DOI: 10.3303/CET2294232 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper Received: 7 May 2022; Revised: 12 July 2022; Accepted: 2 August  2022 
Please cite this article as: Azmy I., Samsuri S., Amran N.A., Safiei N.Z., Jusoh M., Ab Hamid F.H., 2022, Heat Transfer Model: Preservation of 
Antioxidant via Progressive Freeze Concentration, Chemical Engineering Transactions, 94, 1393-1398  DOI:10.3303/CET2294232 
  

 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 94, 2022 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.cetjournal.it 

Guest Editors: Petar S. Varbanov, Yee Van Fan, Jiří J. Klemeš, Sandro Nižetić 
Copyright © 2022, AIDIC Servizi S.r.l. 

ISBN 978-88-95608-93-8; ISSN 2283-9216 

Heat Transfer Model: Preservation of Antioxidant via 

Progressive Freeze Concentration 

Imran Azmya, Shafirah Samsurib, Nurul Aini Amranb, Nor Zanariah Safieic, Mazura  

Jusohd,e, Farah Hanim Ab Hamida* 

a School of Chemical Engineering, College of Engineering, Universiti Teknologi MARA, Selangor, Malaysia 
b Chemical Engineering Department, Universiti Teknologi PETRONAS, Seri Iskandar, Perak, Malaysia. 
c UniKL MICET, Lot 1988, Kawasan Perindustrian Bandar Vendor, Taboh Naning, Alor Gajah, Melaka, Malaysia. 
d Institute of Bioproduct Development, Universiti Teknologi Malaysia, Malaysia 
e Advanced Material and Separation Processes Research Group, School of Chemical and Energy Engineering, Faculty of 

Engineering, Universiti Teknologi Malaysia, Malaysia 

 farah88@uitm.edu.my 

Antioxidants have been a vital component of several pharmaceutical and food industries due to their numerous 

benefits such as reducing the risk of diseases. Cucumbers are known to contain considerable amounts of 

antioxidants and a significant amount of water, which increase the probability of microorganism growth. 

Therefore, it is essential to find out the best approach to reduce the water content and preserve the antioxidants 

in cucumbers. Progressive Freeze Concentration (PFC) is a concentration enhancement process, whereby 

impurities are removed in a single ice block. This research is intended to determine the effect of coolant 

temperatures (-2°C to -10°C) on the preservation of antioxidants in cucumbers using the PFC process. The 

antioxidant content in concentrated cucumber juice was assessed by the 2,2-Diphenyl-1-picrylhydrazyl 

(DPPH)  assay. It was determined that the lower the coolant temperature used in the PFC process, the lower 

the amount of antioxidant content. The optimum coolant temperature was discovered at a temperature of -2°C, 

where the antioxidant activity percentage (AA%) was at 93.17 %. A heat transfer model to predict the mass of 

antioxidants procured was also constructed from the study. Data comparison between experimental values and 

the model resulted in the Average Absolute Relative Deviation (AARD) value of 0.74% which is considered 

highly consistent. Therefore, the model constructed to predict the AA% of the concentrated cucumber juice with 

different coolant temperatures was successful. 

1. Introduction 

Antioxidants are molecules that fight free radicals in the human body which are produced through the oxidation 

reaction. Antioxidants are essential to the human body as excessive production of free radicals can lead to over-

concentration and cause oxidative stress, which harms the body (Lobo et al., 2010). Cucumbers are vegetables 

that have considerable amounts of antioxidants. Multiple research and analysis have been conducted in the 

chemical industries to find ways to fully utilize the content of antioxidants in cucumbers that are highly beneficial 

to the human body. 

Progressive Freeze Concentration (PFC) is a process that concentrates a solute in an aqueous solution through 

partial freezing of the solution which separates the solid and liquid phases, resulting in a concentrated solution 

(Munson-Mcgee, 2014). The progressive formation of ice crystal layers forms a single ice block on a cooled 

surface, which ensures an easier separation between the ice crystal and concentrated solution (Rosdi et al., 

2021). 

The 2,2-Diphenyl-1-picrylhydrazyl (DPPH) method was developed by Blois (1958) and was further modified by 

Brand-Williams et al., (1995). The DPPH is a stable, long-lived free radical, and possesses a deep purple colour 

property and strong absorption of around 517 nm (Akar et al., 2017). As the purple colour of the DPPH radical 

1393



solution reacts with antioxidants, a reduced form of the DPPH solution which is pale yellow in colour allows the 

spectrophotometric determination of the antioxidant activity of the tested medium (Gupta, 2015). 

Although the determination of the antioxidant in a food sample has been well developed and widely 

implemented, there is still a lack of studies on how heat transfer affected the amount of antioxidant recovery in 

the PFC process. Therefore, the objective of this research was to determine the effect of coolant temperature 

on the preservation of antioxidants in cucumbers via the PFC process. Additionally, this research was also 

conducted to analyse the heat transfer involved in the PFC process. 

2. Materials and methodology 

2.1 Preparation of cucumber juice 

50 g of fresh Japanese cucumbers were sliced and blended with 500 ml of water using an electric blender 

(LB20ES, Waring, USA). The blended cucumber juice was then sieved to extract the cucumber juice. 

2.2 Preparation of DPPH solution 

Preparation of 0.1 mM of DPPH solution was done by dissolving 3.94 mg of DPPH into 100 ml of methanol in 

a volumetric flask (Samsuri et al., 2020). The solution was then stored in a volumetric flask and wrapped with 

aluminium foil to prevent any contact and reaction with light. The solution was also stored in a darkroom and 

was only taken out before the spectrophotometry test. 

2.3 Progressive freeze concentration method 

The experimental instrument consists of a refrigerated bath, cylindrical crystallizer, stirrer, retort stamp, and 

clamp. The coolant used for the PFC process was a mixture of 50% ethylene glycol and 50% distilled water. 

The coolant was then set to the desired temperature. The cylindrical crystallizer was clamped to a retort stand 

and 500 ml of cucumber juice was poured into the cylindrical crystallizer. The speed of the stirrer was adjusted 

to its desired speed (175 rpm) and the timer was started simultaneously for 15 minutes. 

After a fixed time of 15 minutes, the stirrer was stopped and taken off the refrigerated bath. The concentrated 

cucumber juice was collected and stored in a beaker and was measured for its volume. 10 ml of the concentrated 

solution was measured and transferred into a test tube for DPPH assay. The experiment was repeated with 

different coolant temperatures (-2°C, -4°C, -6°C, -8°C, and -10°C). Figure 1 shows the setup of the  PFC process 

of cucumber juice. 

 

Figure 1: PFC equipment setup 

2.4 Analysis 

2.4.1 Antioxidant value 

As the concentrated cucumber juice undergoes the DPPH assay, its absorption reading was conducted using 

the UV-Vis spectrophotometer at 517 nm (Pyrzynska & Pȩkal, 2013). 2.5 ml of concentrated cucumber juice 

was mixed with 1 ml of DPPH solution and its absorbance reading was measured and recorded. The radical 

scavenging activity for antioxidant value (AA%) can be calculated using Eq (1), where Asample is the absorbance 

reading of the solution, and Acontrol is the absorbance reading of the DPPH solution with nothing added (blank). 

Scav. activity (AA%)= (1 - 
Asample

Acontrol
)  x 100% (1) 

2.4.2 Heat transfer analysis 

To develop the model in predicting the AA%, a few assumptions based on previous studies were made to 

simplify the development of the model (Samsuri et al., 2018). 

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1) All the heat transferred to or from the ice is utilized for the melting or freezing of the ice. 

2) Ice crystal on the surface of the crystallizer offers resistance, but no thermal capacity. 

3) The thickness of ice formed around the surface of the crystallizer is uniformly thick. 

4) Physical properties of cucumber juice and ice, such as density, specific heat capacity, and viscosity do 

not change during the PFC process. 

5) The temperature gradient across the heat transfer surface is assumed to be linear. 

6) Thermal property variation of the heat transfer surface material due to temperature change is negligible. 
7) Loss of heat to the surrounding is negligible. 

8) The temperature of the concentrated cucumber solution, Ts, during the PFC process is at 0 °C. 

3. Results and discussion 

3.1 Relationship between coolant temperature and antioxidant activity of cucumber juice 

In order to discover the relationship between coolant temperature and antioxidant activity, the other parameters 

such as operating time, stirrer speed, and initial concentration of cucumber juice were kept constant. The 

volumes of concentrated juice and ice produced were tabulated in Table 1. The collected concentrated 

cucumber juice was taken for a spectrophotometer test using the UV-Vis equipment to measure its 

concentration. From the data recorded in Table 1, the volume of ice increased with the decrease in temperature, 

which is in line with previous research findings (Miyawaki & Inakuma, 2021). However, the amount of ice 

formation also affected the antioxidant activity inside the cucumber juice. Therefore, the higher efficiency of ice 

formation does not lead to better extraction of antioxidants in the cucumber juice as the tendency for the solute 

(antioxidants) to be trapped in the ice formation increases (Mohd Rosdi et al., 2020). 

Table 1: Volume of concentrated juice and ice at different coolant temperatures 

Temperature (°C) -2 -4 -6 -8 -10 

Volume of conc. juice (ml) 390 380 355 320 285 

Volume of ice (ml) 110 110 140 165 210 

 

From Figure 2(a), it is observed that the lower the coolant temperature used in the PFC process, the lower the 

antioxidant activity (AA%) found in the cucumber juice. The optimum temperature at which the highest amount 

of AA% was found in the cucumber juice is at -2°C with 93% of AA% detected, showing that at this temperature, 

most of the antioxidant is successfully preserved. Meanwhile, the least amount of AA% was found at a coolant 

temperature of -10°C. The decrease in coolant temperature led to an increase in ice thickness but a lower AA%. 

This would further support the discussion whereby the efficiency of the PFC process in terms of the separation 

of solute and impurities via ice formation does not necessarily lead to a high AA%. Although the PFC process 

was successful in terms of ice formation with the decrease in coolant temperature, however, a coolant 

temperature that is too low will reduce the antioxidant activity of the cucumber juice. Therefore, it is crucial to 

determine the optimum coolant temperature at which the maximum amount of antioxidant activity is detected 

while collecting the maximum amount of ice formed. Figure 2(b) correlates the relationship between the mass 

of cucumber juice obtained post-PFC process and their respective AA%. The graph highlights that the AA% 

decreased as the mass of cucumber juice collected decreased. This would further support the conclusion that 

the antioxidants were trapped in the formation of ice as the temperature of the coolant decreased. 

  
Figure 2: Relationship between coolant temperature, antioxidant activity % and (a) ice thickness, and (b) ice 

mass 

3.2 Heat transfer analysis and model development 

Figure 3 illustrates the proposed heat transfer activities for the PFC process. T represents the temperature for 

each layer of the interface, whereas Ts is the temperature of the cucumber juice, Tm is the temperature of the 

1395



ice-liquid interface, Ti is the temperature at the ice-vessel wall interface, Tw is the temperature at the vessel wall-

coolant interface and Tc is the temperature of the coolant. Furthermore, q represents the heat transfer entering 

and leaving the cucumber juice. Lastly, dm/dt is the mass rate of formation of ice. 

 

 

Figure 3: Schematic diagram of heat transfer activities of PFC equipment 

3.2.1 Model formulation 

The model for predicting the AA% in the cucumber is based on previous studies (Samsuri et al., 2018), with 

several modifications. The model was based on the basic understanding whereby the heat that is released by 

the ice, vessel wall, and coolant, q1, is equal to the heat released by the cucumber juice, q2, and the product of 

mass of rate of formation of ice, dm/dt, and its latent heat of fusion, ∆H. The equation is expressed in Eq (2). 

 q
1
= q

2
+ (

dm

dt
)  ∆H (2) 

Since q1= Uo∆T, and q2= ∆T/R, Eq (2) can be further expanded into Eq (3), 

 Uo∆T= 
∆T

R
+ (

dm

dt
)  ∆H (3) 

where Uo represents the overall heat transfer coefficient (W. m-2. °C -1), ∆T is the temperature difference ( ° C), 

and R is the resistance (m2. °C . W-1). Thus, Eq ( 3) can be expressed as Eq (4), 

(
Tm- Tc

(
r

k.A
)

ice
+ (

r
k.A
)

wall
+ (

r
h.A
)

coolant

) = 

(

 
 Ts- Tm

(
1

h.A
)

juice)

 
 

+ (
dm

dt
)  ∆H (4) 

where, xice is the thickness of the ice crystal (m), and xw is the thickness of the vessel wall (m). Acoolant represents 

the surface area of the coolant (m2), Ajuice is the surface area of the cucumber juice (m2), kice is the thermal 

conductivity of ice (W. m-1. °C -1), and kwall is the thermal conductivity of the vessel wall (stainless steel) (W. m-

1. ° C -1). hcoolant  and  hjuice are the convective heat transfer coefficient (W. m-2. ° C -1)  for the coolant and cucumber 

juice, respectively. This study follows the assumption from a previous study (Samsuri et al., 2018), where Tw 

matches the average temperature between Tc and Ts since the two temperatures gave the most significant effect 

to Tw as compared to the other temperatures. Tm is also assumed be the water melting temperature (0° C ). In 

addition, the composition of the ice crystal is assumed as pure water. Thus, Eq (4) is converted to, 

𝑀 ice=  

(

 (
- Tc

(
r

k.A
)

ice
+ (

r
k.A
)

wall
+ (

r
h.A
)

coolant

) - Ts (h.A)juice

)

 t (5) 

Using a simple mass balance, the masses of the concentrated cucumber juice and ice can be obtained. 

MT refers to the total mass of solution, which consists of the mass of ice (Mice) and concentrated cucumber juice 

(Mconc.juice). Eq (6) shows the simplified equation after considering all the elements discussed. The experimental 

values are listed in Table 3 and constant values involved are listed in Table 4, respectively. 

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AA(%)= (
0.1742Tc

(
x

2.2 (A)
)

ice

+447.11
) -64.52 (MT - Mconc. juice-1.555) (6) 

Table 3: Data collected from PFC experiment 

Temperature (° C ) xice (m) Aice (m
2) Aconc. juice (m

2) MT (kg) Mconc. juice (kg) 

-2 0.0079 0.0031 0.0112 0.4750 0.3705 

-4 0.0087 0.0034 0.0109 0.4655 0.3610 

-6 0.0106 0.0042 0.0102 0.4703 0.3373 

-8 0.0135 0.0052 0.0092 0.4608 0.3040 

-10 0.0165 0.0062 0.0082 0.4703 0.2708 

Table 4: Constant values 

Parameter Value Unit 

kice 2.2 W/m. ° C 

kwall 15 W/m. ° C 

hcoolant 676.42 W/ m
2. ° C 

hconc. juice 2,273.45 W/ m
2. ° C 

Acoolant 0.0473 m
2 

Awall 0.0071 m
2 

xwall 0.015 m 

∆H 334,000 J/kg 

t 900 s 

 

3.2.2 Error analysis 

Table 5 displays the comparison between the AA% of the concentrated juice obtained from the experiment trials 

and the model in Eq ( 6). Both data from the experiment and model show a decrease in AA% with the decrease 

in coolant temperature. Thus, it can be concluded that the model can be used to forecast the AA% of a 

concentrated cucumber juice from a PFC process. 

Table 5: Comparison of AA (%) from model and experiment 

Temperature (°C) AAmodel (%) AAexp (%) 
|
AAexp-AAmodel

AAexp
| 

-2 93.30 93.17 0.001 

-4 93.03 93.02 0.0001 

-6 92.93 91.72 0.009 

-8 89.13 90.52 0.015 

-10 86.11 86.95 0.010 

Total Σ = 0.037 

 AARD = 0.74% 

 

The Average Absolute Relative Deviation (AARD) is used to determine the deviation between the data obtained 

from the model and the experimental values. Eq (7) expresses the equation for AARD. 

AARD (%)= 
1

N
 ∑

|AAexp- AAmodel|

AAexp
 x 100%

N

i
 (7) 

where N is the number of collected data. According to the data, the proposed model seems to have a good 
correlation with AARD value of 0.74%. The small value of AARD reflects a consistency between experimental 
data and predictable data. The AARD value less than 10% in margin of   error is considered rational and 
acceptable (Khair et al., 2017). On a laboratory scale, AARD values below 5% are highly consistent (Lucas et 
al., 2004). Therefore, the model developed can be used to predict the AA% of the concentrated cucumber juice 
with varying coolant temperatures. 

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4. Conclusions 

The extraction of antioxidants from cucumbers can be crucial as a means for preservation and prolonging their 

lifespan. The PFC process preserves the antioxidants with the removal of water which is one of the conditions 

for microorganisms to thrive. The coolant temperature has a significant effect on the antioxidant activity of 

cucumber in a PFC process. The lower the coolant temperature, the lower the antioxidant activity contained in 

the concentrated cucumber juice. It can be concluded that the optimum temperature at which contains the 

highest antioxidant activity percentage (93.17%) is obtained at -2°C. The model for predicting the AA% obtained 

was also successfully developed and can be used to predict the preservation of antioxidant of cucumber juice 

as the AARD value calculated was 0.74%. AARD values that are less than 5% on laboratory scale are 

considered highly efficient. This model shows the high accuracy in predicting the antioxidant recovery when 

varies temperature of coolant has been applied and it can be good guidance in determining the antioxidant 

activity particularly in the food industry. 

Acknowledgments 

The authors gratefully appreciate the support from Universiti Teknologi Malaysia under Collaborative Research 

Grant (CRG) 100-TNCPI/GOV16/6/2 (032/2020) and Universiti Teknologi MARA Shah Alam for technical and 

facilities supports. Not to forget the collaborators from Universiti Teknologi Petronas and UniKL. 

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	122cet-Azmy
	Heat Transfer Model: Preservation of Antioxidant via Progressive Freeze Concentration