Optimal defrost cycle for air coolers revisited: A study of fan-supplied tube-fin evaporators

Accepted Manuscript

Optimal defrost cycle for air coolers revisited: A study of fan-supplied tube-fin evaporators Diogo L. da Silva , Christian J.L. Hermes PII: DOI: Reference:

S0140-7007(18)30055-0 10.1016/j.ijrefrig.2018.02.009 JIJR 3889

To appear in:

International Journal of Refrigeration

Received date: Revised date: Accepted date:

18 October 2017 4 February 2018 5 February 2018

Please cite this article as: Diogo L. da Silva , Christian J.L. Hermes , Optimal defrost cycle for air coolers revisited: A study of fan-supplied tube-fin evaporators , International Journal of Refrigeration (2018), doi: 10.1016/j.ijrefrig.2018.02.009

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ACCEPTED MANUSCRIPT

Highlights Optimal defrost of fan-supplied tube-fin evaporators is investigated

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Numerical models are used to predict the operation between defrost cycles

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Optimal time to defrost is identified based on the on-off cycle efficiency

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Operating conditions, defrost power and evaporator geometry are evaluated

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ACCEPTED MANUSCRIPT Submitted to International Journal of Refrigeration

Optimal defrost cycle for air coolers revisited: A study of fan-supplied tube-fin evaporators

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Diogo L. da Silva 1, Christian J. L. Hermes 2,*

Laboratory of Vehicular Refrigeration, Department of Mobility Engineering, Federal University of Santa Catarina Joinville, SC 89218-035 Brazil 2

POLO Research Laboratories, Department of Mechanical Engineering, Federal University of Santa Catarina

*

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Florianópolis, SC 88040-970 Brazil

Corresponding author: 55 48 3721 7902, [email protected]

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ABSTRACT

The performance of fan-supplied tube-fin evaporators is assessed in the present paper aiming at identifying

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the key parameters which affect the cooling capacity under frosting conditions and defrost cycle performance. The analysis was carried out by means of a mathematical model comprised of a frost formation

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submodel, which was developed by the authors in a prior publication, together with an improved defrosting

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submodel. A performance evaluation criterion to account for the periodic defrosting, the so-called cooling cycle efficiency, was employed as an objective function for the defrost cycle optimization. The results

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pointed out that there does exist an optimal runtime which maximizes the evaporator performance even for variable air flow rate conditions. Moreover, it was observed that the optimal runtime rises either by increasing the heat transfer surface (while keeping the fin spacing) or the coil surface temperature, and diminishes by either increasing the power supplied to the heater, or the relative humidity of the inlet air. Keywords: frost; defrosting; evaporator; fan-coil unit; modelling; optimization

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ACCEPTED MANUSCRIPT NOMENCLATURE

As, surface area [m2] Ac, minimum (core) free flow passage [m2] Cf, Fanning friction factor [-] cp, specific heat of moist air [J kg-1 K-1]

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D, water vapor diffusivity in air [m2 s-1] E0, frost-free cooling load [J] Ed, effective defrost energy [J] Eeff, effective cooling load [J]

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EL, energy losses [J] EQ, on-cycle cooling load [J] H, evaporator height [mm]

ho, heat transfer coefficient [W m-2 K-1] isl, latent heat of solidification [J kg-1]

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hm, mass transfer coefficient [kg m-2 s-1]

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isv, latent heat of sublimation [J kg-1]

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kf, frost thermal conductivity [W m-1 K-1] L, evaporator length [mm]

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Le, Lewis number [-] M, frost mass [kg]

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 , mass flow rate [kg s-1] m

m , frost mass to surface area ratio [kg m-2] p, pressure [Pa]

Q , heat transfer rate [W] T, temperature [K] t, time [s]

 , air flow rate [m3 s-1] V -3-

ACCEPTED MANUSCRIPT W, evaporator width [mm]

 , power [W] W

Wd" , defrosting heat flux [W m-2] xf, frost thickness [m]

Greek

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, porosity [-] ηd, defrost efficiency [-] ηQ, cooling cycle efficiency [-] ηs, finned surface efficiency [-]

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, relative humidity [-] , density [kg m-3] , tortuosity [-]

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, humidity ratio [kgv kga-1]

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Subscripts

d, defrost

f, frost

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i, inlet

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dew, dew point

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a, air

lat, latent

off, off-cycle on, on-cycle

s, frost surface sat, saturation sen, sensible v, vapor -4-

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w, wall

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ACCEPTED MANUSCRIPT INTRODUCTION

Finned-tube evaporators are largely used worldwide, particularly in household and commercial applications where favorable conditions for frost formation can be found. The presence of a frosted medium raises both the thermal and the hydraulic resistances in the air side of the evaporator. These combined effects deteriorate the cooling capacity and increase the compressor runtime to accomplish the desired cooling effect. To

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mitigate these issues, periodic defrosting operations are usually performed by different means, such as hotgas reverse cycles, nonstop fan operation, ultrasonic vibration, electro-hydro-dynamic technique and electric heating (Joppolo et al. 2012; Zhao et al. 2015; Amer and Wang, 2017), each one requiring a proper control strategy (Kim and Lee, 2015). Although the latter is widely used, only part of the heat is effectively used to

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melt the frost on the evaporator. Consequently, a substantial amount of thermal energy is dissipated inside the refrigerated compartments and must be removed by the refrigeration system (Knabben et al., 2011). Therefore, the amount of heat dissipated, the time required for a defrost operation, and the time between two consecutive defrosting operations are key parameters that must be accounted for in a proper design of the

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defrosting system.

In his pioneering work, Zakrzewski (1984) evaluated the effect of the frost layer on the depletion of the

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effective cooling capacity of air coolers. The author defined the effective cooling capacity as the difference between the energy removed by the evaporator during the compressor runtime and the energy dissipated by

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the defrost system that is not used for melting the frost. He observed that there is an optimum time between two consecutive defrost operations that improves the effective cooling capacity. Machielsen and

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Kerschbaumer (1989) revisited the Zakrzewski’s work and proposed two dimensionless parameters, X and Y – the first related to the effective cooling capacity during a complete cycle of operation, and the second to the average energy required to carry out the defrost process – which allowed the determination of the optimum operating time for defrosting. Radcenco et al. (1995) developed a thermodynamic model to take into account the effects of evaporator frosting and defrosting on the performance of a refrigerator, observing an optimum runtime that minimizes the inverse of the COP. However, such a model assumed that the frost layer grows at a constant rate, while a quadratic relationship between frost thickness and time has been observed in typical

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ACCEPTED MANUSCRIPT conditions for refrigeration applications. One should note that the time to start defrosting has also been subject matter for recent investigations – see for instance the work of Steiner and Rieberer (2015), who analyzed the effect of the defrosting operation in heat pump systems designed for electric vehicles.

It is worth noting that all of the works mentioned before considered a constant air flow supply to the cooler, whereas recent studies have pointed out that the airflow reduction due to a fan constraint is the main cause of

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the evaporator capacity depletion, while the additional thermal resistance related to the frost layer plays a minor role (Padhmanabhan et al., 2011; Da Silva et al., 2011a; Da Silva et al., 2017). Therefore, one might expect that the optimal defrost conditions achieved for constant air flow supply may be quite different than those observed in the cases when the air flow rate diminishes with evaporator frosting, rapidly degenerating

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the cooling capacity, thus requiring more frequent defrosting operations. The present communication focuses on revisiting and extending Zakrzewski’s (1984) work for fan-supplied air coolers. To do so, an evaporator frosting model, developed by the authors in a prior publication (Da Silva et al. 2011b), was used together with an improved defrosting model. The latter model is advanced here following up the work of

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Zakrzewski’s (1984) but using new defrost efficiency data published recently by Mohs and Kulacki (2015). This approach was used to figure out the most influencing design parameters that lead to the optimal cooling

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cycle efficiency for fan-supplied tube-fin evaporators.

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EVAPORATOR FROSTING MODEL

The mathematical model for the evaporator frosting assumes each row of tubes as a control volume. Also,

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the following simplifications are adopted: (i) the processes of heat and mass diffusion in the frost layer are considered quasi-steady; (ii) the evaporator temperature is uniform; (iii) the thickness of the frost layer is uniform over the control volume surface; (iv) the Chilton-Colburn analogy for heat and mass transfer is applicable; and (v) the psychrometric properties of air were considered uniform at the entrance and exit of each control volume (Da Silva et al., 2011b). Figure 1 shows schematic representations of the evaporator geometry, control-volume and the frost layer on the evaporator surface. Applying energy and mass balances

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ACCEPTED MANUSCRIPT on the frost surface, and within the frost layer, the frost surface temperature Ts was obtained as a function of the evaporator surface temperature Tw for each control volume (Hermes et al., 2009),

Ts  Tw 

Q



 Qlat x f asat,w isv D  sat,s    1  As kf kf   sat,w 

sen

(1)

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where As is the total heat transfer surface, xf is the thickness of the frost layer, kf is the thermal conductivity of frost, isv is the latent heat of sublimation of ice, D is the diffusivity of water vapor in air, and  and  are the frost porosity and tortuosity, respectively. The 2nd and the 3rd terms on the right-hand side of Eq. (1) are related to the heat transfer and the mass transfer inside the frost layer, respectively. The 3rd term plays a

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minor role and can be dropped out because sat,ssat,w. The rate of frost accumulation, the sensible and latent heat transfer rates, and the air side pressure drop are calculated as a function of the air flow rate, respectively, from the following equations:

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   s A s h o      1  exp    f  a V m sat ,s i 23       c V Le     a p ,a 

(2)

(3)

 m  f i sv Q lat

(4)

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A p  Cf a s Ac

 2  V    Ac 

(5)

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1 2

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     V  c T  T 1  exp   s A s h o  Q sen a p ,a s i     c V  a p ,a  

 is the air flow rate. The where Ac is the minimum free flow passage, Le is the Lewis number, and V convective heat transfer coefficient ho and the Fanning friction factor Cf were both calculated from the correlations proposed by Wang et al. (2000). The main difference between this particular model and others from the open literature lies in its capability to predict the fan air flow degeneration caused by the rise in the air side pressure drop due to frost blocking. To consider the performance of an axial fan, typical for small-8-

ACCEPTED MANUSCRIPT capacity refrigeration systems, the airflow rate was calculated as a function of the air side pressure drop using the characteristic curve (static pressure vs. air flow rate) depicted in Fig. 2 (Da Silva et al., 2011a). The time evolution of the frost thickness was computed from the total mass conservation principle written in the following form (Hermes et al. 2009):

f dx f x f df m   dt f dt f A s

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(6)

where the 1st and the 2nd terms on the left-hand side accounts for the frost layer growth and densification, respectively. The frost density was calculated as an empirical function of the frost surface temperature and

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dew point of the air stream,

 f   exp Ts  Tdew 

(7)

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where the coefficients   494 kg m-3,   0.11°C-1 e   0.06 °C-1 were fitted to experimental data obtained from Da Silva et al. (2011a). Using the chain rule to differentiate Eq. (7) with respect to space and

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time (Hermes et al. 2009), and substituting it into Eq. (1) (without the 3rd term), yields

 dx f   dt

(8)

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 Q  Q d f lat  f  sen dt A k s f 

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Substituting Eq. (8) into Eq. (6), the following integral equation for the frost thickness is achieved:

x f t  t   x f t   

t  t

t

f m dt  m  f i sv  f A s  x f  f k f  Q sen

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

(9)

In this work, a 2nd-order predictor-corrector method with adaptive step-size control was used for the numerical integration of Eq. (9). Figure 3 illustrates a comparison between the simulated and experimental

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ACCEPTED MANUSCRIPT cooling capacities over time, where an agreement within the experimental uncertainty of ±10% thresholds is observed. Further model results, validation and applications can be found in Da Silva et al. (2011b).

EVAPORATOR DEFROSTING MODEL

In this work, the modeling approach introduced by Zakrzewski (1984) was improved using new experimental

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data for the defrost efficiency obtained from Mohs and Kulacki (2015). The defrost model relies on the total mass of frost accumulated on the evaporator over time, which is calculated from:

 f dt M m t on

(10)

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 f is the water vapor mass flow rate from air to the frost layer, calculated from Eq. (2), ton is where m refrigerator runtime (when frost is formed) and toff is the defrost time (when the system is switched off). The

energy dissipated by the defrost system,

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Ed Wd t off

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(11)

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d 

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defrost efficiency is defined as the ratio between the energy amount needed to melt the ice Ed and the total

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where E d  M i sl  c p,f T , isl is the latent heat of solidification, and cp,f is the specific heat of frost. Moreover, it is considered that the latent heat parcel is much larger than the sensible one, E d  Misl , and

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 , is constant and uniform. that the electric power supplied to the heater, W d

The amount of the energy supplied by the defrosting system that is not used to melt the ice, which dissipates inside the internal compartments of refrigerator in the form of thermal loads, can be expressed as follows

EL  Misl 1 d  1

(12)

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For a known defrost efficiency, the defrosting time toff can be calculated from Eq. (11). In this work the defrost efficiency was determined from an empirical model based on experimental data published by Mohs and Kulacki (2015). As suggested by Zakrzewski (1984), the model relies on a 2nd-order polynomial fit of the defrost efficiency as a function of the frost mass-to-surface area ratio, m  M A s , as follows:

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d  c0  c1  c2mm

(13)

where, according to Zakrzewski (1984), c0=–0.02828, c1=3.447 [m2 kg-1] and c2=5.976 [m4 kg-2] for Ts=– 5C, and c0=–0.02828, c1=3.447 [m2 kg-1] and c2=5.976 [m4 kg-2] for Ts=–15C. Figure 4 illustrates Eq. (13)

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for both surface temperatures, where one can see defrost efficiencies up to 45% for Ts=–5C and 30% for Ts=–15C. Figure 4 also compares the predictions of Eq. (13) with the experimental data from Mohs and Kulacki (2015), where a poor agreement is observed. Therefore, Eq. (13) was additionally best-fitted to

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Mohs and Kulacki’s data, coming out with c0=0, c1=1.285 [m2 kg-1] and c2=0.5 [m4 kg-2], and a fitting coefficient R20.89. Albeit most of the data points (8 out of 11) have fallen within the 10% thresholds,

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errors up to 40% were observed for the lower defrost efficiencies (≲40%). These large deviations could be resulted due to the small figures of mass-to-surface ratio, which produce higher relative errors and are more

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sensitive to the measurement uncertainties.

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Originally, the dataset of Mohs and Kulacki (2015) comprised 12 data points covering surface temperatures

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from -20.2 to -9.6C, air temperatures from -8.6 to 0.0C, and air dew point temperatures from -19.0 to 8.3C. The test surface was an aluminum flat plate with 38 mm x 38 mm. One out of the twelve data points was discarded in the fitting process (test#6, the one with the highest defrost efficiency, 93.7%), as it is far out of the trends described by the other data points. The curve was fitted for frost mass-to-surface area ranging from 0.25 to 1.5, as depicted in Fig. 4. According to Eq. (13), a maximum defrost efficiency (83%) is observed for m1.25 kg m-2. Such a behavior lacks a proper physical explanation, being probably due to the existence of only one experimental point for frost mass-to-surface area ratios higher than 1.0 kg m-2. In the

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ACCEPTED MANUSCRIPT present work, it is emphasized that the investigated frost mass-to-surface area ratios were smaller than 0.5 kg m-2.

Figure 5 shows a schematic of the defrosting model, where one can note the cooling capacity integrated over time (EQ<0, as it removes energy from the air) and the energy lost (EL>0, as it increases the thermal loads). The cooling cycle efficiency was defined by Zakrzewski (1984) as the ratio of the effective amount of heat

E eff E0

(14)

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Q 

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removed by the evaporator to the quantity of heat taken in by the clean, “frost-free” evaporator.

where the effective cooling load ( E eff ) represents the difference between the energy removed by the evaporator during the on-cycle ( E Q ) and the energy losses by the defrost system ( E L )

t on

Q

sen



 Qlat dt  Misl 1 d  1

(15)

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0

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Eeff  



x f 0

t

on

 t off 

(16)

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E0  lim Qsen  Qlat

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In turn, the evaporator frost-free cooling load can be evaluated considering xf0 as

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Substituting Equations (15) and (16) in Eq. (14) it is obtained

Q

 

t on

0

 dt  Mi  i 1   1 Q sen sv sl d

(17)

 M isl   m  f i sv  t on   lim Q sen    x f 0 W d d  





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ACCEPTED MANUSCRIPT Equation (17) shows that the cooling cycle efficiency depends on the on and off cycles times, the rate of frost accumulation, the heat transfer rates in the evaporator, and the power supplied to the heater.

RESULTS AND DISCUSSION

The numerical analyses were performed using the operating conditions proposed in Table 1, which are

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typical for commercial refrigeration applications. The geometries G1 and G2 stand for evaporators with 2 rows of tubes. The width, height and length equal to 320 mm, 152 mm and 45 mm, respectively. The evaporators differ in the number of fins, 127 for the evaporator G1 and 168 for G2, which represents a surface area increase of 30% with respect to G1. Table 2 compares the results of optimum runtime (optimum

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ton) and the corresponding maximum cooling cycle efficiency obtained using the new defrost efficiency correlation (best-fitted to Mohs and Kulacki’s (2015) data) and the one proposed by Zakrewski (1984). One can see that the later underestimates the optimum runtime and overestimate the cooling cycle efficiency as it provides higher figures for the defrost efficiency in the range of mass-to-surface area under analysis (≲0.5

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kg m-2).

In the following analyses, the new defrost efficiency correlation was employed. Figure 6 shows the cooling

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cycle efficiency as a function of runtime ratio, i.e. t on/(ton+toff), calculated from Eq. (17) for the conditions depicted in Table 1. One can see in Fig. 1 that an optimal runtime ratio can be seen for each case. For

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instance, for case 1, the optimum runtime ratio is 75%, when the maximum efficiency corresponds to 67%. Table 2 summarizes the optimal runtimes for starting the defrosting operation and the associated efficiency

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for all cases depicted in Fig. 6. Based on the comparisons of cases 1 and 5 it is observed that the increase in the number of fins by 30% reduces not only the optimum runtime to start defrosting from 86 to 69 minutes, but also the maximum cooling cycle efficiency from 67% to 58%. Similar conclusions are drawn by comparing cases 2 and 6, cases 3 and 7 and cases 4 and 8 of Table 2, indicating that the decrease of fin spacing not only causes the reduction in the cooling cycle efficiency but also in the optimal runtime before starting the defrosting operation.

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ACCEPTED MANUSCRIPT In addition, further comparisons between cases 1 and 2, and 5 and 6, illustrated in Fig. 6, reveal that an increase in the defrosting power flux reduces the defrosting time, which in turn increases the cooling cycle efficiency. This result is one of the reasons why refrigerators manufactures use relatively high power defrost heaters. Moreover, by comparing cases 1 and 3, and 5 and 7, one verifies that a higher evaporating temperature causes a significant increase in the optimum runtime, thus increasing the cooling cycle efficiency. Such a behavior can be explained by the lower mass transfer rate and the higher frost density

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observed for higher coil temperatures. Also, the influence of the air relative humidity at the evaporator inlet can be assessed by comparing cases 1 and 4, and cases 5 and 8, revealing that an increase in the relative humidity causes the reduction of both the optimum runtime and the cooling cycle efficiency, which is mainly

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due to an increase in the rate of frost accretion and a lower frost density.

The effect of the evaporator heat transfer surface on the defrosting cycle was additionally evaluated by comparing the evaporator G1 with a third one (G3) having the same number of tubes rows and fin spacing but a larger width of 420 mm. In this analysis, 200 W m-2 of defrosting power flux was employed, while the

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temperature and the relative humidity of the air at the evaporators inlet were maintained at 4°C and 85%, respectively. The operating temperatures of the evaporators G1 and G3 were selected as -10.0°C and -8.7°C,

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respectively, to maintain the same initial cooling capacity when the evaporators are clean (i.e. frost-free).

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This comparison was also carried out with the fan characteristic curve depicted in Fig. 2.

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Figure 7a compares the frost mass and the total cooling capacity ( Qsen  Qlat ) of the two geometries as a function of time, where a fairly constant rate of frost deposition during the first stages can be observed. The

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reduction in the frost accumulation rate observed for G1 around 40 min is due to the reduction of the air flow due to the obstruction imposed by the frost build-up. The simulation of evaporator G1 is finished after 60 min, when the airflow reaches its minimum value (30 m3 h-1). Since evaporator G3 has a larger surface area, it is capable of accumulating larger amounts of frost before the airflow reaches the minimum allowable figure, around 90 min. It is clear from Fig. 7a that albeit both geometries have the same initial cooling capacity and fin spacing, evaporator G3 is more robust under frosting conditions. For example, after 30 min, when the two evaporators contain approximately 130 grams of frost, the cooling capacities of the evaporators - 14 -

ACCEPTED MANUSCRIPT G1 and G3 are equivalent to 582 W and 630 W, respectively. While the cooling capacity of evaporator G1 diminished by 8% during the first 30 minutes, evaporator G3 had no reduction in its cooling capacity at the same time range. It should be noticed that, in addition to having a smaller surface area to accommodate the frost layer, G1 also operates at a lower temperature, which reduces the frost density as predicted by Eq. (7).

Figure 7b compares the defrost efficiency (Eq. 13) and the cooling cycle efficiency (Eq. 17) obtained for

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evaporators G1 and G3. One can see that a presence of an optimum cooling cycle efficiency is observed for the two geometries, albeit the defrost efficiencies experienced a monotonic growth for both evaporator coils. An analysis of the curves points out that the replacement of G1 by G3 raises the maximum cooling cycle efficiency from 55% to 64%, the latter requiring a higher runtime (~70%) than the former (~55%), resulting

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in a reduction in the number of defrost operations for evaporator G3. It is clear from Fig. 7b that the optimal cooling cycle efficiency does not occur simultaneously with the higher defrost efficiency value.

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CONCLUDING REMARKS

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Zakrzewski’s (1984) pioneering study of the optimal defrost cycle for air coolers was revisited, and extended for cases where the air flow rate is supplied by an axial fan, which is sensitive to the pressure drops caused

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by frost accretion on the finned-coil over time. A frost formation model put forward by the authors in a previous publication was used together with an improved semi-empirical model for evaporator defrosting

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based on the original Zakrzewski’s formulation, but using new data for the defrost efficiency. When compared to the original Zakrzewski’s defrost efficiency correlation, the proposed one overestimates the

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optimum runtime and underestimates the cooling cycle efficiency as it provides smaller figures in the range of mass-to-surface area under analysis (m<0.5 kg m-2), where just a few experimental data points are available. An experimental investigation of the defrosting process for low mass-to-surface area figures would be subject matter for further investigations.

The optimization exercise confirmed the existence of an optimum runtime for the defrost operation in which the maximum cooling cycle efficiency is obtained. In the cases of fan-supplied evaporators, the air flow rate - 15 -

ACCEPTED MANUSCRIPT fed to the air cooler diminishes as frost builds-up over the finned-coil, thus degenerating the cooling capacity more rapidly. In addition, it was found that the optimal cooling cycle efficiency (Eq. 17) is independent from the inflection observed for the defrost efficiency in Fig. 4 (at m 1.25 kg m-2), being explained by the tradeoff between the cooling capacity degradation over time and the increasing power consumption with the number of defrosting operations.

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Simulations have also been carried out for three tube-fin evaporator geometries at different running conditions considering a constrained fan characteristic curve (pressure drop vs. air flow rate, as depicted in Fig. 2). The effects of key design parameters on the performance of fan-supplied tube-fin evaporators are as

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follows:

An increasing defrosting power flux decreases the optimum runtime, but rises the cooling cycle efficiency, being the former an undesirable effect, whilst the latter is desirable;

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An increasing coil surface temperature rises both the optimum runtime and the cooling cycle

An increasing relative humidity (for the same inlet air temperature) diminishes both the optimum

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

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efficiency, being both positive effects;

runtime and the cooling cycle efficiency, being both negative effects; An augmented fin spacing (with a reduction on heat transfer surface as a side effect) increases both

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

the optimum runtime and the cooling cycle efficiency; An augmented heat transfer surface (by increasing the heat exchanger width, but keeping the fin

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

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spacing constrained) increases both the optimum runtime and the cooling cycle efficiency.

ACKNOWLEDGMENTS

This research work was performed under the auspices of the Brazilian Government funding agency CNPq (Grant No. 465448/2014-3).

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ACCEPTED MANUSCRIPT REFERENCES

Amer M., Wang C.C., Review of defrosting methods, Renew. Sustainable Energy Rev. 73 (2017) 53–74. Da Silva D.L., Hermes C.J.L., Melo C., Experimental study of frost accumulation on fan-supplied tube-fin evaporators, Appl. Therm. Eng. 31 (2011a) 1013-1020.

tube-fin evaporators, Appl. Therm. Eng. 31 (2011b) 2616-2621.

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Da Silva D.L., Hermes C.J.L., Melo C., First-principles simulation of frost accumulation on fan-supplied

Hermes, C.J.L., Piucco, R.O., Barbosa, J.R., Melo, C., A study of frost growth and densification on flat surfaces. Exp. Therm. Fluid Sci. 33 (2009), 371-379.

presence, Int. J. Refrig. 35 (2012) 468-474.

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Joppolo C.M., Molinaroli L., De Antonellis S, Merlo M., Experimental analysis of frost formation with the

Kim M.-H., Lee K.-S., Determination method of defrosting start-time based on temperature measurements, Appl. Energy 146 (2015) 263–269

Knabben F.T., Hermes C.J.L., Melo C., In-situ study of frosting and defrosting processes in tube-fin

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evaporators of household refrigerating appliances, Int. J. Refrig. 34 (2011) 2031-2041

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Machielsen C.H.M., Kerschbaumer H.G., Influence of frost formation and defrost on the performance of air coolers: standards and dimensionless coefficients for the system designer, Int. J. Refrig. 12 (1989)

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283-290.

Mohs W.F., Kulacki F.A., 2015. Heat and Mass Transfer in the Melting of Frost, Springer, Chs. 4 and 5.

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Padhmanabhan S.K., Fisher D.E., Cremaschi L., Moallem E., Modeling non-uniform frost growth on a finand-tube heat exchanger, Int. J. Refrig. 34 (2011) 2018-2030.

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Radcenco V., Bejan A., Vargas J.V.C., Lim J.S., Two design aspects of defrost refrigerators, Int. J. Refrig. 18 (1995) 76-86.

Steiner A., Rieberer R., Simulation based identification of the ideal defrost start time for a heat pump system for electric vehicles, Int. J. Refrig. 57 (2015) 87-93. Wang C.C., Chi K.Y., Chang C.J., Heat transfer and friction characteristics of plain fin-and-tube exchangers, Part II: Correlation, Int. J. Heat Mass Transfer 43 (2000) 2693-2700.

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ACCEPTED MANUSCRIPT Zhao H., Wang L., Lai Y., Han J., Li W., Effects of weak magnetic fields on frosting process on surface of copper tube, Refrigeration Science and Technology (2015) pp. 1013-1020. Zakrzewski B., Optimal defrost cycle for the air cooler, Int. J. Refrig. 7 (1984) 41-45.

FIGURE CAPTIONS

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Figure 1. Schematics of the evaporator geometry and the frost layer (Adapted from Da Silva et al., 2011b) Figure 2. Characteristic curve of the evaporator fan used in current study (Da Silva et al., 2011a)

Figure 3. Comparisons between numerical (lines) and experimental (bullets) results for sensible, latent, and total cooling capacities (Da Silva et al., 2011b)

correlation, and the best-fitting of Eq. (13)

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Figure 4. Comparison between the defrost efficiency data of Mohs and Kulacki (2015), Zakrzewski’s (1984)

Figure 5. Schematic of cooling and defrost cycles (modified from Zakrzewski, 1984) Figure 6. Comparison between the cooling cycle efficiency for the cases of Table 1 as a function of the

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runtime ratio (W=320 mm, H=152 mm, L=45 mm, G1=127 fins, G2=168 fin) Figure 7. Comparison between geometries G1 and G3 (same fin spacing but a larger width) for (a) the frost

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mass and cooling capacity, and (b) the defrost efficiency and cooling cycle efficiency ( W d =200 W m-2,

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Ta=4°C, i=85%)

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ACCEPTED MANUSCRIPT First tubes row C.V.

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Figure 1.

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[kg area ratio [kg m-2] Frost mass to surface

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Figure 5.

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ACCEPTED MANUSCRIPT 0.8

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ACCEPTED MANUSCRIPT Table 1. Summary of the proposed geometric and operating conditions used in the numerical simulations of Fig. 6 Geometry

Tw [oC]

Ta [oC]

 [%]

W d [W m-2]

1 2 3 4 5 6 7 8

G1 G1 G1 G1 G2 G2 G2 G2

-10.0 -10.0 -8.0 -10.0 -10.0 -10.0 -8.0 -10.0

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74 74 74 90 74 74 74 90

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ACCEPTED MANUSCRIPT Table 2. Optimal runtime and cooling cycle efficiency Defrost efficiency model Case #

Best fit of Mohs and Kulacki’s (2015) data Optimum runtime Cooling cycle efficiency [min] [-] 86 0.67 78 0.76 121 0.74 60 0.57 69 0.58 60 0.67 92 0.66 47 0.47

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Zakrzewski’s (1984) correlation Optimum runtime Cooling cycle efficiency [min] [-] 65 0.77 61 0.84 92 0.82 45 0.69 51 0.72 47 0.80 74 0.78 35 0.63

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