Methodology for predicting frost growth trends on a subcooled cylindrical surface is developed and implemented for multitube array configuration. Extension of conventional analysis and a novel technique for understanding frost formation phenomenon on the cylindrical surfaces is proposed; later one takes into account the nonsteady temperature field, which affects the density and thermal conductivity at a local level in the growing frost mass, for more accurate prediction of thermal resistance. The influence of migration of liquid water due to tortuosity effect is also considered. The results due to new model are found to be in good agreement with the data in the open literature. Data for frost thickness ratio (FTR) versus time for a section of array with four (tube) rows in the airstream are presented and thoroughly analyzed. The trends of FTR noted are complex and considerably dependent on the tube location, temperature of subcooled surface (Ts), airflow velocity (Ua), and the relative humidity (RHa) values. Approximate ranges for important parameters are 30Ts5.0°C, 1.0Ua5.0m/s, and 0.20RHa0.80. Presented analysis and the results are valuable in order to predict probable locations and precursors to partial or complete choking of airflow passages due to frost deposition in the evaporator coils.

1.
Dietenberger
,
M. A.
, 1983, “
Generalized Correlation of the Water Frost Thermal Conductivity
,”
Int. J. Heat Mass Transfer
0017-9310,
26
, pp.
607
619
.
2.
Tao
,
Y. X.
,
Besant
,
R. W.
, and
Rezkallah
,
K. S.
, 1993, “
A Mathematical Model for Predicting the Densification and Growth of Frost on a Flat Plate
,”
Int. J. Heat Mass Transfer
0017-9310,
36
, pp.
353
363
.
3.
Na
,
B.
, and
Webb
,
R. L.
, 2003, “
A Fundamental Understanding of Factors Affecting Frost Nucleation
,”
Int. J. Heat Mass Transfer
0017-9310,
46
, pp.
3797
3808
.
4.
Hao
,
Y. L.
,
Iragorry
,
J.
, and
Tao
,
Y. X.
, 2005, “
Frost-Air Interface Characterization Under Natural Convection
,”
ASME J. Heat Transfer
0022-1481,
127
, pp.
1174
1180
.
5.
Östin
,
R.
, and
Andersson
,
S.
, 1991, “
Frost Growth Parameters in a Forced Air Stream
,”
Int. J. Heat Mass Transfer
0017-9310,
34
, pp.
1009
1017
.
6.
Yun
,
R.
,
Kim
,
Y.
, and
Min
,
M. K.
, 2002, “
Modelling of Frost Growth and Frost Properties With Airflow Over a Flat Plate
,”
Int. J. Refrig.
0140-7007,
25
, pp.
362
371
.
7.
Cheng
,
C. H.
, and
Wu
,
K. H.
, 2003, “
Observation of Early-Stage Frost Formation on a Cold Plate in Atmospheric Air Flow
,”
ASME J. Heat Transfer
0022-1481,
125
, pp.
95
102
.
8.
Buyruk
,
E.
, 1999, “
Heat Transfer and Flow Structures Around Circular Cylinders in Cross-Flow
,”
Turk. J. Eng. Environ. Sci.
1300-0160,
23
, pp.
299
315
.
9.
Abu-Hijleh
,
Bassam A/K
, 2001, “
Laminar Forced Convection Heat Transfer From a Cylinder Covered With an Orthotropic Porous Layer in Cross-Flow
,”
Int. J. Numer. Methods Heat Fluid Flow
0961-5539,
11
(
2
), pp.
106
120
.
10.
Verma
,
P.
,
Bullard
,
C. W.
, and
Hrnjak
,
P. S.
, 2002, “
Design Strategies for Reducing Performance Degradation Due to Frosting of Display Case Heat Exchangers
,” IIF-IIR–Commission D1/B1–Urbana, IL.
11.
Mago
,
P. J.
, and
Sherif
,
S. A.
, 2002, “
Modeling of the Cooling Process Path of a Dehumidifying Coil Under Frosting Conditions
,”
ASME J. Heat Transfer
0022-1481,
124
, pp.
1182
1191
.
12.
Mago
,
P. J.
, and
Sherif
,
S. A.
, 2003, “
Heat and Mass Transfer on a Cylinder Surface in Cross Flow Under Supersaturated Frosting Conditions
,”
Int. J. Refrig.
0140-7007,
26
, pp.
889
899
.
13.
Sommers
,
A. D.
, and
Jacobi
,
A. M.
, 2006, “
An Exact Solution to Steady Heat Conduction in a Two-Dimensional Annulus on a One-Dimensional Fin: Application to Frosted Heat Exchangers With Round Tubes
,”
ASME J. Heat Transfer
0022-1481,
128
, pp.
397
404
.
14.
Schneider
,
H. W.
, 1978, “
Equation of the Growth Rate of Frost Forming on Cooled Surfaces
,”
Int. J. Heat Mass Transfer
0017-9310,
21
, pp.
1019
1024
.
15.
Storey
,
B. D.
, and
Jacobi
,
A. M.
, 1999, “
The Effect of Streamwise Vortices on the Frost Growth Rate in Developing Laminar Channel Flows
,”
Int. J. Heat Mass Transfer
,
42
, pp.
3787
3802
. 0017-9310
16.
Lee
,
H.
,
Shin
,
J.
,
Ha
,
S.
,
Choi
,
B.
, and
Lee
,
J.
, 2004, “
Frost Formation on a Plate With Different Surface Hydrophilicity
,”
Int. J. Heat Mass Transfer
,
47
, pp.
4881
4893
. 0017-9310
17.
Na
,
B.
, and
Webb
,
R. L.
, 2004, “
New Model for Frost Growth Rate
,”
Int. J. Heat Mass Transfer
0017-9310,
47
, pp.
925
936
.
18.
Tanda
,
G.
, and
Fossa
,
M.
, 2006, “
Free Convection Frost Growth in a Narrow Vertical Channel
,”
Int. J. Heat Mass Transfer
,
49
, pp.
1946
1957
. 0017-9310
19.
Kwon
,
J. T.
,
Lim
,
H. J.
,
Kwon
,
Y. C.
,
Koyama
,
S.
,
Kim
,
D. H.
, and
Kondou
,
C.
, 2006, “
An Experimental Study on Frosting of Laminar Flow on a Cold Surface With Local Cooling
,”
Int. J. Refrig.
0140-7007,
29
, pp.
754
760
.
20.
Sherif
,
S. A.
,
Raju
,
S. P.
,
Padki
,
M. M.
, and
Chan
,
A. B.
, 1993, “
A Semi-Empirical Transient Method for Modelling Frost Formation on a Flat Plate
,”
Int. J. Refrig.
0140-7007,
16
(
5
), pp.
321
329
.
21.
Abdel-Wahed
,
R. M.
,
Hifni
,
M. A.
, and
Sherif
,
S. A.
, 1984, “
Heat and Mass Transfer From a Laminar Humid Air Stream to a Plate at Subfreezing Temperature
,”
Int. J. Refrig.
0140-7007,
7
(
1
), pp.
49
55
.
22.
Raju
,
S. P.
, and
Sherif
,
S. A.
, 1993, “
Frost Formation and Heat Transfer on Circular Cylinders in Cross-Flow
,”
Int. J. Refrig.
0140-7007,
16
, pp.
390
401
.
23.
Anderson
,
C. R.
, and
Reider
,
M. B.
, 1996, “
High Order Explicit Method for the Computation of Flow About a Circular Cylinder
,”
J. Comput. Phys.
0021-9991,
125
, pp.
207
224
.
24.
Ismail
,
K. A. R.
,
Salinas
,
C.
, and
Goncalves
,
M. M.
, 1997, “
Frost Growth Around a Cylinder in a Wet Air Stream
,”
Int. J. Refrig.
0140-7007,
20
, pp.
106
119
.
25.
Sengupta
,
S.
,
Sherif
,
S. A.
, and
Wong
,
K. V.
, 1998, “
Empirical Heat Transfer and Frost Thickness Correlations During Frost Deposition on a Cylinder in Cross-Flow in the Transient Regime
,”
Int. J. Energy Res.
,
22
, pp.
615
624
. 0363-907X
26.
Lee
,
Y. B.
, and
Ro
,
S. T.
, 2001, “
An Experimental Study of Frost Formation on a Horizontal Cylinder Under Cross Flow
,”
Int. J. Refrig.
0140-7007,
24
, pp.
468
474
.
27.
Szczepanik
,
K.
,
Ooi1
,
A.
,
Aye
,
L.
, and
Rosengarten
,
G.
, 2004, “
A Numerical Study of Heat Transfer From a Cylinder in Cross Flow
,” 15th Australasian Fluid Mechanics Conference, Dec. 13–17,
University of Sydney
,
Sydney, Australia
.
28.
Tso
,
C. P.
,
Cheng
,
Y. C.
, and
Lai
,
A. C. K.
, 2006, “
An Improved Model for Predicting Performance Finned Tube Heat Exchanger Under Frosting Condition, With Frost Thickness Variation Along Fin
,”
Appl. Therm. Eng.
,
26
, pp.
111
120
. 1359-4311
29.
Yang
,
D. K.
,
Lee
,
K. S.
, and
Song
,
S.
, 2006, “
Modeling for Predicting Frosting Behaviour of a Fin-Tube Heat Exchanger
,”
Int. J. Heat Mass Transfer
,
49
, pp.
1472
1479
. 0017-9310
30.
Iragorry
,
J.
,
Tao
,
Y. X.
, and
Jia
,
S.
, 2004, “
A Critical Review of Properties and Models for Frost Formation Analysis
,”
HVAC&R Res.
,
10
(
10
), pp.
393
420
. 0017-9310
31.
Iragorry
,
J.
, and
Tao
,
Y. X.
, 2005, “
Frost Temperature Relations for Defrosting Sensing System
,”
ASME J. Heat Transfer
0022-1481,
127
, pp.
344
351
.
32.
McCabe
,
W. L.
, and
Smith
,
J. C.
, 1967,
Unit Operations of Chemical Engineering
,
2nd ed.
,
McGraw-Hill
,
New York
.
33.
Yonko
,
J. D.
, and
Sepsy
,
C. F.
, 1967, “
An Investigation of the Thermal Conductivity of Frost While Forming on a Flat Horizontal Plate
,”
ASHRAE Trans.
,
73
, pp.
1.l.l
1.1.10
. 0017-9310
34.
Klein
,
S.
, and
Alvarado
,
F.
, 1995, Engineering Equation Solver, F-Chart software, Middleton, WI.
35.
ASHRAE
, 2006,
ASHRAE Handbook-2006 Refrigeration
,
The American Society of Heating, Refrigeration and Air-Conditioning Engineers
,
Atlanta, GA
.
36.
Parish
,
H. C.
, and
Sepsy
,
C. F.
, 1972, “
A Numerical Analysis of the Frost Formation Under Forced Convection
,”
ASHRAE Trans.
,
78
, pp.
236
251
. 0017-9310
37.
Andrichak
,
S. M.
, 1962, “
Formation of a Layer of Frost on a Cylinder in Crossflow of Air
,” MS thesis, Ohio State University, Columbus, OH.
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