Applied Energy 88 (2011) 1549–1556

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Applied Energy

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Experimental investigation of frost formation on a parallel flow evaporator

Jianghong Wu a,⇑, Guang Ouyang a, Puxiu Hou a, Haobin Xiao b

a School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510641, PR Chinab GuangDong Siukonda Air Conditioning Co., Ltd., 528216 Guangdong, PR China

a r t i c l e i n f o a b s t r a c t

Article history:Received 21 May 2010Received in revised form 20 October 2010Accepted 7 November 2010Available online 9 December 2010

Keywords:Parallel flow evaporatorSurface temperatureFrost formationIce crystalsMicrochannel

0306-2619/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.apenergy.2010.11.006

⇑ Corresponding author. Tel.: +86 13580467927; faE-mail address: pmjhwu@scut.edu.cn (J. Wu).

This paper experimentally studied the frosting process of a folded–louvered-fin, parallel flow microchan-nel evaporator in a heat pump central air-conditioning system under three conditions, in which threeopen states of two capillaries were adopted. Surface temperature distribution on evaporator was mea-sured by 16 thermocouples buried on the leeward side. Mesoscale frost formation processes on its frontview surface for three different test conditions were observed using a Charge Coupled Device (CCD)camera. The results showed that the surface temperature distribution on the parallel flow evaporatorwas uneven and initial frost formation generally started on some partial surface areas of the louvered finswhose surface temperature was lowest after the heat pump system running 6 min later under conditionsB and C, while the evaporator began to frost after 8 min under condition A. The non-uniform surface tem-perature distribution caused by the unequal distribution of the refrigerant flux in the flat tubes’ micro-channels resulted in uneven distribution of frost. The ice crystals distribution and frost thickness infrost period could be obtained by the digital image processing method in which the initial pictures wereconverted into binary image. The results indicated that in a thin layer near fins’ surface, ice crystals hadrelatively high occupancy rate in the frost growing period and full growth period; the occupancy rate ofice crystals decreased almost linearly with the increasing of the frost thickness (frost height), where thedecreasing rate in the frost full grown period was less than that in the frost growing period (in 0.1 mmfrost thickness condition, the occupancy rate of ice crystals decreased to 58% in the frost growing period,while in the frost full grown period occupancy rate of ice crystals decreased to 90%; and in 0.25 mm frostthickness, they were 0%, 45% respectively). Furthermore, it can be found that the frost thickness increasedas the time increasing and then finally reached maximum values of 0.3 mm, 0.35 mm, and 0.32 mmrespectively at three conditions.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

The parallel flow heat exchangers are new kind of high efficientand compact heat exchangers which were developed from the tra-ditional expanded, round tube ones. In the past few years, the par-allel flow heat exchangers had been successful applied in theautomotive air-conditioning systems. Recently, these heatexchangers have been found increasing usage as condensers inother refrigeration devices, especially in heat pump conditionersand air-conditioning systems, where they operate under dry-sur-face conditions. However, now there is becoming more and moreinterested in using parallel flow heat exchangers as evaporatorsdue to the superior thermal performance as compared with conven-tional fin-tube heat exchangers, which save space, weight andrefrigerant charge, but microchannel evaporators have to be subjectto wet and frosting operating conditions [1], the thermal–hydraulic

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performance and proper design to control frost, defrost processesmust be considered seriously.

Frost formation on evaporator surfaces can be extremely detri-mental to their efficient operation since the frost will act as a ther-mal insulator and weaken the capacity of surface heat transfer,also, accumulations of the frost often become thick enough to re-strict and block air flow [2]. A parallel flow evaporator is madeup of flat tubes and wave-shaped fins with louvered strips, so un-der cold and wet conditions, the wave-shaped fins which have lou-vered strips are much easier to frost. The apertures on the finsurface are susceptible to be blocked by the thick frost layer sothey are not only completely lost the possibility of heat transferenhancement but reduce the heat transfer area, therefore prevent-ing and delaying frost formation is of most important for parallelflow evaporator application.

Frost formation is a complicated transient phenomenon that avariety of heat and mass transfer mechanisms are taking placesimultaneously [3]. For several decades, there have been variousnumerical, experimental, and semi-empirical studies about the

Con

dens

or

Evap

orat

or

T

P

PT

T

P

PT

Throttle Device (Capillaries)

Compressor

Data Acquisition System

PC PC

CCD CameraFanFan

Fig. 1. Schematic diagram of experimental apparatus.

1550 J. Wu et al. / Applied Energy 88 (2011) 1549–1556

frost formation and defrost on plates, cylinders, parallel plates,complex heat exchangers, systems etc.

Xia et al. [1] experimentally studied thermal–hydraulic perfor-mance of the folded–louvered-fin, microchannel heat exchangersduring frost, defrost, and refrost period. Yan et al. [4] investigatedthe performance of frosted finned-tube heat exchangers of differ-ent fin types by experiments and found that the heat exchangerwith re-direction louver fins had the highest amount of frost for-mation. Martinez-Frias and Aceves [5] developed a transient frostformation model by applying the equations of conservation ofmass, momentum, and energy, as well as empirical correlations,to calculate the growth and densification of the frost layer on a par-allel plate heat pump evaporator. Tahavvor and Yaghoubi [3] alsoproposed a mathematical model to predict the transition time dur-ing the two frost growth process (early-stage or one-dimensionalgrowth of ice columns and multidimensional growth in the formof a porous structure) over a cooled horizontal cylinder. Tso et al.[6] developed a distributed model considering the uneven walland air temperature distribution inside the coil to predict the dy-namic behavior of a finned-tube heat exchanger both under non-frost and frost conditions. Luo et al. [7] did similar research onthe frost formation processing of fin tube evaporators. Huanget al. [8] conducted compared experiments on two identical fin-and-tube heat exchangers to study the frost release performance.Experimental observations showed that the coating on the finsbrought no significant thermal resistance to the heat transfer dur-ing the frost process and the coated heat exchanger had pooreranti-frosting performance than the uncoated one in defrosting cy-cles. Wu and Webb [9] did a test to investigate the possibility ofusing the hydrophilic or hydrophobic coating to release frost froma cold surface, and they came to a conclusion that a hydrophiliccoating was probably preferable.

Despite a large number of studies dealing with frost formation,the frost mechanism especially parallel flow evaporators’ has notyet been accurately explained. The purpose of our study is to inves-tigate on the causes of frost formation on a louvered and folded-finparallel flow evaporator. The frost processes of the microchannelevaporator used in R22 heat pump central air-conditioning sys-tems under three conditions were investigated carefully. The sur-face temperature of the evaporator was measured by 16thermocouples which buried on the leeward side and mesoscalefrost formation processes on the front view surface were observedusing a CCD camera.

At present, some researchers begin to apply the digital imageprocessing method to analyze the frost formation process[10,11]. Thus, it is also introduced in our study. It is believed thatthe investigation will provide insights into the frost formationmechanism in microchannel evaporator under different test condi-tions, and stimulate further application of the microchannelevaporators.

Table 1The parameters of the evaporator.

Characteristics of the evaporator

Face area (m2) 0.3937Fin density (fins/in.) 16Tube depth (mm) 11Tube length (mm) 674Pass number 1Row number 49Port inner diameter (mm) 0.89Port number 18Fin height (mm) 8.0Fin thickness (mm) 0.09Fin pitch(mm) 2.7Louver pitch(mm) 1.2Louver angle (�) 30Collecting tube inner diameter (mm) 27

2. Experimental apparatus and procedure

Fig. 1 schematically illustrates the experimental apparatus usedin this research, which mainly consists of a test section, a dataacquisition system and a microscopic image acquisition system(CCD camera). The test system is an R22 heat pump residentialair-conditioning system, which consists of a 2.57 kW scroll com-pressor (C-SB261H5B, Sanyo, Japan), a fin-tube condenser(length �width � height: 935 mm � 75 mm � 381 mm), two cap-illaries which have different dimensions and a parallel flow evap-orator. The length of the smaller capillary is 800 mm, and itsouter and inner diameters are 4.76 mm and 3.0 mm respectively;while the dimension of the lager one is 780 mm and its outerand inner diameters are 6.35 mm and 3.34 mm respectively. An

enthalpy difference experiment apparatus which was installed be-tween two separate environmental chambers was used to providesimulating indoor and outdoor surroundings. The test evaporator isa brazed aluminum parallel flow evaporator with two collectingtubes. The mass of the refrigerant charge was adjusted by control-ling the valves which installed upstream of the two capillaries, andthe upwind flow rate of the evaporator was controlled by changingrotating speed of axial flow fan. The detail geometrical parametersof the outdoor evaporator are showed in Table 1.

To test the frost characteristic of the outdoor parallel flow evap-orator, two pressure gauges (type: P51) were set on the inlet andoutlet of the condenser; and two pressure gauges (type: T61DP5E22B3C2) and two thermocouples were installed on the in-let and outlet of the evaporator; and 16 thermocouples were equa-bly buried on the grooves between the fins of the evaporator tomeasure the surface temperature. Fig. 2 shows the locations oftemperature measurement for the test section (The refrigerantflows into the evaporator from left bottom and leaves on the upperright). The specifications of the thermocouples and pressuregauges are listed in Table 2. The thermocouples used in the exper-iment were all precisely calibrated before tests. While on the airside of heat exchangers, the indoor and outdoor environmentwas simulated by enthalpy difference experiment apparatus. Allthe temperature of the measurement points was recorded at time

(a)

(b)

Fig. 2. The schematic diagram of the test evaporator: (a) locations of temperature measurement for the test section (between the flat tubes are the fins); (b) dimensions ofwave-shaped fins with louvered strips.

Table 2Specifications of the thermocouples and pressure gauges.

Item Type Range Accuracy

Thermocouples PT100 �20 �C–150 �C ±0.2 �CPressure gauge I P51 0–60 bar ±2%Pressure gauge II T61DP5E22B3C2 0–186 kPa ±2%

Table 3Three operating conditions.

Conditions Indoor temperature(�C)

Outdoor temperature(�C)

Opening state oftwo capillaries

Dry-bulb/wet-bulb Dry-bulb/wet-bulb

A 20.00/15.00 14.71/12.98 Larger oneopening

B 19.95/16.25 16.25/16.09 Smaller oneopening

C 19.98/15.79 14.07/11.27 Both opening

J. Wu et al. / Applied Energy 88 (2011) 1549–1556 1551

intervals of 1 min by the HP34970 data acquisition system con-necting to a computer which might avoid personal data-reading er-rors. The processes of frost formation on the evaporator surfacewere observed and recorded by a CCD camera connected to an-other computer. However, the frosting formation processes onthe surface of the parallel flow evaporator were shot by a commondigital camera. The CCD camera mainly took the pictures of themost serious frosting area. The test performed under A, B, and Coperating conditions and the parameters were shown in Table 3.

3. Results and discussion

3.1. Surface temperature distribution

Fig. 3 shows the surface average temperature distribution ofthe evaporator in the initial 7 min under condition B. It can beseen that the surface temperature distribution of the parallel flowevaporator under condition B was very non-uniform, the highestsurface temperature was 14.71 �C and the lowest surface temper-ature was �13.76 �C (according to error analysis method proposed

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

1 2 3 4Points

Tem

pera

ture

( )

1st Row 2nd Row 3rd Row 4th Row

Fig. 3. Surface average temperature distributions of evaporator (under condition B).

1552 J. Wu et al. / Applied Energy 88 (2011) 1549–1556

by de Souza and Brasil [12], the uncertainties of testing tempera-ture include the instrument and random errors. The final errorrange of temperature measurement in the experiment is ±2.97%–±5.03%, and the sensitivity of results to the environmental temper-ature is ±2.67%). The lowest surface temperature occurred near the

(a)

(b)

Fig. 4. Variation of evaporating temperature (Fig. 4a) and evaporator pressure dr

left flow tube and the second row of thermocouples, and the high-est surface temperature lied in the third column of thermocouples(point 3).

In experiment, the air flow distribute relatively uniform in dif-ferent locations on the upwind of the evaporator, and refriger-ant-side maldistribution has remarkable influence on themicrochannel heat pump system performance especially underthe frost conditions [13,14], so it is reasonable to deduce that theuneven surface temperature distribution is probably caused bythe maldistribution of the refrigerant flux in the microchannelsof flat tubes. The temperature of point 2 of the first row of thermo-couples is higher than other rows. The reason is that the micro-channels near point 2 could only receive less liquid refrigerant;thus the relatively less liquid refrigerant absorbs heat from airand refrigerant phase changed into vapor state, furthermore super-heat state, resulting in temperature of point 2 going up.

Fig. 4 shows the variation of inlet and outlet temperature andpressure drop of the evaporator in the initial 7 min under conditionC. The inlet and outlet temperature of evaporator increased a little inthe initial 7 min under condition C (see Fig. 4a). It also shows thatoutlet temperature of the evaporator is lower than inlet. The reasonis that the evaporator has relative high pressure drop which isincreasing during the initial 7 min (see Fig. 4b) (the final error rangeof measuring pressure is ±2.913–±8.402%, and the sensitivity of

op (Fig. 4b) in the initial 7 min after the system start up under condition C.

Fig. 5. Three typical shapes of frosting surface: (a) under condition A; (b) undercondition B; (c) under condition C.

J. Wu et al. / Applied Energy 88 (2011) 1549–1556 1553

results to the environmental temperature is 4.0% referring to the er-ror analysis method proposed by de Souza and Brasil [12]). Becausetwo capillaries were used under condition C, the refrigerant mass in-creased. However, the heat transfer area and air flow rate on the airside was not changed in the experiment, thus excessive refrigerantin evaporator could not evaporated completely. Much refrigerantin gas–liquid phase was in the parallel flow evaporator, this in turnled the high pressure drop and low evaporating temperature.

3.2. Frost formation

Frosting formation processes on the front view surface of theparallel flow evaporator were shot by a common digital camera.However, the mesoscale frost formation processes on the coldbrazed aluminum partial surface for three different test conditionswere observed using a CCD camera. Although the frost formationmechanism is quite complicated, the observations showed thatthe surface of the louvered fins began to frost at the left of the evap-orator after the heat pump system started for 6 min and the frostedge then slowly diffused from left to right. The area near the sec-ond row of thermocouples frosted most seriously under conditionC, while on the other two conditions the frost processes were sim-ilar (The frosts began to form and grow on the centre and then frostedge diffuse to its left under condition A; however, the frosts beganto form and grow on the left and then frost edge fast diffuse to theright under condition B). Fig. 5 show three typical shapes of frostingsurface (Fig. 5a, b and c represents the frosting surface under condi-tions A, B and C respectively). It can be seen from the pictures thatfrost growing along evaporator surface was non-uniform, and thearea near the second row of thermocouples frosted most seriously.As the temperature of second row was lowest, so the frost forma-tion began in the low temperature areas (see Fig. 3).

It is supposed that tubes with lower surface temperature havemore refrigerant flux. The incomplete evaporation of refrigerantin some tubes may lead to its folded–louvered-fins easily frost atrelative high environmental temperature. However, thick frostson the fins’ surface can easily block the air flow and reduce the heattransfer area, thus in turn affect the evaporation of refrigerant.What is more, literature [15] indicated that the frost formationon a cold surface generally began with the formation and growthof water droplets, then freezing of the super-cooled condensatedroplets, formation of initial frost crystals on the frozen droplets,then growth of frost crystals accompanied by falling down of someof the crystals, then formation and growth of the frost layer and fi-nally aging of the frost layer. However, it is more difficult for thelouvered fins to get rid of the condensate droplets, so the surfaceof the parallel flow evaporator is easier to frost.

The reason for uneven distribution of frost on evaporator is thatthe surface temperature distribution is non-uniform and also theinertia effect in the microchannel evaporator collecting tube [13].Surface temperature is one of major factor that affect the growthof frost, this can explain that the lower the surface temperatureis, the easier the frost formation (see Fig. 3). Maldistribution ofrefrigerant in tubes’ microchannels led to uneven surface temper-ature field. Frosts begin on the lowest surface temperature area ofmicrochannel evaporator (on the left), because the accumulatedfrosts on the evaporator decreases the local heat transfer amountof air side, the evaporating process of refrigerant becomes slowly,and then the frost boundary moves from left to right.

3.3. Images of heat exchanger during frost

The mesoscale frost formation processes on the coldfolded–louvered-fin surface under three different test conditionswere observed and the images of the evaporator surface were cap-tured using the CCD camera. Fig. 6 presents the images of frosting

surface (under condition B), with several fins appearing in the fieldof view. Bright spots in the images were water droplets in initialfrost process. The corner formed by two adjacent fins hinderedthe drainage of droplets, so the frost began (see Fig. 6a) as soonas temperature decreasing. As the frosting cycle ensued, the drop-lets then froze into ice; later, frost grew on that frozen ice and theirvolume expanded (see Fig. 6b). At the full growth period of thefrosting cycle, the deposited frost almost totally blocked the air-flow passage (see Fig. 6c).

3.4. Frost thickness

3.4.1. Digital image processing method introductionDigital image processing method dating from 1920s is playing

an increasingly important role in engineering practice now[10,11]. In this paper, image segmentation technology (one of the

Fig. 6. Images of frosting: (a) initial frost; (b) growth of the frost; (c) full growthperiod of frost layer.

Fig. 7. Ice crystals distributions: (a) frost growing period; (b) frost layer full grownperiod.

1554 J. Wu et al. / Applied Energy 88 (2011) 1549–1556

most important digital image processing techniques) was used toquantitatively analyze the images obtained from the experiment.

Frost layer is composed of ice crystals and air in porous media.The initial experimental pictures have a certain range of brightnessvalues, in which the larger ones are ice crystals and the smaller arethe contexts. In order to clearly distinguish the ice crystals with thebackgrounds in the initial pictures, the gray level thresholding seg-mentation was applied.

The gray level thresholding segmentation’s basic idea is to se-lect an appropriate gray threshold, and then to compare the grayvalue of every pixel with this gray threshold. If the gray of pixelis greater than the gray threshold, the maximum gray is distrib-uted; however, if the gray of pixel is lesser than the gray threshold,the minimum gray is distributed, so the initial image can be con-verted to a binary image.

If the gray range of image h(x, y) is between g1 and g2 and Tðg1 6 T 6 g2Þ is chosen as the gray threshold, the converted binaryimage is as following equation:

gTðx; yÞ ¼1; hðx; yÞP T0; hðx; yÞ < T

�ð1Þ

In this paper, the maximum variance method was taken to cal-culate the value of the threshold T. Dividing pixels and making thedistance of these diving pixels reach a maximum value, and thenan appropriate threshold was determined.

Assume that the gray level of initial image is L, and the numberof pixels which have gray values of i is ni, so the total number ofpixels is N = Rni and appearing probability of every gray is gi = ni/N.

Gray threshold value T divides the image pixels into parts A andB, thus the respectively appearance probability of A and B is in fol-lowing equation:

pA ¼XT

i¼1

gi pB ¼XL

i¼Tþ1

gi ð2Þ

After obtaining the average gray value of A and B, the between-cluster variance r2

b and total variance r2T can be acquired. Defining

that gðtÞ ¼ r2b=r2

T as a judging criterion, the optimum threshold va-lue T is:

T ¼ arg max06t6L�1

gðtÞ ð3Þ

Because the binary images have two gray values of 0 and 1, thegray value of ice crystals and contexts is 1 and 0 respectively. Byanalyzing every pixel of the binary images, the distribution of icecrystals can be obtained.

J. Wu et al. / Applied Energy 88 (2011) 1549–1556 1555

3.4.2. Distribution of ice crystalsCalculating the occupancy rate of ice crystals on different frost

thickness, the frost thickness can be obtained.Processed image is actually an m rows and n columns matrix,

and every element of the matrix of is a pixel. If its value is 1, it isthe ice crystal; if not, it is the background. First, calculating thenumber of pixels whose gray value is 1 on the m row as follow:

Mi ¼Xn

j¼1

qðm; jÞ ð4Þ

where q(m, j) is the pixel value of m row and j column, so the occu-pied percent of ice crystals is ri = Mi/n.

From the curve of m vs. Mi/n, the ice crystals distributionaccording to different frost thickness can be seen.

Fig. 7 indicates the distribution of ice crystals in frost growingperiod and full growth period under condition B. It can be shownthat in a thin layer near to fins’ surface, ice crystal was very densein the frost growing period (Fig. 7a) and frost layer full grown per-iod (Fig. 7b). With the increasing of the frost thickness(frostheight), the occupancy rate of ice crystals reduced approximate lin-early, but decreasing rate in the frost growing period was fasterthan that in the full grown period. In 0.1 mm frost thickness, theoccupancy rate of ice crystals decreased to 58% in the frost growingperiod, while in the frost full grown period occupancy rate of icecrystals decreased to 90%. In 0.25 mm frost thickness, the occu-pancy rate of ice crystals was 0%, 45% respectively. It could be ex-plained that in the frost growing period, the growing of crystalsaccompanied by falling down of crystals, however, in the fullgrown of frost layer period, the frost layer had formed and thedecreasing rate of the crystals became more slowly.

Fig. 8 illustrates the variation curves of frost layer thicknesswith time. The figure shows that the frost thickness increased astime increasing and then finally reached maximum values of0.3 mm, 0.35 mm, and 0.32 mm respectively at three conditions.The frost thickness had reached 0.1 mm, 0.05 mm under conditionsB and C respectively in 6 min, on the other hand, concerning tocondition A, the frost began to grow after 8 min and frost thicknessarrived only 0.05 mm in 14 min.

When the R-square is greater than 0.9 and confidence boundsare 95%, the three curves are fitted as following equations:

Fig. 8. Frost layer thickne

(1) Under condition A

f ðkÞ ¼ �0:4773k�0:9508 þ 0:0811 ð6 min 6 k 6 24 minÞ�682:6e�0:04304k þ 680:3e�0:04289k ð24 min < k 6 38 minÞ

(

ð5Þ

(2) Under condition B

f ðkÞ ¼ 0:2097e0:02202k � 10:98e�0:7282k ð6 min 6 k 6 24 minÞ0:35 ð24 min < k 6 38 minÞ

(

ð6Þ

(3) Under condition C

f ðkÞ ¼246:5e�0:03084k � 246:6e�0:03096k ð6 min 6 k 6 24 minÞ�4:304�10�6k3þ0:3053k�8:134

k�25:9 ð24 min < k 6 38 minÞ

(

ð7Þ

where f (k) is the frost thickness and k represents the system run-ning time.

Because inertia effect of the heat pump system and only the lar-ger diameter capillary was used, the frost rate and frost thicknesswas the lowest under condition A among the three conditions.The most uneven surface temperature distribution of evaporator,high pressure drop and the initial frost cycle effect under conditionA led to microchannel evaporator fastest frost growth than that un-der condition B. Concerning condition C, the frost rate and thick-ness is between the two other conditions.

4. Conclusions

This paper experimentally studied the frosting processes of afolded–louvered-fin, parallel flow evaporator in a R22 heat pumpcentral air-conditioning system under three different conditions.The surface temperature of the evaporator was measured by 16thermocouples which were buried on the leeward side and meso-scale frost formation processes on the evaporator surface for threedifferent test conditions were observed using a CCD camera. It canbe concluded as following:

ss curves with time.

1556 J. Wu et al. / Applied Energy 88 (2011) 1549–1556

� The surface temperature distribution on the parallel flow evap-orator was uneven and initial frost formation generally startedon some partial surface areas of the louvered fins whose sur-face temperature was lowest after the heat pump system run-ning 6 min later under conditions B and C, while theevaporator began to frost after 8 min under condition A. Thenon-uniform surface temperature distribution which wascaused by the unequal distribution of the refrigerant flux inthe flat tubes’ microchannels resulted in uneven distributionof frost.� The ice crystals distribution and frost thickness in frost period

could be obtained by the digital image processing method inwhich the initial pictures were converted into binary image.The results indicated that in a thin layer near fins’ surface, icecrystals had relatively high occupancy rate in the frost growingperiod and full growth period in frost layer; the occupancy ratedecreased almost linearly with the increasing of the frost thick-ness (frost height), where the decreasing rate in the frost fullgrown period was less than that in the frost growing period(in 0.1 mm frost thickness condition, the occupancy rate of icecrystals decreased to 58% in the frost growing period, while inthe frost full grown period occupancy rate of ice crystalsdecreased to 90%; and in 0.25 mm frost thickness, they were0%, 45% respectively.).� Furthermore, it can be found that the frost thickness increased

as the time increasing and then finally reached maximum val-ues of 0.3 mm, 0.35 mm, and 0.32 mm respectively at three con-ditions. High evaporator pressure drop and initial frost cycleeffect under condition A lead to fastest frost growth under con-dition B.

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