Modelling of a Batch Deep-Fat Frying Process for Tortilla Chips

IChemE 0960- 3085/97 /$1 0.00+0.00 @ Institution of Chemical Engineers

MODELLING OF A BATCH DEEP-FAT FRYING PROCESS FOR TORTILLA CHIPS

Y. CHEN and R. G. MOREIRA

Department of Agricultural Engineering, Texas A&M University, Texas. USA

he process of deep-fat frying involves simultaneous heat and mass transfer and both frying and cooling conditions are critical to the final product quality. An understanding T of the complex frying mechanism is helpful to improve the quality of the final product. The frying process was simulated by applying energy and mass balance equations to a single chip and a batch of tortilla chips. The temperature, moisture content, and oil content were calculated as a function of frying time. Finite difference technique was used to solve the set of partial differential equations. Experiments were conducted to validate the mathematical model. The temperature of the chips and the temperature of the oil during frying were measured and comparisons between predicted and observed results showed that the model successfully simulated the batch frying processes for tortilla chips. The good agreements also validate the frying mechanism proposed by this study. The mathematical model was used to analyse the effects of different frying conditions on the oil, moisture, and temperature profiles during the frying of tortilla chips. Keywords: simulation; crust; core; thickness; oil content

INTRODUCTION Pravisani and Calvelo3 determined the minimum cooking time for potato strips under different frying conditions. Deep-fat frying is a very important food processing Gamble et al.4related the oil absorption with the remaining operation which offers unique texture and flavour to the moisture content while Moreira et al.5 indicated that the product and is commonly used by the multi-million dollar cooling process after frying affects the oil content of the snack food industry. About 65% of all snack products in the final products. Gamble and Rice6.7studied the effects of pre- United States are deep-fat fried. In 1995,.deep-fat fried frying treatments and the product shape on the frying foods contributed to approximately $9.82 billion in annual process of potato slices. Pinthus et al.8analysed the effect of sales, according to the Snack Food Association. initial porosity on the oil absorption of restructured potato Tortilla chips are a popular snack food in the United products and Pinthus and Saguy9 studied the relationship States ranking second only to potato chips in the salted between initial interfacial tension and oil uptake for snack food market and are considered to be one of the restructured potato products. fastest-growing segments of the grain-based food industryl. Few articles studied the dimensional changes of food Although different types of products and different types products during frying. Moreira et al.lO,using the magnetic of fat/oil are used in the frying operation, they have to be resonance image (MRI) technique, found that the thickness subjected to a frying oil temperature ranging from 160- of a tortilla chip after 60 seconds of frying increases by 200°C. Basically two types of fryers exist: the smaller static about 40 percent as a result of expansion caused by an batch fryers used by the catering/restaurant/fast food outlet increase in porosity. and the large continuous fryers used on the industry scale to Many attempts have been made to combine heat and mass produce high volumes of frying products. Typical batch transfer principles to describe the temperature and moisture fryers have capacities ranging from 5 to 25 litres. The contentprofilesin a productin deep-fat frying processes10-13. industrial continuous fryer size can range from 100kg to All these models deal with the frying of a single piece of a 4oo0kg product per hour 2. product and assumed constant physical properties. The Many physical, chemical, and nutritional changes occur practical importance of these informations are limited in foods during deep-fat frying. Many of these changes are because foods are seldom fried as individual pieces. Instead, functions of oil temperature, product moisture, oil content, tortilla and potato chips, French fries, etc., are fried either in and product residence time in the fryer. Undesirable effects a stationary (batch fryer) or moving bed (continuous fryer). could be minimized and the process could be better Depending on the fryer size, oil volume, batch size, and controlled if temperature, moisture, and oil distributions in water content of the product, a temperature drop of 30 to food with respect to time could be accurately predicted. 45°C of the frying oil can be observed in industrial Research has been focused on different aspects of the frying operationsl4. Isothermal frying is only possible when operation to obtain' a better understanding of the process. frying a single piece of a product. In addition, the significant 181 182 CHEN and MOREIRA changes in the physical properties of a product during frying fully understand the frying mechanism. This is not the cannot be neglected. subject of this paper and the reader should refer to Moreira The objectives of this study were: and Barrufet15for a detailed description of oil absorption (1) to develop a mathematical model to analyse heat and mechanism during cooling. mass transfer duringbatch frying of tortilla chips considering changes in the properties of the product during frying; Assumptions (2) to validate the model; and (3) to use the mathematical model to study the effect of The assumptions made in this study were the following: frying conditions (temperature of the frying oil, thickness, (1) The tortilla chip is considered to be initially isotropic and initial moisture content of the chip) on the heat transfer, and isothermal. The initial moisture and temperature mass transfer, and oil absorption rates during frying. distributions in the chip are uniform. (2) Because the thickness of the tortilla chip is smaller than MATHEMA TICAL MODEL DEVELOPMENT the other dimensions, an infinite slab model was assumed in the study. A one dimensional heat and mass transfer model The Problem Description was considered. Figure 1 shows the cross section of a tortilla chip being (3) The heat required for chemical reactions (i.e., starch fried. Heat is transferred by convection from the oil to the gelatinization, protein denaturation) is small compared to surface of the chip, and by conduction to the centre of the the heat required to evaporate the water. chip. There is, however, a certain transfer of heat coupled to (4) Changes in the length of tortilla chip is negligible the transfer of water or vapour that is the energy carried by compared to changes in thickness during frying. Tortilla the water vapour. Most of the water escapes from the tortilla chips puff during frying (i.e., become thicker)lO. chip in the form of vapour during frying, and a small (5) Thermal and physical properties are functions of local percentage of the frying oil also diffuses into the chip5. temperature and moisture content during the frying process. Diffusion of moisture and diffusion of oil are in two (6) A 'microscopically uniform' porous medium is formed opposite directions. While the moisture content decreases, after frying. The surface of the chip is covered with a the oil content increases causing the chip to become more uniform layer of oil after frying and most of the oil diffuses porous during frying. into the chip after frying during the cooling period. Two regions, crust and core, exist during frying. The (7) In this study,the volumeof frying oil in the fryer kettle to crust/core interface moves towards the centre of the chip the volume of chips ratio was around 15, i.e., around 20-50 during frying. At the interface, the temperature remains at chips were placedin a 5x 10-4m3basket and then into a fryer the water boiling point for a short period of time to allow for kettle containing 7.5x 10-3m3 of oil. It was observed that the water presented in that region to evaporate. only the oil that was in direct contact with the chips (in Thermal and physical properties change greatly during between the chips) was affected by the chips moisture loss frying. The bulk density of the food material decreases duringfrying,whereasthe changein temperatureof therest of during frying and the food becomes more porous. The the oil in the kettle was negligible.Therefore,it was assumed thermal conductivity decreases as the porosity increases and that the fryer consistedof two oil zones, and the exchange of the specific heat decreases as moisture content decreases energybetweenthese two zoneswasby convectiononly. This while oil content increases during fryinglO. would not be true for the case of continuous frying or if the When a tortilla chip is taken out of the fryer, it is covered volume oil/volume chips ratio was small. with a thin layer of oil. As the temperature of the tortilla chip decreases by natural convection with ambient air, the vapour pressure within the pores of the chip decreases, Governing Equations forcing the surface oil to flow into the chips. Because of its symmetry, the computational domain may Moreira et al.5 indicated that almost 80 percent of the oil be simplified to a half section of a tortilla chip. The is absorbed by the tortilla chips during the cooling period. temperature (0), moisture content (M), and oil content (F) in Investigation of the cooling process is very important to

Batch fryer with tortilla chips

.L I q I Oil Oil :I- I F F - I -

Crust Cote Crust I I , tortilla chips temperature,8(X,t) x=-U2 x!o x=U2 'oilat varying temperature, T(t)

Figu~e 1. Tortilla chip undergoing frying. Figure 2. Batch fryer of tortilla chips.

Trans IChemE, Vol 75, Part C, September 1997 MODELLING OF A BATCH DEEP-FAT FRYING PROCESS FOR TORTILLA CHIPS 183 a batch of tortilla chips as well as the oil temperature (T) (equations (13) and (15)) slow the rate of heat transfer and change dramatically during frying. Energy and mass therefore the rate at which the product cooks and water balances were written on a differential volume located at vapourizes. an arbitrary position in a batch fryer containing tortilla chips Two boundary conditions and one initial condition are (see Figure 2). The basic one dimensional heat and mass needed for each governing equation. The first boundary diffusion equations were employed. Thus, these four condition is a symmetric condition at the centreline of the balances result in four equations. slab (equation 6). The second boundary condition is a convection surface condition (equations (7)-(9)). (I) The governing differential equation describing the At x = 0 (centreline) for any time, no temperature, temperature change in the product during frying is, moisture, or oil gradient exists at the centre of tortilla chips, ~ /}O _ a(rCpwO) = a(PbCpO) (I) ax( ax) ax at axao = 0; aMax = 0; aFax= 0 (6) The second term in the left side of the equation represents At x = :t U2 (surface) for any time, the energy the heat transfer caused by diffusion of water vapour, where transferred by convection from the oil to the chip's surface r is the water vapour flux, is equal to the sum of energy required for transferring heat to the centre of the product by conduction, for evapourating r = _ a(PbDwM)ax (2) water from the chips, and for heating the water vapour evaporated from the chips at temperature 0 to the oil (2) Fick's Law of diffusion was used to calculate the mass temperature T, transfer rate in the product in two different directions: ao moisture (water vapour) diffuses from the chip to the oil and the oil diffuses from the surface to the centre of the chip, h(Osur- T) = -k ax + hfgr + rCpw(Osur- T) (7a) . The second term at the right side of equation (7a) is ~ D aM = a(PbM) 3 ax wPbax at ( ) eliminated when the temperature of the chip is above the ( ) boiling point of water, ao ~ D aF = a(PbF) (4) ax ( 'fPbax) at h(Osur- T) = -k ax+ rCpw(Osur- T) (7b) (3) The temperature of the oil will decrease significantly withtwo masstransferboundaryconditions, during the first seconds of frying when tortilla chips are kdPb(Msur- M_) = -r (8) dropped into the fryer. The change in enthalpy of the oil with respect to time in the void space (between tortilla where M_ = Me= 0, i.e. the moisture content of the chips) is equal to the sum of energy required for heating the surrounding oil. And, product, for evaporating water from the chips, for heating a(F) the water vapour evaporated from the chips, and for kf(Fsur - F_) = -Dfax (9) exchanging energy to the surrounding oil. The equation for calculating the changes in the temperature of the oil is, where F_ = Fe = 1, i.e. oil content of the surrounding oil. The mass transfer coefficients (kf and kd) should be a aT ao a(PbM) function of the mass flux of water leaving the chip. The use of constant values are a limitation to the model; however, at Poi/Cpoi/ at= [-k ax + hfgDw~ present these data are not available and further work will provide the necessary information on the coefficients. + rCpw(Osur - T)] (I ~ cf» The initial conditions for any location x in the chip at time zero are the following, + hsS(Tfo- T) (5) O(x,O) = 00; M(x, 0) = Mo; Equations (I) to (5) are used to describe temperature and F(x,O) = Fo;T(x, 0) = Tfo (10) moisture changes at all points in the chip (i.e. core and crust). Inside the crust there is an evapouration zone that The above four governing equations and 10 boundary moves towards the centre of the product. In the evapouration conditions can be solved simultaneously by using finite zone, the temperature is constant, and the energy is mainly difference technique. Heat and mass transfer equations are used to evaporate the water. The duration of this constant coupled by the transport properties and thermal properties period depends on the water content in that location. As the which are functions of moisture content and temperature. water content is reduced at the level corresponding to Me, Equation (5) is used to calculate the temperature of the oil the temperature increases rapidly and this part of the product between the chips at each time step and this value is then becomes part of the crust. Different thermal properties were used in equations (1)-(4) to obtain the temperature, used in this study (equations (11)-( 17))for the two different moisture content and oil content profiles in the chip zones in the product. When the temperature of the chip was during batch frying process. higher than the boiling temperature of water, the properties of vapour instead of liquid water were used to predict Solution of the Mathematical Model temperature and moisture changes in the product. The crust has thermal and physical properties of an insulating This study employed a control-volume formulation to material. Its low 'thermal conductivity and porosity discretize the governing equations, initial conditions and

Trans IChemE, Vol 75, Part C, September 1997 184 CHEN and MOREIRA boundary conditions. The continuous physical space define when the computed results no longer depended on the (infinite slab) was divided into a number of non-overlapping choice of.::lxand tJ..t. control volumes in the x-direction so that one control Explicit finite difference technique was used in this study. volume surrounded each node. The differential equations The temperature, moisture content, and oil content of any were integrated over each control volume, and the control node at t+tJ..t was calculated from the knowledge of volume formulation method obtained the finite-difference temperatures, moisture contents, and oil contents at the equation by applying conservation of energy to a control same and neighboring nodes for the preceding time t. volume around each node. The most attractive feature of Hence, the determination of a nodal temperature and this method is the resulting solution would imply that the moisture/oil content at one time is independent of integral conservation of energy is exactly satisfied over any temperatures and moisture/oil content at other nodes of group of control volumes and over the whole calculation the same time. In this method, the choice of.::lxis based on a domain. compromise between accuracy and computational time After the discretization of heat and mass transfer requirements, as mentioned above. Once this selection has equations for every node, a set of simultaneous algebraic been made, however, the value of tJ..tmay not be chosen relationships were obtained and solved to obtain the independently. It is, instead, determined by stability transient temperature, moisture content, and oil content at requirements. For a one-dimensional node, the following each node. The flowchart for the computational procedure criterion was used to select the maximum allowable value of of the frying process is shown in Figure 3. Fo, and hence dt, to be used in the calculation:

Fo(1 + Bi) :S! (11) Grid Sensitivity and Stability where Fo = Fourier number, Fo = at/P; a = thermal From the mathematical point of view, the development of the mathematical model could not be ended at this step. diffusivity, a = k/pCp [m2/s-I]; I = half of the thickness [m]; t = time,s, andBi = Biotnumber,Bi = hl/k. Even when the finite difference equations have been A series of tests were conducted for the model to properly formulated and solved, the results might still determine the effect of time and distance grid size (.::lx,tJ..t) represent a coarse approximation to the exact solution. A on the output of the program. The output was the numerical simulation enables determination of the temperature at only discrete points which represents the average temperature at the surface and the centre, average moisture value of the surrounding region. content, and average oil content. The following tests and results, as shown in Table I, were accomplished with a However, the finite difference approximations could be made more accurate as the nodal network was refined. The constant frying oil temperature of 190°Cand frying time of 80 seconds. cost is that the computer takes longer CPU time to complete The temperature outputs were almost identical but Test 2 the iterations. A grid sensitivity study was performed to and Test 3 required longer computation time. To minimize the time required for processing and yet give the maximum accuracy, a time step of 0.01 s and distance step of 0.1 mm were chosen and further tests were done to test the convergence and stability of the program. For a time step of 0.01 s, the program was still convergent if.::lxchanged in a certain range. But Test 4 could hardly satisfy the accuracy requirement. The output of Test 6 was also not satisfied and Test 7 failed to converge because equation (II) was not satisfied. Therefore, all computations were performed with a PC- mM (Pentium 90, 8MB Ram), with time step of 0.01 sand distance step 0.1 mm16.The computer program to solve the above problem was written using MATLAB (The Math- Works, Natick, Ma).

Thermal and Physical Properties Used in the Model The mathematical model requires physical and thermal property data of the material to be fried and the process conditions used. While most property data were obtained from values reported in the literature, some of the properties were analysed and determined in this study. Thermal conductivity, k, of the tortilla chip during frying was found to have the following correlationsI?: for ():S lOO°C(R2 = 0.98) k[W/m°C] = 0.1085 + 0.OO9986()

Figure 3. Row diagram of the computer program. - 5.203 x lO-6()2 (12)

Trans IChemE, Vol 75, Part C, September 1997 MODELLING OF A BATCH DEEP-FAT FRYING PROCESS FOR TORTILLA CHIPS 185

Table 1. Time and space size test of the numerical simulation of the frying problem.

Temperature* Moisture** Oil** Test number , rnrn ilt, s rOC] [%wb] [%wb]

I 0.1 0.01 184.65 6.9 4.1 2 0.05 0.0025 185.08 6.5 3.1 3 0.025 0.001 185.87 6.3 2.8 4 0.1 0.02 186.36 6.7 4.1 5 0.1 0.005 183.86 7 4.1 6 0.2 O.oI 181.41 8.1 7.4 7 0.05 O.oI error error error

* Centre temperature of the chip; ** Average moisture/oil content of the chip

for (» 100°C (R2= 0.99) determine the effect of process parameters and product initial conditions on the frying process of tortilla chips. k[W/m°C] = 0.06938 + 9.997 x 1O-5()

+ 6.327 x 1O-8()2 (13) MATERIALS AND METHODS

Changes in the tortilla chips specific heat (Cp) with The model was designed to predict temperature, moisture temperature were small compared to changes with moisture and oil profile of tortilla chips during the frying process. The content. The effect of moisture content on the tortilla chip's model can be used to analyse the effect of different process specific heat was calculated as17, variables and initial product conditions on the final quality of frying products. Cp[kJkg-10C] = 2.506 + 2.503Md - 1.557MJ (14)

where Md is moisture content in decimal (db) for Tortilla Chip Preparation 1.22

where [MC is the initial moisture content (decimal, wb) before2 frying and Tabs is the absolute temperature, K Table 2. Parameters used in the simulation of a batch of tortilla chips fried (R = 0.94) . at 190°C for 80 s. Oil diffusion during frying increases as the initial Parameter Value Source moisture content of the tortilla chip increases18(R2 = 0.99), kd 0.00128ms-1 Moreira and SunlS (17) h 285Wm-2K-1 Moreira and SunlS kf 1.3 x 10-6 ms-I Chenl6 the diffusion coefficients (Df and Dw) should be a function hfg 2250kJk -I Moreira and SunlS hs 12ooWm-K-l Chenl6 of the x and local moisture content; however, at present CPw 4.2kJkg-lK-1 Chenl6 these data are not available and futher work will provide the CPv 2.0kJkg-lK-1 Chenl6 necessary information on these coefficients. CPf 2.2kJkg-1K-l Choi and OkOS21 Other property data used in the program are given in S 0.0459 m2m-3 Chenl6 cf> 0.5 Chenl6 Table 2. Symbols explanation is in the nomenclature A 0.00276m2m-3 Chenl6 section. The mathematical model was then used to

Trans IChemE, Vol 75, Part C, September 1997 186 CHEN and MOREIRA tortilla chips were then cooled down, sealed in zipped Temperature Changes During Frying plastic bags and stored in a desiccator for further analysis. The temperatures at the centre of the tortilla chip during Tortilla chips with different initial conditions and frying predicted by the model and obtained experimentally different process conditions were prepared for various are shown in Figures 4 and 5 for single and batch processes, purposes: respectively. As it was expected, the temperature at the 1) Tortilla chip thickness-two levels: 1.6mm and 2.6mm. centre of the chip increased to the boiling point of water, The thickness was obtained by adjusting the roller gap of the remained constant until all water vapourized (10-15 s), then sheeter/former. continued to rise and reached the oil temperature. 2) Baking time of the tortilla chips-three levels: no baking In both cases, single and batch, the model was able to (0 second), 45 seconds, and 90 seconds. This test was predict the temperature profile behaviour of the chips during designed to obtain tortilla chips with different initial the process very well. The difference, however, between the moisture contents before frying. predicted and observed temperature data for both processes 3) Temperature of the frying oil-three levels: 190°C, could have been caused by the difficulty to accurately locate 160°C,and 130°C. The frying time was 60 seconds for the and maintain the thermocouple at the centre of the chips, 1.6mm thick tortilla chips and 80 seconds for tortilla chip especially during the batch frying process when the chips with thickness of 2.6 mm. The temperature history at the are continuously in motion. This factor also resulted in a centre of the chip (thickness of 2.6 mm) was measured by relatively large standard deviation (see error bar in Figures 4 inserting a thin thermocouple (Type E,-0.25 mm) in the and 5) in the temperature measurements. centre of the chips. The temperature of the frying oil was For a single chip frying process, the temperature of the oil measured with a thermocouple (Type E,-0.81 mm). At least is almost constant during the entire frying process. three measurements were made for each test condition. However, for batch frying, the oil temperature drops 4) Batch frying and single chip frying were compared by substantially and then increases gradually to the fryer frying one chip at a time and a batch of chips (20 to 50) at a setting temperature. Figure 6 shows the predicted and time using the same fryer. observed results of the frying oil temperature change during a batch frying process for tortilla chips. Good agreement Moisture and Oil Content Measurements was obtained between the model and the experimental results with the exception of the first five seconds of frying. Moisture contents at different frying times were measured. This could be caused by lack of uniformity in the oil bath Approximately 10 pieces of each sample were ground in a temperature before the batch of chips was placed into the householdgrinder (Regal,Model 7450, China). The moisture fryer. As the frying proceeded, however, the chips spread content was determined by weight loss after drying the uniformly in the basket so the temperature distribution ground sample 24 hours at 103-105°C in a forced air oven19. became more uniform and better agreement between Oil contents at different frying and cooling times were experimental and predicted data was obtained. determinedwith the petroleum ether extractionmethod19in a Both experimental and predicted results indicate that the Soxhlet apparatus (Model HTl043, Tecator, Sweden). temperature of the oil changes greatly during the initial All the measurements in this study were made at least in seconds in batch frying process. The study of this process is triplicate. very important for industrial practice.

RESULTS AND DISCUSSION Using the thermal and physical properties specified in the Moisture Content Changes During Frying previous section, computer simulations were conducted to The average moisture content was calculated in the compare the mathematical model with the experimental computer program by numerically integrating the moisture results. profile at each time step. This average moisture content was

200 200

180 180

160 160

~ 140 ~1~ 'Q; 120 ~ 120 :; .a OJ100 ~ 100 Q; Q) c. ~ 80 E 80 - Predicteddata Q) - Predicteddata Q) :t: Experimental data I- 60 :t: Experimentaldata I- 60 40 40

20 20 o o o w ~ ~ ~ W ~ ro M 00 o 10 20 30 ~ 50 60 70 80 Time[s] Time[s]

Figure 4. Predicted and experimental results of tortilla chip's centre Figure 5. Predicted and experimental results of tortilla chip's centre temperature during frying (oil temperature = 190°C; initial moisture temperature during frying (oil temperature = 190°C; initial moisture content = 48.8% wb; chip thickness = 2.6mm; single chip frying). content = 48.8% wb; chip thickness = 2.6 mm; batch frying of 50 chips).

Trans IChemE, Vol 75, Part C, September 1997 MODELLING OF A BATCH DEEP-FAT FRYING PROCESS FOR TORTILLA CHIPS 187

200 0.5

190 T=130.C 0.4 - 180 - - T=160.C :c .! . . . T=190.C ~ 170 ';' 160 0.3 :; E m 150 8 Q; I . 0.2 '"~ 140 u; t- 130 Predicted '0 . :t: Experimental 120 0.1

110

100 0.0 .20 .10 0 10 20 30 40 50 60 70 80 90 100 o 10 20 30 40 50 60 Tlme[s) Tlme[s)

Figure 6. Oil temperature change during batch frying process (settling Figure 8. Predicted and experimental results of tortilla chip's average temperature of the oil = 190°C; chip thickness = 2.6 mm; initial moisture moisture content during frying as affected by frying oil temperature (initial content = 48.8% wb; batch frying of 50 chips). moisture content = 44% wb; chip thickness = 1.6mm, batch frying of 20 chips). then compared with the experimental data. As expected, the moisture content decreased greatly at the beginning of the model developed and verified the frying and cooling frying process and then reached equilibrium at the end of the mechanisms proposed by this study. The following frying process (see Figure 7). Moisture loss reached sensitivity analysis was conducted to analyse the effect of equilibrium in 60 s of frying for tortilla chips fried at different processing parameters on the frying and cooling 190°C oil temperature, requiring longer time for tortillas processes of tortilla chips. fried at lower temperature (see Figure 8). The predicted data were in good agreement with the experimental data. Convection heat transfer coefficient In this study, the convection heat transfer coefficient (h) value of 285 W m-2K-l 17was used throughout the frying Oil Content Changes During Frying process. During the deep-fat frying process, the water The average oil content during the frying process was vapour bubbles escaping the surface of food would cause determined by numerically integrating the oil profile at each turbulence in the oil and increase the convection heat time step in the computer program. Only the average oil transfer coefficient between the oil and the chips. The content was calculated during the cooling process and this convection heat transfer coefficient is also enhanced due to average value was then compared with experimental data as the movement of the chips during the batch process. A shown in Figure 9. Both the experimental and the simulation sensitivity test was performed by increasing the h value of results indicated that the diffusion of oil is very slow during 285 W m-2K-l by 25 percent and 50 percent (356 and the frying process. 427 W m-2K-1, respectively), to examine the effect of this parameter on the frying process of tortilla chips. The centre temperature of the chip during batch frying process did not Analysis of the Frying Process change significantly even when the convection heat transfer The good agreement between the predicted and the coefficient was 50 percent higher (see Figure 10). As the experimentaldata confirmedthe validity of the mathematical centre temperature of the chip is not affected by the value of the convection heat transfer coefficient, it is concluded that

0.6 0.12 0.5 . experimental - IMC = 0.54 w.b. - predicted 0.10 - - IMC = 0.44 w.b. i 0'4 \ . . . . IMC = 0.27 w.b. - \ :c 0.08 ~ \ .! 0.3 "\. E g .$ 0.06 . ~ . \. c: 0 :; ".',. "- u .!!2- 0.2~ '. "- o "...... 5 0.04 ~ 0.1-1 ...... ,~~~ . 0.02 0.0 o 10 20 30 40 50 60 Time [s) 10 20 30 40 50 60 Tlme[s] Figure 7. Predicted and experimental results of tortilla chip's average moisture content during frying as affected by tortilla chip's initial moisture Figure 9. Predicted and experimental results of tortilla chip's average oil content (oil temperature = 190°C;chipthickness= 1.6mm,batchfrying content during frying (oil temperature = 190°C; initial moisture con- of 20chips). . tent = 44% wb; chip thickness = 1.6 mm).

Trans IChemE, Vol 75, Part C, September 1997 188 CHEN and MOREIRA

200 200 0.5

180 180 - _.-'~ ~,.., ~ ~.~ , -" - 160 /./.- 160 .-"., f-0.4 ,,/." /. /../. thickness= 1.6 mm .ci /. / /./ Thickness =2.6mm ~ 140 /. 140 = ~ /." ~ /.: 0.3 'E /..: 120 CD ~ 120 ~ 'E ~ ...>::/ / o e (.) ~ 100 ~ 100 E E 2! 0.2 ~ ~ 80 80 en ~ '0 h 3 285 W/m2K :::;; 60 - 60 .. h. 356 W/m2K 0.1 40 -- h=427W/m2K 40 20 "~~ o 10 20 20 I I r I" I I . I ' . , I I I' . I 10.0 30 40 50 60 70 80 o 10 20 30 40 50 60 70 80 90 100 110 Tlme[s] Time[s]

Figure 10. The effect of convection heat transfer coefficient on the centre Figure 12. The effect of thickness on the temperature and average moisture temperature of tortilla chips during batch frying process (oil content of tortilla chips during frying (oil temperature = 190°C; initial temperature = 190°C; initial moisture content = 48.8% wb; chip thick- moisture content = 44% wb; chip thickness = 1.6 mm; batch frying of 20 ness = 2.6 mm; batch frying of 50 chips). chips). the frying process and the quality of the final frying products temperature profile in the core region was unaffected by are not sensitive to changes in the convection heat transfer the oil temperature. coefficient. This result indicates that the convection heat The average moisture content of the chips decreased transfer is of minor importance during frying because the faster when the oil temperature was higher, as expected (see main resistance to heat transfer is inside the product, as Figure 11). The higher the oil temperature, the higher the observed by Hallstrom2o. diffusion coefficient and thus the higher mass transfer of water vapour. To achieve the same final moisture content Frying oil temperature (2% wb), chips fried at 190°Coil temperature only needed Thefryingoiltemperatureisanimportantparameterin frying 60 seconds of frying while 90 seconds was required to fry because the oil serves as a heating medium in the process. the chips in the frying oil maintained at 160°C. Differentoiltemperatureswereusedin themodelto analysethe It was observed17that as the water evaporates from the effecton temperatureand moisturecontentof the chips. chip, during the first 10s of frying, the product becomes Figure 11 shows the temperature history at the centre of harder (crust formation) due to faster water evapouration the chip using different frying oil temperature (160°C and resulting in the formation of a structure with a number of 190°C). The temperature of the chip increased up to the small pores. As frying continues, the pore starts to enlarge boiling point of water at the same rate regardless of the (due to vapour expansion), the material expands and temperature of the frying oil. It was observed that the centre becomes crispier (decreased hardness). In the last stage of temperature in the chip increased much faster for the chip frying (30-60 s), the pore stops expanding due to the fried in the oil at 190°C than fried in the oil at 160°C. increase in the matrix complex viscosity since the amount of However, in both cases the temperature of the chips reached plasticizing water has been greatly reduced. Similary to the temperature of the frying oil after 60 seconds of frying. drying, it is believed that the average Tg of the material A similar phenomenon was observed by Farkas et al.12,who elevates above the frying temperature thus stopping suggested that the temperature profile in the crust region expansion rates and increasing porosity. The bulk porosity was mainly a function of oil temperature while the is then formed only at the end of the frying process.

200 0.5 - IMC=0.27wb 180 200]180 -- IMC=O.54wb __ fo.6 0.5 160 0.4 160 .ci .ci 140 ~ 140 0.4 ~ 0.3 'E CD 'E 2! 120 CD CD ::J 'E :; 120 e 0.3 g CD 100 8 e (.) Co ~loo CD E 0.2 E :; 80 en '0 ~ 80 0.2 .!io :::;; 60 :::;; 0.1 60 r--- 0.1 40 40

0.0 20 0.0 10 20 30 40 50 60 70 80 90 o 10 20 30 40 50 60 Time Is] Time [s]

Figure 11. The effect of oil temperature on the centre temperature and Figure 13. The effect of initial moisture content on the temperature and average moisture content of tortilla chips during frying (initial moisture average moisture content of tortilla chips during frying (oil content = 44%; chip thickness = 1.6 mm, batch frying of 20 chips). temperature = 190°C;chip thickness = 1.6mm; batch frying of 20 chips).

Trans IChemE, Vol 75, Part C, September 1997 MODELLING OF A BATCH DEEP-FAT FRYING PROCESS FOR TORTILLA CHIPS 189

200 200

190 180 ...... 160 180 \'.. 170 I., ~ 140 U I CD """,""""'- ~ 160 \ 5 120 ,,' / e \ ~ ,;. ./ ~ 1501 \ Q) -"""",,""""---- ~ 100 E ~14O Q) {!!. 80 I- 130 60 - One chip - One chip 120 30chips 40 30chips - - 60chips - - 60 chips 110 20 100 o 10 20 30 40 50 60 o 10 20 30 40 50 60 Time[s] Time [s]

Figure 14. The effect of batch frying process on the centre temperature of Figure 15. The effect of batch frying process on the frying oil temperature the tortilla chips during frying (oil temperature = 190°C; chip thick- during frying (settling temperature of the oil = 190°C; chip thickness = 1.6mm; initial moisture content = 44% wb). ness= 1.6mm; initial moisture content = 44% wb).

Tortilla chip thickness in temperature of the oil depend on how many chips are Figure 12 shows the effect of chip thickness on the centre fried at the same time. The temperature of the oil decreases temperature. As expected, the thinner chip reached a higher greatly at the moment the chips are placed into the oil, then temperature faster than the thicker chip. The plateau for the increases gradually to the setting temperature as observed in thicker chip was much longer because the thermal resistance Figure 6. increased significantly due to the low thermal conductivity Figure 14 shows the centre temperature of the chips of the frying product. during a batch frying process. The temperature of the chip Moisture removal rate was slower for the chips with a increased slowly when more chips (around 60) were fried at thickness of 2.6mm than for the chips with 1.6mm (see the same time. The temperature of the oil dropped more Figure 12).More than 1()(}seconds were required for the thicker dramatically (volume of oiVvolume chips decreased) when chips to reach the equilibrium moisture content (2% wb). more chips were fried at the same time, as shown in Thicker chips result in a fried product with a lower oil Figure 15. content. A previous study also suggested that higher surface-to-mass ratio of the food increases oil absorption 7. CONCLUSIONS Initial moisture content A predictive mathematical model based on the funda- The effect of initial moisture content on the frying mental principles of heat and mass transfer was developed process was studied by frying tortillas with initial moisture to simulate the temperature, moisture content, and oil contents of 54% wb and 27% wb. Figure 13 shows the content during the frying process of tortilla chips. This temperature at the centre of the tortilla chip. The model can be used to analyse processes for a single chip and temperature of the chip with higher initial moisture (54% a batch of chips. wb) content was a little lower at the beginning of the frying To validate the model, experiments were also conducted. process and soon reached the same temperature of the chip Temperature at the centre of the chip during both the frying with lower initial moisture content (27% wb). The and cooling processes, temperature of the oil during the temperature profile was not greatly affected by the chip's frying process, moisture and oil contents of the chip at initial moisture content during frying. The higher the initial different frying times were measured. moisture content, the higher the diffusion coefficient and Good agreement was obtained between the model and the thus, the higher mass transfer of water vapour. experimental results. This agreement also validates the Moisture loss rate was faster for the tortilla chips with a frying mechanism proposed in this study. Batch frying is higher initial moisture content (see Figure 13). The quite different from a single chip frying process because the equilibrium moisture content was reached in 50 seconds temperature of the oil changes significantly during the batch of frying for both cases. frying process. Analysis of this process is very important for It is known from a previous study5 that chips with a industrial practice. higher initial moisture content will have a higher final oil content. This is related to the effective porosity of the chip. Chips with a higher initial moisture content have more space available for oil absorption after the moisture is removed NOMENCLATURE during frying. A tortilla chip surface area per unit bed volume, m2m-3 Bi Biot number Batch frying process Cp specific heat of chip, Jkg-1K-1 As described before, batch frying is quite different from Cpf specific heat of the oil, J kg-I K-1 single chip frying process. It is very important to study batch Cpw specific heat of water vapour, J kg-I K-1 Df mass diffusivity of oil, m2S-I frying because this is the process actually used by the food Dw mass diffusivity of moisture, m2S-I industry. For a single chip frying, the temperature of the oil F oil content of the tortilla chip in wet basis, defined as: (kg oil is assumed to be constant while for a batch process, changes absorbed)f(kg product), wb

Trans IChemE, Vol 75, Part C, September 1997 190 CHEN and MOREIRA

Fe final oil content at surface interface between batch and the bath oils, 5. Moreira, R. G., Sun, X., and Chen, Y., 1997, Factors affecting oil wb uptakes in tortilla chips in deep-fat frying, J Food Eng, 31: 485-498. Fo Fourier number 6. Gamble, M. H. and Rice, P., 1987, Effect of pre-fry drying of oil uptake F~ oil content of the surrounding oil, decimal, wb and distribution in potato crispy manufacture, Inti J Food Sci Technol, Fo initial value of oil content of the chip, decimal, wb 22: 535-548. Fsur surface oil content of the chip, decimal, wb 7. Gamble, M. H. and Rice, P., 1988, The effect of slice thickness on IMC initial moisture content, decimal, wb potato crispy yield and composition, J Food Eng, 8: 31-46. h convection heat transfer coefficient between the oil and the chip, 8. Pinthus, E. 1., Weinberg, P., and Saguy, I. S., 1995, Oil uptake in deep- Wm-2K-1 fat frying as affected by porosity, J Food Sci, 60: 767-772. convection mass transfer coefficient of water vapour, m S-I 9. Pinthus, E. 1. and Saguy, I. S., 1994, Initial interfacial tension and oil convection mass transfer coefficient of oil at the surface of chips, uptake by deep-fat fried foods, J Food Sci, 59(4): 804-807. ms-1 10. Moreira, R G., Palau, J. E., and Sun, X., 1995a, Deep-fat frying of latent heat of vapourization, J kg-I tortilla chips: an engineering approach, Food Technol, 49(4): 146-152. convection heat transfer coefficient between frying oil and II. Farkas, B. E., Singh, R P. and Rumsey, T. R, 1996, Modeling heat and surrounding oil, Wm-2K-1 mass transfer in immersion frying. I: model development, J Food k thermal conductivity, W mK-1 Engineering, 29: 211-226. I half thickness of product, m 12. Farkas, B. E., Singh, R. P. and Rumsey, T. R., 1996, Modeling heat and M moisture content of the tortilla chip in wet basis, defined as: (kg mass transfer in immersion frying. II: solution and verification, J Food water evaporated)/(kg product), wb Engineering, 29: 227-248. moisture content of the tortilla chip in dry basis, defined as: (kg 13. Ateba, P. and Mittal, G. S., 1994b, Modelling the deep-fat frying of water evaporated)/(kg product - evaporated water), db beef meatballs, Int J Food Sci and Tech, 29: 429-440. equilibrium moisture content, wb 14. Benson, C. K., Caridis, A. A. and Klein, L. F., 1992, Continuous food moisture content of the surrounding oil, wb processing methods, United States Patent number 5,/37,740. initial value of moisture content, wb 15. Moreira, R. G. and Barrufet, M. A., 1997, A new approach to describe surface moisture content of the chip, wb oil absorption in fried foods: a simulation study, submitted to the surface area of the frying oil per unit volume of oil, m2m-3 Journal of Food Engineering. time, s 16. Chen, Y., 1996, Simulation of a deep-fat frying process for tortilla temperature of the frying oil between the chips, °C chips, Master Thesis, (Department of Agricultural Engineering, Texas absolute temperature of the frying oil between the chips, K A&M University, USA). set temperature of the frying oil, °C 17. Moreira, R. G., Palau, J. E., Sweat, V. E., and Sun, X., 1995b, Thermal initial value of oil temperature, °C and physical properties of tortilla chips as a function of frying time, J product thickness, m Food Proc Preserv, 19: 175-189. thermal diffusivity, m2 S-I 18. Moreira, R G. and Sun, X., 1997, Snack foods: tortilla chips porosity of the bed of tortilla chips, processing, in Deep fat frying, Blumenthal and Pokorny, (ed) water/vapour flux, kgm-2s-1 (Chapman & Hall, New York) in press. temperature of the chip, °C 19. AACC, 1986, Approved Methods of the American Association of initial values of temperature, °C Cereal Chemists, (St. Paul, MN). surface temperature of the chip, °C 20. Hallstrom, B., 1979, Heat and mass transfer in industrial cooking, in bulk density of the chip, kg m-3 Food Process Engineering, Linko, P., Malkki, Y., Olkku, 1., and density of the oil, kg m-3 Larinkari, J., (eds) vol. I, (Applied Science Publishers Ltd., London) pp. 457-465. 21. Choi, Y. and Okos, M., 1986, Thermal properties of liquid foods- REFERENCES review, in: Physical and Chemical Properties of Food, Okos R M., (ed) (ASAE Publication, St. Joseph, MI). 1. Don, A., 1991, Reduce the fat but not the taste, Supermarket Bus, 42(9): 173. 2. Morton, I. D. and Chidley, J. E., 1988, Methods and equipment in frying, in Frying of Food, Principles, Changes, New Approaches, ADDRESS Varela, G., Bender, A. E., and Morton, I. D. (ed) (VCH Publishers, Chichester, England) . Correspondence concerning this paper should be addressed to Professor 3. Pravisani, C. I. and Calvelo, A., 1986, Minimum cooking time for R G. Moreira, Department of Agricultural Engineering, Texas A&M potato strip frying, J Food Sci, 51: 614-617. University, 201 Scoates Hall, College Station, Texas 77843-2117, USA. 4. Gamble, M. H., Rice, P., and Selman, J. D., 1987, Relationship between oil uptake and moisture loss during frying of potato slices The manuscript was received 21 January 1997 and accepted for from c.v. Record U.K. tubers, Inti J Food Sci Technol, 22: 233-241. publication after revision 5 June 1997.

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