DETERMINATION OF HEAT AND MASS TRANSFER PARAMETERS DURING FRYING OF POTATO SLICES by Ludwika Bergens

Journal of Food Engineering 79 (2007) 11–17 www.elsevier.com/locate/jfoodeng

Determination of heat and mass transfer parameters during frying of potato slices Aygu¨n Yıldız, T. Koray Palazog˘lu *, Ferruh Erdog˘du Department of Food Engineering, University of Mersin, C¸iftlikko¨y 33342, Mersin, Turkey Received 21 August 2005; accepted 7 January 2006 Available online 28 February 2006

Abstract In this study, effective heat (heat transfer coefficient) and mass transfer (mass transfer coefficient and moisture diffusivity) parameters were determined during frying of potato slices (8.5 · 8.5 · 70 mm) in sunflower oil at 150, 170 and 190 C. These parameters were evaluated from the plots of dimensionless temperature and concentration ratios against time. Heat transfer coefficient was found to decrease with increasing oil temperature. Mass transfer coefficient increased linearly, whereas moisture diffusivity increased exponentially with an increase in frying temperature. An Arrhenius type of relationship was found between the frying temperature and the effective moisture diffusivity. 2006 Elsevier Ltd. All rights reserved. Keywords: Frying; Heat transfer coefficient; Mass transfer coefficient; Moisture diffusivity

1. Introduction Knowledge of accurate heat and mass transfer parameters is important for modeling processes during which simultaneous heat and mass transfer take place. Deep-fat frying of potatoes is one such process which is performed by immersing the food material in hot (generally between 150–200 C) edible oil until it is cooked (Farkas, Singh, & Rumsey, 1996). During the frying process, heat is transferred from the hot oil to the surface of the food material, while moisture is transferred from the interior to the surface. As a result, high temperature and low moisture conditions develop as frying proceeds, and bring about the desirable characteristics (color, texture, and ﬂavor) of French fries. Recent research, however, shows that high temperature and low moisture conditions also gives rise to the formation of acrylamide, a potentially carcinogen substance. Acrylam-

Corresponding author. E-mail address: koray_palazoglu@mersin.edu.tr (T. Koray Palazog˘lu).

ide has been shown to form during heating of certain foods due to the interaction between asparagine and reducing sugars (i.e. glucose, fructose) at high temperatures and low moisture conditions associated with frying, baking, and roasting (Go¨kmen, Palazog˘lu, & S ß enyuva, 2005). Therefore, knowledge of critical processing variables is needed for improved product safety and quality. Designing of frying processes is possible through the use of mathematical models. Banga, Alonso, Gallardo, and Perez-Martin (1993) stated that a reliable simulation of the process using a mathematical model is essential for process optimization and control. The success of a model, however, depends on the accuracy of the knowledge of critical processing variables, namely heat transfer coefficient and mass transfer parameters (mass transfer coefficient and moisture diffusivity) in the case of frying. Since heat and mass transfer during frying are inter-related, they both need to be taken into account during investigation of a frying process. There is not enough research on the heat and mass transfer parameters during frying of potato slices. The few investigations have been limited to the determination

A. Yıldız et al. / Journal of Food Engineering 79 (2007) 11–17

Nomenclature heat transfer Biot number, hL k mass transfer Biot number, kDc L equilibrium moisture content of potato slice or moisture content of frying medium (0 kg/kg solids) Ci initial uniform moisture content of potato slice (kg/kg solids) C(x, t) moisture content at any point any time (kg/kg solids) CðtÞ average moisture content at time t (kg/kg solids) D eﬀective moisture diﬀusivity (m2/s) D0 Arrhenius constant (m2/s) Ea activation energy (kJ/mol) Bih Bim C1

of heat transfer coefficient, which generally involved the use of the lumped system approach or a simplified geometry (infinite plate or infinite cylinder). Several researchers (Budzˇaki & Sˇeruga, 2004; Costa, Oliveira, Delaney, & Gekas, 1999; Farkas & Hubbard, 2000; Hubbard & Farkas, 1999; Sahin, Sastry, & Bayindirli, 1999a, Sahin, Sastry, & Bayindirli, 1999b) determined the heat transfer coefficient by various methods during frying of potato dough and potatoes of different geometries. Sahin et al. (1999a) determined heat transfer coefficient during frying at temperatures between 150 and 190 C. They found the heat transfer coefficient during frying of the one-dimensional potato slice (50 · 50 · 3 mm) to be between 90 and 200 W/m2 K within the temperature range studied. They also reported that heat transfer coefficient increased, while moisture content and thermal conductivity decreased with the increasing oil temperature. Costa et al. (1999) investigated the effect of water loss rate on heat transfer coefficient during frying at 140 and 180 C using the lumped system approach and the surface temperature data. They found that heat transfer coefficient reached a maximum value of 443 W/m2 K at 140 C and 650 W/m2 K at 180 C for French fries. They reported that although the bubble movement during frying increase the rate of heat transfer, maximum levels of water loss rates may hinder the heat transfer. Hubbard and Farkas (1999) determined the heat transfer coefficient during frying of infinite potato cylinders at 180 C from the time–temperature data acquired at the product surface and reported that heat transfer coefficient increased from its initial value of 300 W/m2 K to 1100 W/m2 K during the frying process. This study was undertaken to develop a more realistic approach for determining heat and mass transfer parameters during frying of potato slices. The time–temperature and time–moisture content data experimentally obtained with the potato slices having a two-dimensional geometry

h k kc L R t T1 Ti T(x, t) x y

effective heat transfer coefficient (W/m2 K) thermal conductivity of potato (W/m K) effective mass transfer coefficient (m/s) half thickness (m) universal gas constant (8.314 · 10 3 kJ/mol K) time (s) temperature of frying medium ( C) initial uniform temperature of potato slice ( C) temperature at any point any time ( C) location where temperature is measured in infinite plate (0 6 x 6 L) location where temperature is measured in infinite plate (0 6 y 6 L)

were utilized to determine the heat and mass transfer parameters during frying from the dimensionless temperature and concentration ratio plots, respectively. 2. Materials and methods 2.1. Frying of potato slices Potato was cut into slices (8.5 mm · 8.5 mm) using a French fry cutter, and the length was adjusted to 70 mm. Potato slices were fried at 150, 170, and 190 C in a 5 L oil bath (Precisterm, J.P. Selecta, Spain) using sunflower oil by immersing only one strip at a time. Frying experiments were conducted in triplicate. 2.2. Temperature measurement Temperature was acquired, with an accuracy of 0.2 C, every 1 s using a digital multimeter (Model 2700, Keithley, Cleveland, OH) coupled with a 20-channel multiplexer (Model 7700, Keithley, Cleveland, OH) and a personal computer. Two thermocouples (36-gauge type-T, Omega Engineering, Inc., Stamford, CT) were inserted into the slice from both ends until the tip of the thermocouples were near the geometric center and far enough from the ends. This was done to eliminate the end effects since a two dimensional solution was adopted for the evaluation of heat transfer coefficient (Fig. 1). Oil temperature was also monitored and recorded using another thermocouple. 2.3. Determination of heat transfer coefficient Heat transfer coefficient was determined by starting from the solution of the differential equation for one dimensional heat conduction in Cartesian coordinates (Eq. (1)) employing the boundary conditions presented in Eq. (2).

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Fig. 1. Schematic of the experimental setup.

o2 T 1 oT ; 0 6 x 6 L for t > 0 ¼ ox2 a ot oT oT ¼ 0 k ¼ hðT jx¼L T 1 Þ ox x¼0 ox x¼L

ð1Þ T jt¼0 ¼ T i

ð2Þ

The following infinite series solution gives the temperature at any location within the infinite plate as a function of time: X 1 T ðx; tÞ T 1 2 sin ln ¼ Ti T1 l þ sin ln cos ln n n¼1 x at cos ln exp l2n 2 ð3Þ L L For the Fourier numbers ðLat2 Þ greater than 0.1, using only the first term of Eq. (3) provides sufficiently accurate results (Crank, 1975). The reduced form of Eq. (3) can be used to obtain the solution for the French fry geometry (finite in two dimensions) by making use of the superimposition rule (Eq. (4)). French fry geometry is, in fact, the intersection volume of two infinite plates with the same thickness intersecting each other perpendicularly (Fig. 2). T ðx; y; tÞ T 1 T ðx; tÞ T 1 ¼ Ti T1 Ti T1 finite plate infinite plate T ðy; tÞ T 1 Ti T1 infinite plate ð4Þ The first-term solutions for the two infinite plates with the same half thickness are given in Eqs. (5) and (6). The

Fig. 2. French fry geometry obtained by applying the superimposition rule.

product of these two equations (Eq. (7)) gives the solution for the French fry geometry. T ðx; tÞ T 1 2 sin l1 ¼ Ti T1 l1 þ sin l1 cos l1 x 2 at cos l1 exp l1 2 ð5Þ L L T ðy; tÞ T 1 2 sin l1 ¼ Ti T1 l1 þ sin l1 cos l1 y at cos l1 exp l21 2 ð6Þ L L T ðx; tÞ T 1 T ðy; tÞ T 1 2 at ¼ A exp 2l1 2 ð7Þ Ti T1 Ti T1 L

A. Yıldız et al. / Journal of Food Engineering 79 (2007) 11–17

oC ¼0 ox x¼0

Table 1 Thermophysical properties of potato Property

Value

Thermal conductivity, k (W/m K) Density, q (kg/m3) Speciﬁc heat, cp (J/kg K)

0.554 1090 3517

Source

Palaniappan and Sizer (1997) Singh and Heldman (2001)

ð8Þ

After taking the natural logarithm of both sides, Eq. (7) takes the following form: T ðx; y; tÞ T 1 at ln ð9Þ ¼ ln A 2l21 2 Ti T1 L 1 Þ is plotted against time, slope of the linWhen lnðT ðx;y;tÞ T T i T 1 ear section of this graph is equated to 2l21 La2 . Since the thermal diffusivity (a) and half thickness (L) are known, l1 can be determined. After this, the heat transfer Biot number (Bih) and the heat transfer coefficient are determined by using Eqs. (10) (the characteristic equation for infinite plate) and (11), respectively. Thermophysical properties of potato presented in Table 1 were assumed constant.

Bih ¼ l1 tan l1 hL Bih ¼ k

ð10Þ ð11Þ

2.4. Determination of mass transfer parameters Potato slice (8.5 · 8.5 · 70 mm) was mounted on a stainless steel wire and immersed into the frying medium and fried for different time intervals at 150, 170, and 190 C. Fried potato samples were sampled at 10, 20, 30, 45, 60, 75, 90, 105, 120 s and every following 30 up to 480, 360, and 240 s of the frying process for 150, 170, and 190 C, respectively. Surface oil was removed with a paper towel immediately after the removal of the samples from the oil bath and the moisture content of samples was determined by drying the samples to constant weight at 105 ± 1 C (AOAC, 1975). Four replicates were conducted for each frying temperature. Time–moisture content data of the potato samples of different time intervals were used in the mathematical method for the determination of the mass transfer parameters. The equation that gives the concentration as a function of time and location for an infinite plate (Eq. (14)) was obtained by solving the differential equation (Eq. (12)) with the given boundary conditions (Eq. (13)). o2 C 1 oC ; ¼ ox2 D ot

0 6 x 6 L for t > 0

oC ¼ k c ðCjx¼L C 1 Þ Cjt¼0 ¼ C i ox x¼L ð13Þ

Singh and Heldman (2001)

where A is deﬁned by the following equation: 2 x y 2 sin l1 A¼ cos l1 cos l1 L L l1 þ sin l1 cos l1

ð12Þ

Cðx; tÞ C 1 2 sin ln ¼ Ci C1 ln þ sin ln cos ln x 2 Dt cos ln exp ln 2 L L

ð14Þ

By taking only the first term of the infinite series solution given in Eq. (14) (for long processing R Vtimes) and integrating it throughout the whole volume ðV1 0 Cðx; tÞdV Þ, the equation for average moisture concentration in an infinite plate (Eq. (15)) was obtained. CðtÞ C 1 2 sin2 l1 2 Dt exp l1 2 ¼ ð15Þ Ci C1 l1 ½l1 þ sin l1 cos l1 L where CðtÞ is the average concentration at a certain time in kg/kg solids. By using the superimposition rule, Eq. (16) for the twodimensional French fry geometry is obtained. CðtÞ C 1 Dt ð16Þ ln ¼ 2 ln E 2l21 2 Ci C1 L where E is defined as follows: E¼

2 sin2 l1 l1 ½l1 þ sin l1 cos l1

ð17Þ

1 From the intercept of lnðCðtÞ C Þ–t plot, the first root of the C i C 1 characteristic equation (l1) was calculated. After determining moisture diffusivity, D, from the slope of the same plot, mass transfer Biot number (Bim) and mass transfer coefficient (kc) were obtained by using the relation given in Eq. (18).

Bim ¼ l1 tan l1 ¼

kcL D

ð18Þ

The temperature dependence of moisture diﬀusivity was determined using an Arrhenius type equation (Eq. (19)). Ea D ¼ D0 exp ð19Þ RT 3. Results and discussion Temperature inside the potato slices remained around 103–104 C throughout the whole frying process in all experiments. This observation was attributed to the interior not being dry enough to allow for internal energy increase. When the temperature reaches the boiling point of water, use of energy to vaporize the water keeps temperature from increasing until there is almost no water to vaporize. According to Claeys, De Vleeschouwer, and Henrickx (2005), temperatures above the boiling point of water are reached only when the food is almost completely dry. The boiling point of water within potato is reported to

A. Yıldız et al. / Journal of Food Engineering 79 (2007) 11–17

be slightly higher than that of pure water due to the presence of dissolved solutes (Budzˇaki & Sˇeruga, 2004). The plots of dimensionless temperature ratio against time obtained for different frying temperatures are presented in Fig. 3. As one can see from the figure, heating rate of the potato slice decreased with increasing frying temperature. The slopes of the linear sections of these plots (Fig. 4) were obtained through linear regression analysis and used to determine the effective heat transfer coefficient as explained above. A higher rate of heating is indicated by a larger slope. Effective heat transfer coefficient values for different frying temperatures, with their standard deviations, are presented in Table 2. These values are within the range of heat transfer coefficient values determined by different methods using various geometries by other researchers (90–1100 W/m2 K). According to the table, heat transfer Biot number (Bih), and hence h value decreased with increasing oil temperature. This may be attributed to the frying medium that is at a higher temperature resulting in water loss from the product at a greater rate. The greater the water loss rate, the larger the amount extracted from the incoming energy. This will reduce the

⎛

Table 2 Heat transfer Biot number and heat transfer coeﬃcient values with their standard deviations for diﬀerent frying oil temperatures Oil temperature ( C)

Biot number (Bih)

Heat transfer coeﬃcient (W/m2 K)

150 170 190

2.20 ± 0.12 1.74 ± 0.06 1.39 ± 0.05

286.7 ± 15.4 227.3 ± 8.0 181.3 ± 6.5

amount of energy available for internal energy increase and as a result the effective heat transfer coefficient will decrease. This finding contradicts those of Costa et al. (1999), Sahin et al. (1999a), and Budzˇaki and Sˇeruga (2004), who reported an increase in convective heat transfer coefficient with an increase in frying oil temperature. Effective mass transfer coefficient and moisture diffusivity values were determined from the slopes of the dimensionless concentration ratio vs time plots (Fig. 5). The slope, and hence the water loss rate was greater for higher oil temperature. The even greater slopes observed at the beginning of the frying processes are a result of the sudden Time (s) 60 80

100

120

-0.2

150° C

-0.4

190° C

140

170° C

-0.6

⎛

⎛Τ − Τ ⎛ In Τ − Τ∞ ∞ i

-0.8 -1 -1.2 Fig. 3. Dimensionless temperature ratio vs time plots obtained during the frying experiments.

Time (s) 0

0 -0.1

⎛

170° C 190° C

-0.3

⎛

⎛Τ − Τ ⎛ In Τ − Τ∞ ∞ i

-0.2

150° C

-0.4 -0.5 -0.6 -0.7

Fig. 4. Slopes of the linear sections of dimensionless temperature ratio vs time plots used in the heat transfer coeﬃcient determinations.

A. Yıldız et al. / Journal of Food Engineering 79 (2007) 11–17

Time (s) 0

100

200

300

400

500

600

0 150° C

-0.2

170° C 190° C

⎛

⎛C − C ⎛ In C − C ∞ ∞ i

-0.4 -0.6 -0.8 -1 -1.2

Fig. 5. Dimensionless concentration ratio vs time plots obtained during the frying experiments.

loss of free surface moisture. The linear sections of the plots attained as the frying proceeded were used in determining the mass transfer parameters. The values of these parameters, with their standard deviations, are given in Table 3. As one can see from the table, both parameters increased with increasing oil temperature. However, the increase in effective mass transfer coefficient was linear while that in effective moisture diffusivity was exponential. Activation energy (Ea) from the Arrhenius plot (Fig. 6) was found to be 27.6 kJ/mol (R2 = 0.931), which falls within the range of activation energies reported by McMinn and

Table 3 Mass transfer Biot number and mass transfer parameter values with their standard deviations for diﬀerent frying oil temperatures Oil temperature ( C)

Biot number (Bim)

Mass transfer coeﬃcient kc · 105 (m/s)

Moisture diﬀusivity D · 109 (m2/s)

150 170 190

5.32 ± 1.54 6.28 ± 1.21 4.84 ± 0.63

1.12 ± 0.22 1.58 ± 0.23 2.07 ± 0.24

9.2 ± 1.1 11.0 ± 1.0 18.2 ± 0.7

Magee (1996) for drying of potato cylinders (25.2– 36.2 kJ/mol). 4. Conclusion In this study, a methodology for determination of heat and mass transfer parameters during frying of potato slices was proposed. The method is based on the measurement of time-dependent temperature and moisture content of the potato slice. Previous methods for determining heat transfer coefficient rely on measuring surface temperature of the potato slice during frying. However, obtaining reliable surface temperature data using thermocouples involves difficulties. Furthermore, the fact that surface temperature will vary depending on the location where the measurement is taken (unless heat transfer takes place only in one dimension) only adds up to the difficulty of the task. The approach proposed for heat transfer coefficient determination in the present study does not require the knowledge of thermocouple location, thereby eliminating the potential errors associated with the methods that use surface temperature data. Acknowledgement

-1

0.0021 -17.7 -17.9

0.00215

0.0022

1/T (K ) 0.00225

0.0023

0.00235

0.0024

y = -3316.8x - 10.714

This research was supported by the Scientiﬁc and Technical Research Council of Turkey, TUBITAK (Project no.: MAG-103M061). References

ln D

-18.1

R = 0.931

-18.3 -18.5 -18.7 Fig. 6. Temperature dependence of the eﬀective moisture diﬀusivity.

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