation on a horizontal cylinder in natural

convection. The aim of this study is to find experimentally and theoretically the

effects of various environmental parameters on natural frost formation growth rate

and heat transfer rate during transient processing of frost formation on a horizontal

cylinder.

2. The apparatus and instrumentation

Schematic view of the experimental apparatus is shown in Fig. 1. The test section and

the measuring instruments were placed in a test room which could be regulated and

controlled in the range of desired values of air condition. The test room ambient

temperature is controlled by refrigeration cycle which is design and built in

laboratory. The secondary refrigerant (60/40 ethylene-glycol/water solution) is used

for control and keep the test section surface temperature at constant value. A cross

section of the test section is depicted in detail in Fig. 2. The test section lengths and

diameter is 300 mm and 80 mm. The outer and inner tube was constructed of

aluminum and between these two layers filled with an insulating material to provide a

measurable heat flux. The outer and inner diameter of cylinder was 80 and 17 mm.

The tube was cooled by internal circulation of the secondary refrigeration. Small holes

of 1.2 mm in diameter were drilled at four circumferential positions at 0, 90, 180,

and 270o

in the inner and outer tube to measure radial temperature distribution in the

cylinder. Two locations in longitudinal direction is chosen to calculate average heat

flux and minimized the error. We used total of 16 thermocouples to measure

temperature distribution in the hollow cylinder. Copper- constant thermocouples were

inserted in each hole. The thermocouples first calibrated at the required temperature

range with an uncertainty of Co1.0 . The frost thickness is measured with two

digital cameras (Cannon, power shot S3I), with estimated uncertainty 0.05 mm. Image

data from top and bottom surface of cylinder were acquired. Frost thickness is

measured every 30 min automatically and the other data were sampled every 2 min.

All data were saved in a computer for later analysis.

3. Experimental procedure and measurements

The experiments were conducted with variable ambient parameters and cold surface

temperature. The three dominant parameters are considered herein: The ambient

temperature varied in the range of 15-22 Co , the humidity ratio of air varied from 6.4

to 8.4 DAkgg , and the temperature of cold cylinder surface is changed from -8 to

-4 Co . Before cooling the test cylinder, the surface had been covered by a thin

polyethylene film so that water vapor could not condense on the test cylinder surface.

After test surface reached to the prescribed temperature, the test is started by taking

off the film. The duration of each test was 8 hr. The heat flux and frost was measured

at regular time intervals (typically 30 min) after starting the test.

The cylinder is used as a heat flux meter. Heat flux can be calculated from the radial

temperature difference between inner and outer tube with known thermal conductivity

of the insulator (0.1711KmW ). Because of high thermal conductivity of aluminum

(170 11KmW ), its thermal resistance is ignored. The maximum temperature

difference in longitude direction was less than 0.5 Co and hence its effect is

negligible. The average heat flux is measured with the outer surface of the cylinder at

the center of the longitudinal location using thermocouples. Based on the well –

known conduction equation, heat flux is given by the following equation:

(1)

Cold smoke is used for flow visualization because the frost surface temperature is low

and the smoke must not have any effects on frost surface. A thin sheet smoke which

DrrLn

TTkq

inout

inout

)(

)(2'

is produced from chemical materials that comprise of colidric acid ( ClH ) and

ammoniac ( 3NH ) is used for smoke test. Fig. 3 shows typical smoke test smoke test

that is conducted at Raleigh number 6102 ( CT oa 20 , CT o

s 6 ). Flow

visualization shows separation did not happened in the bottom of cylinder and flow

around the cylinder is laminar. The figure also shows that the cold plum velocity is so

small that frost roughness has not caused any turbulence or mixing of the boundary

layer.

6. Theoretical modeling

The frost formation process involves simultaneous heat and mass transfer during

varying thermo-physical properties. To simplify the analysis, following assumptions

are made.

1- Heat and mass transfer is one dimensional (only in radial direction).

2- Thermal system is assumed to be quasi-steady state.

3- Frost deposition is homogeneous over the cylinder surface.

4- The frost layer is to be characterized by average properties.

5- The air near the frost surface is saturated.

Heat that transfer from frost layer comprises, convection, radiation and phase change

that show with following equation.

)()(44

fsavsfsa TTfmLTThq (2)

Since the cylinder surface area ratio to the test room area is very small, radiation

factor f is assumed equal to the frost emmissivity, f .

Mass flux of water vapor transferring to the frost surface that is related to the heat

transfer coefficient is

)(.

fsam wwhm (3)

Mass transfer coefficient mh is related to heat transfer coefficient by the Lewis

number [Traybal, 1990].

pm CLe

hh

. (4)

Where Le is the Lewis number that is assumed to one for the system contains air and

water vapor, Cp is calculated at the average temperature, 2)( afsave TTT .

Convection coefficient kDNuh is derived from experimental results obtained by

Martyneko and Khramtsov( 2005) for heat transfer around horizontal cylinder in free

convection .

,125.0

,48.0

,85.0

,02.1

,675.0

333.0

25.0

188.0

148.0

058.0

RaNu

RaNu

RaNu

RaNu

RaNu

107

74

42

22

210

1010

1010

1010

1010

1010

Ra

Ra

Ra

Ra

Ra

(5)

The fluid properties such as density, viscosity and thermal volumetric expansion

coefficient in the Raleigh number are calculated at average temperature 2)( afsave TTT .

The heat conducted from the frost surface in the frost layer is,

wf

wfs

rrLn

TTLKq

2

(6)

Combination of Eqs. (2, 3 and 6) results,

)()()()(

)(2 44fsavsfsamfsa

wf

fswef TTfLwwhTThrrLn

TTLk

(7)

Where the latent heat of sublimation is (Fossa and Tanda, 2002)

fsvs TL 1951088.2 6 (8)

Absolute humidity calculated by,

)(

)(62198.0

s

s

PP

Pw (9)

The saturation pressure over ice for temperature range of KTK 15.27315.173 is (Mago,

and Sherif, 2005],

)()( 64

53

42

3210 TLndTdTdTdTdd

T

dPLn s (10)

Where

16

125

84

63

22

11

40

1041635019.0

109484024.0

1020747825.0

1062215701.0

109677843.0

10152305.5

1056745359.0

d

d

d

d

d

d

d

The saturation pressure over liquid water for temperature range of KTK 15.47315.273

is (Mago and Sherif, 2005)

)()( 53

42

3210 TLncTcTcTcc

T

cPLn s (11)

Where

16

46

14

13

11

40

1065459673.0

1014452093.0

1041764768.0

1048640239.0

105516256.0

1058002206.0

c

c

c

c

c

c

The effective thermal conductivity of frost, efk , is derived from experiential results is

(Fossa and Tanda, 2002),

963.0001202.0 fefk (12)

The above equation is valid for the temperature down to -22 Co and density up to 500

3mKg . It is derived by the following relation (Fossa and Tanda, 2002)

)]15.273(227.0exp[650 fsf T (13)

The deposition mass of frost per unit area of cylinder surface in a given time interval

is,

tmm.

(14)

With the above equation the frost thickness growth during t can be calculated,

ff

mS (15)

and the frost thickness at the new time can be calculated by,

fff SSS (16)

The calculation procedure can proceed as follows:

1- fsT is taken equal to wT at the initial time t=0;

2- A given time interval t is chosen;

3- Eqs. (3)-(5), (8) and (12)–(14) are used to determine .

m , mh , h , vsL efk , f and m .

4- Heat flux is evaluated buy Eq. (2).

5- The thickness fS of frost is evaluated by Eq. (15).

6- Frost temperature, fsT , is updated iteratively by solving Eq. (7).

7- The values of .

m , mh , h , vsL , efk , f and m are updated.

8- Heat flux is evaluated by Eq. (2).

9- Thickness fS at the updated time will be determined by Eq. (16).

7. Result and discussion

Experimental data for each run were stored in the computer as a function of time,

contains ambient temperature, humidity and surface temperature. Table 1 summarizes

the range of experimental conditions. For each experiment variation of frost layer

thickness with respect to time is plotted in Fig. 4. Frost thickness increases with

respect to time. This increase differs around cylinder primates. Frost layer on the top

are thicker than the bottom. This can be attributed to higher heat and mass transfer

coefficient on the top of cylinder ( o180 ) compare to the bottom of cylinder

( o0 ). At o180 , the thickness of boundary layer is very thin in comparison to

stagnation point o0 , which is high. At the beginning of the each experiment frost

thickness grow is rapid and then it reduces and became linear. Tanada an Fossa(2002)

showed that the surface temperature increases rapidly and then converge to a constant

value. Due to high temperature difference at the begging of each experiment, driving

force for mass transfer is high and then reduces. For this stage mass transfers

contribution is mostly on frost growth and less on diffusion insides the frost.

Figure 5 shows the effect of the cylinder surface temperature on the frost growth

layer. In this case all parameters except the cylinder surface temperature were

remained constant. A lower cylinder surface temperature induced a thicker frost layer.

Average frost thickness at top and bottom of cylinder surface are compared with

modeling results in Fig. 5. Results from the theoretical model tend to underestimate

frost thickness, especially at the higher cold plate temperature ( Co4 ). In Fig. 5

modeling shows that at the beginning frost thickness growth increases rapidly and

then became linear. The effect of air humidity on the frost growth layer is shown in

Fig.6. With increasing air humidity, the frost layer became thicker. As the humidity

ratio of the ambient air increases, the concentration gradient over the cylinder surface

and consequently the concentration driving force, which arises from the concentration

gradient, transports a greater amount of water vapor from the ambient air to the frost

layer. The effect of ambient air temperature on the frost growth layer at constant air

humidity ratio is presented in Fig. 7. With increasing ambient air temperature the frost

layer thickness become thinner. When the air temperature raises, the air – frost

interface temperature increases and it causes the air humidity ratio in the vicinity of

the frost surface to increase. It decreases the concentration driving force, which is the

difference between the humidity ratio of the air in the free stream and that of the air –

frost interface. This reduces frost deposition rate and consequently the frost layer

thickness as discussed (Lee and Ro, 2002). Lee and Ro(2001) showed that with

increasing ambient air temperature the mass transfer and the frost density increases.

The reason of increasing the frost density is melting of fragile frost surface and

diffuses of water to frost layer. However the mass transfer is increased but the amount

of increasing is low and its effect compared with frost density is minor and frost layer

thickness decrease.

For refrigeration and cooling application heat transfer from ambient air to tubes

containing cold fluid is important. The total heat flux during the frost formation is

combination of convection, radiation and phase change. Figure 8 shows variation of

heat flux with time for various cylinder surface temperatures. The heat flux increases

at the begging of the frost formation and then reduces to a constant value. The heat

transfer coefficient is; strongly dependent on the roughness of the frost surface and

flow conditions. The Stanton number for a rough surface is approximately 60% higher

than that for a smooth surface (Yun et. al, 2002). Hayashi divided the frost formation

process into three periods:” crystal growth period,” “frost layer growth period,” and

“frost layer full growth period” (Hayash et. al, 1977). The frost roughness had the

peak value in crystal growth period (Yun et. al, 2002). At this stage the roughness is

like a fin that increases the heat transfer area and its coefficient. Riedy(1983) reported

that heat transfer coefficient increased at about 10 to 15% at the begging of

experiment and then decreases. Such behavior is also observable in the present

experiments, Fig. 8. Theoretical model predicts heat flux well but it can not show the

raised of heat flux at the beginning of the experiment. The modeling is based on the

smooth cylinder surface and it can not induce frost surface roughness in its

computation. Fig. 8 also shows the effect of cooling surface temperature on heat flux.

Total heat flux was found to be higher at the lower cold surface. The effect of ambient

temperature on the heat flux is depicted Fig. 9. It shows that, with increase of ambient

temperature, heat flux increased. The effect of air humidity is illustrated in Fig. 10.

The effect of air humidity on the frost growth is less rather than the ambient

temperature and cooling surface effect. Its shows that, phase change has minor effect

on total heat flux rather than cooling cylinder surface temperature and ambient air

temperature. This is due to the fact that air humidity only affects the phase change

3464.2*9724.1706681.4*)1(104505.6 TwFoS f

heat transfer but cooling surface temperature affects convection, radiation and phase

change heat transfer.

Many correlation for frost layer thickness are reported by previous researchers

in force convection (Sengoupta et. al, 1989; Schneider, 1978; Yang and Lee, 2004).

In free convection Cramers and Mehra(1982) derived a correlation for frost thickness

on a vertical cylinder, but their correlation was obtained as a function of limited

parameters. In this study a dimensionless thickness is expressed as a function of

dimensionless frosting parameters by using dimensionless analysis. Variables for

dimensionless analysis are chosen as follow: ambient air temperature, cylinder surface

temperature, air absolute humidity, average frost thickness, triple point temperature of

water, mass diffusivity of water vapor in air, time and cylinder diameter.

For dimensional analysis parameters D , vD and sa TT are chosen as characteristic

parameters. The correlation for dimensionless thickness could be:

bcbf TwaFoS **

)1( (17)

Where dimensionless temperature and dimensionless time are:

wa

tpa

TT

TTT *

2D

tDFo v

(18)

By least square method using all the experimental data a dimensionless correlation for

frost thickness is derived as follows:

(19)

Figure11a and 11 b illustrate comparison between this correlation and experiment data

from Chen and Oosthuizen (1994). For the two range of dimensionless times the

present correlation for frost layer thickness agrees well with experiment data of Chen

and Oosthuizen(1994) for the specified condition.

.

9. Uncertainty analysis

Analysis of uncertainty is required in order to evaluate the accuracy of measurement

and proposed correlation. Lists the experimental values of different parameters and

associated uncertainties for proposed correlation originate in Table 2. The maximum

error uncertainties of measurements are determined according to tTble. 2 is less than

9%.

10. Conclusion

Based on the experiments carried out and laminar flow observed by smoke test the

following conclusions can be made.

1-Higher air humidity ratio and lower cooling surface of cylinder temperature resulted

in thicker frost layer, and greater quantity of heat flux.

2-As the ambient air temperature increased, the frost thickness decreases slightly but

the heat flux increases which means higher frost densities.

3-The frost layer on top of the cylinder is thicker than the thickness at bottom of the

cylinder.

4- The analytical heat and mass transfer model can predict well frost thickness for low

temperature, but the error at the beginning and for high temperature cylinder is large.

5- For practical applications, a correlation for frost growth over a horizontal cylinder

based on experiments is developed which shows good agreement with other

experimental studies.

Appendix A

The total uncertainty U comprises uncertainties of many components, influence on the

experiment [Teoch et al., 2002]. For a measurement M, whose results depend on

uncorrelated input estimates nxxx ...,, 21 , the standard uncertainty of the measurement

is obtained by appropriately combining the standard uncertainties of these input

estimates. The combined standard uncertainty of the estimate M denoted by U is

calculated from the following equations [Wang te al., 2004; Wang et al. 2007]

)....,,( 21 nxxxfM (20)

)()( 2

2

1

2

i

n

i i

xUx

fMU

(21)

Where f is the function of M in terms of input, estimates nxxx ...,, 21 , and each )( ixU is

a standard uncertainty of inputs.

By applying Eq. (19) to Eq. (21) average dimensionless frost thickness uncertainty is:

21

2*

2*

2*

2*

2*

*

tt

S

DD

Sw

w

ST

T

ST

T

S

S

f

ffw

w

fa

a

f

f

(22)

References

[1] Barron, R.F., Han, L.S., 1965. Heat and mass transfer to a cryosurface in free

convection. Journal of Heat Transfer. 17, 499-506

[2] Chen, J., Oosthuizen. Frost formation on a horizontal cylinder with free

convection, M.S thesis, Queen’s university, Kingston, Canada,1994.

[3] Cheng, C.H., Wu, K.H., 2003. Observations of early-stage frost formation on a

cold plate in atmospheric air flow. Journal of Heat Transfer. 125, 95-101.

[4] Cremers, C.J., Mehr, V.K., 1982. Frost formation on vertical cylinders in free

convection. Journal of Heat Transfer. 104, 3-7.

[5] Fossa, M., Tanda, G., 2002. Study of frost formation on a vertical plate.

Experimental Thermal and Fluid Science. 26, 661-668.

[6] Hayashi, Y., Aoki, A., Adachi, S., Hori, K., 1977. Study of frost properties

correlating with frost formation types. Int. J. Heat Transfer. 99, 239-245.

[7] Kennedy, L.A., Goodman, J., 1974. Free convection heat and mass transfer under

conditions of frost deposition. Int. J. Heat and Mass Transfer. 17, 477-484.

[8] lee, Y.B., Ro, S.T., 2001. An experimental study of Frost formation on a

horizontal cylinder under cross flow. International Journal of Refrigeration. 24, 468 –

474.

[9] lee, Y.B., Ro, S.T., 2002. Frost formation on a vertical plate in simultaneously

developing flow. Experimental Thermal and Fluid Science. 26, 939 – 945.

[10] Mago, J., Sherif, S.A., 2005. Heat and mass transfer on a cylinder surface in

cross flow under supersaturated frosting condition. International Journal of

Refrigeration. 28, 538-899.

[12] Martyneko, O.G., Khramtsov, P.P., Free-convective heat transfer. Springer,

2005.

[13] Na, B., Webb, R.I., 2004. Mass transfer on and within a frost layer. International

Journal of Heat and Mass Transfer. 47, 899-911.

[14] Ostine, R., Andersoon, S., 1991. Frost growth parameters in a forced air stream.

International Journal of Heat and Mass Transfer. 34, 1009-1017.

[15] Riedy, M.K., 1983. Transient natural convection heat and mass transfer during

refrigeration of air by horizontal tubes. Int. J. Heat and Mass Transfer. 17, 863-867.

[16] Salamanpour, M., Nourani Zonouz O., and Yaghoubi, M., 2008, Analysis of

frost formation through a two- dimensional duct with turbulent flow. Heat Transfer

Research. 39, No. 4, pp.35-58,

[17] Sengoupta, S., Sharif, A.A., Wong, E.Y., 1989. Frost deposition on a cylinder

in cross flow. Int. J. energy Res. 22, 615-622

[18] Schneider, h.W., 1978. Equation of the growth rate of frost forming on cooled

surface. International Journal of Heat and Mass Transfer. 21, 1019-1024.

[19] Teoch, P.L., Shirinzadeh, B., Foong, C.W., Alici, G., 2002. The measurement

uncertainties inthe laser Interferometry-based sensing and tracking technique.

Measurement. 32, 135–150.

[20] R. Traybal, R.E., 1990. mass transfer operations. third edition. McGraw.

[21] Yang, D.R., Lee, K.S., 2004. Dimensionless correlations of frost properties on a

cold plate. International Journal of Refrigeration. 27, 89-96

[22] Yun, R., Kim, Y., Min, M.K., 2002. Modeling of frost growth and frost

properties with airflow over flat plate. International Journal of Refrigeration. 25, 362-

371.

[23] Wang, C.C., Huang, R.T., Sheu, W.j., Chang, Y.J., 2004. Some observations of

the frost formation in free convection: with and without the presence of electric field,

International Journal of Heat and Mass Transfer. 47, 3491-3505.

[24] Wang, X., Bibeau, E., Naterer, G.F., 2007. Experimental correlation of force

convection heat transfer from a NACA air foil, Experimental Thermal and Fluid

Science. 31, 1073-1084.

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formation on a cold surface. Experimental Thermal and Fluid Science. 31, 1043-1048.

Fig. 1. Schematic diagram of the test facilities

2-a- Longitudinal view of test tube

2-b- Cross section of tube with location of thermocouples

Fig. 2.Test cylinder

Fig. 3. Smoke test with cold plume flows

0

0.5

1

1.5

2

2.5

0 100 200 300 400 500 600Time(min)

Fro

st th

ickn

ess(

mm

)

Bottom

Top

Fig. 4. Variation of frost thickness on top and bottom of cylinder with

time( CT oa 22 , DAkggw 4.6 CT o

s 6 )

Bottom

fsT

aTTop

0

1

2

3

4

5

6

0 100 200 300 400 500 600Time(min)

Fro

st th

ickn

ess(

mm

)

Fig. 5. Variation of average frost growth layer for different cylinder surface , ,

DAkggw 9.8 ) CT oa 18 temperature (

CT os 8

CT os 6

CT os 4

: Modeling

Symbols: Experiment

0

1

2

3

4

5

6

0 100 200 300 400 500 600Time (min)

Fro

st la

yer

thic

knes

s (m

m)

Top layer thichness

Fig. 6. Effect of ambient air humidity on the frost layer growth ( CT oa 18 ,

CT os 8 , DAkggw 1.8 )

DAkggw 9.8DAkggw 1.8DAkggw 4.6

0

1

2

3

4

5

0 100 200 300 400 500 600Time(min)

Fro

st th

ickn

ess(

mm

)

Fig. 7. Effect of the ambient air temperature on the frost growth layer

( DAkggw 1.8 , CT os 8 ) .

CT oa 22

CT oa 18

100

200

300

400

500

0 100 200 300 400 500 600Time(min)

Hea

t flu

x(W

/m^2

)

Fig. 8. Effect of cooling surface temperature on the heat flux from air to cylinder

surface.

DAkggw 1.8

CT oa 18

CT os 8

CT os 6

CT os 4

: Modeling

Symbols: Experiment

0

100

200

300

400

0 100 200 300 400 500 600Time(min)

Hea

t flu

x(w

/m^2

)

Fig. 9. Effect of ambient air temperature on the heat flux from ambient air to

cylinder surface.

CT oa 18

CT oa 22

DAkggw 1.8

CT os 4

100

200

300

400

0 100 200 300 400 500 600Time (min)

Hea

t flu

x(W

/m^2

)

Fig. 10. Effect of air humidity on the heat flux from ambient air to cylinder surface.

DAkggw 2.7

DAkggw 9.8

DAkggw 1.8CT o

a 18

CT os 8

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5

11-a

0

0.02

0.04

0.06

0.08

0 5 10 15 20 25

11- b

Fig. 11. Comparison of dimensionless frost growth prediction with other

measurement

CT oa 28.25

CT os 75.11

%18.48RHmmDcylinder 224

Fo

*

fS

Relation (19)

Chen and Oosthuizen (1994)

CT oa 9.28

CT os 18.6

%9.47RHmmDcylinder 158

Fo

*

fS

Chen and Oosthuizen (1994)

Relation (19)

Fig. 1. Schematic diagram of the test facilities

Fig. 2.Test cylinder

2-a- Longitudinal view of test tube

2-b- Cross section of tube with location of thermocouples

Fig. 3. Smoke test with cold plume flows

Fig. 4. Variation of frost thickness on top and bottom of cylinder with

time( CT oa 22 , DAkggw 4.6 CT o

s 6 )

Fig. 5. Variation of average frost growth layer for different cylinder surface

temperature

CT oa 18 , DAkggw 9.8

Fig. 6. Effect of ambient air humidity on the frost layer growth ( CT oa 18 ,

CT os 8 , DAkggw 1.8 )

Fig. 7. Effect of the ambient air temperature on the frost growth layer

( DAkggw 1.8 , CT os 8 )

Fig. 8. Effect of cooling surface temperature on the heat flux from air to cylinder

surface.

Fig. 9. Effect of ambient air temperature on the heat flux from ambient air to

cylinder surface

Fig. 10. Effect of air humidity on the heat flux from ambient air to cylinder surface

Table 1.Experimental condition carried out

Table. 2. Values for the parameters of Eq. (19)

Table 1.Experimental condition carried out

Parameter Range

Air humidity ratio( DAkgg ) 6.4 - 8.9

Surface temperature of cylinder ( Co ) -8.0 - -4.0

Ambient air temperature ( Co ) 18.0 - 22.0

Table. 2. Values for the parameters of Eq. (19)

*

*

f

i

i

f

S

x

x

S

ix ix Parameter

1.2

0.25

0.5

0.5

291.15

295.15

Ambient temperature

( Co)

0.417

0.2

0.5

0.5

-4

8-

Cylinder surface

temperature Co

0.00033

0.02

80

Cylinder diameter

mm

2.3

0.78

10

10

28800

28800

Time (S)

1.6

3.3

1

1

RH=69

RH=39

Humidity (%)