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 PROCESSFOR TORTILLA CHIPS

Y. CHEN and R. G. MOREIRA

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

The process of deep-fat frying involves simultaneous heat and mass transfer and bothfrying and cooling conditions are critical to the final product quality. An understandingof 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 singlechip and a batch of tortilla chips. The temperature, moisture content, and oil content werecalculated as a function of frying time. Finite difference technique was used to solve the set ofpartial 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 andcomparisons between predicted and observed results showed that the model successfullysimulated the batch frying processes for tortilla chips. The good agreements also validate thefrying mechanism proposed by this study. The mathematical model was used to analyse theeffects of different frying conditions on the oil, moisture, and temperature profiles during thefrying of tortilla chips.

Keywords: simulation; crust; core; thickness; oil content

INTRODUCTION

Deep-fat frying is a very important food processingoperation which offers unique texture and flavour to theproduct and is commonly used by the multi-million dollarsnack food industry. About 65% of all snack products in theUnited States are deep-fat fried. In 1995,.deep-fat friedfoods contributed to approximately $9.82 billion in annualsales, according to the Snack Food Association.

Tortilla chips are a popular snack food in the UnitedStates ranking second only to potato chips in the saltedsnack food market and are considered to be one of thefastest-growing segments of the grain-based food industryl.

Although different types of products and different typesof fat/oil are used in the frying operation, they have to besubjected to a frying oil temperature ranging from 160-200°C. Basically two types of fryers exist: the smaller staticbatch fryers used by the catering/restaurant/fast food outletand the large continuous fryers used on the industry scale toproduce high volumes of frying products. Typical batchfryers have capacities ranging from 5 to 25 litres. Theindustrial continuous fryer size can range from 100kg to4oo0kg product per hour 2.

Many physical, chemical, and nutritional changes occurin foods during deep-fat frying. Many of these changes arefunctions of oil temperature, product moisture, oil content,and product residence time in the fryer. Undesirable effectscould be minimized and the process could be bettercontrolled if temperature, moisture, and oil distributions infood with respect to time could be accurately predicted.Research has been focused on different aspects of the fryingoperation to obtain' a better understanding of the process.

Pravisani and Calvelo3 determined the minimum cookingtime for potato strips under different frying conditions.Gamble et al.4related the oil absorption with the remainingmoisture content while Moreira et al.5 indicated that thecooling process after frying affects the oil content of thefinal products. Gamble and Rice6.7studied the effects of pre-frying treatments and the product shape on the fryingprocess of potato slices. Pinthus et al.8analysed the effect ofinitial porosity on the oil absorption of restructured potatoproducts and Pinthus and Saguy9 studied the relationshipbetween initial interfacial tension and oil uptake forrestructured potato products.

Few articles studied the dimensional changes of foodproducts during frying. Moreira et al.lO,using the magneticresonance image (MRI) technique, found that the thicknessof a tortilla chip after 60 seconds of frying increases byabout 40 percent as a result of expansion caused by anincrease in porosity.

Many attempts have been made to combine heat and masstransfer principles to describe the temperature and moisturecontent profiles in a product in deep-fat frying processes10-13.All these models deal with the frying of a single piece of aproduct and assumed constant physical properties. Thepractical importance of these informations are limitedbecause foods are seldom fried as individual pieces. Instead,tortilla and potato chips, French fries, etc., are fried either ina stationary (batch fryer) or moving bed (continuous fryer).Depending on the fryer size, oil volume, batch size, andwater content of the product, a temperature drop of 30 to45°C of the frying oil can be observed in industrialoperationsl4. Isothermal frying is only possible whenfrying a single piece of a product. In addition, the significant

181

182 CHEN and MOREIRA

changes in the physical properties of a product during fryingcannot be neglected.

The objectives of this study were:

(1) to develop a mathematical model to analyse heat andmass transfer duringbatch frying of tortilla chips consideringchanges in the properties of the product during frying;(2) to validate the model; and(3) to use the mathematical model to study the effect offrying conditions (temperature of the frying oil, thickness,and initial moisture content of the chip) on the heat transfer,mass transfer, and oil absorption rates during frying.

MATHEMA TICAL MODEL DEVELOPMENT

The Problem Description

Figure 1 shows the cross section of a tortilla chip beingfried. Heat is transferred by convection from the oil to thesurface of the chip, and by conduction to the centre of thechip. There is, however, a certain transfer of heat coupled tothe transfer of water or vapour that is the energy carried bythe water vapour. Most of the water escapes from the tortillachip in the form of vapour during frying, and a smallpercentage of the frying oil also diffuses into the chip5.Diffusion of moisture and diffusion of oil are in twoopposite directions. While the moisture content decreases,the oil content increases causing the chip to become moreporous during frying.

Two regions, crust and core, exist during frying. Thecrust/core interface moves towards the centre of the chipduring frying. At the interface, the temperature remains atthe water boiling point for a short period of time to allow forthe water presented in that region to evaporate.

Thermal and physical properties change greatly duringfrying. The bulk density of the food material decreasesduring frying and the food becomes more porous. Thethermal conductivity decreases as the porosity increases andthe specific heat decreases as moisture content decreaseswhile oil content increases during fryinglO.

When a tortilla chip is taken out of the fryer, it is coveredwith a thin layer of oil. As the temperature of the tortillachip decreases by natural convection with ambient air, thevapour pressure within the pores of the chip decreases,forcing the surface oil to flow into the chips.

Moreira et al.5 indicated that almost 80 percent of the oilis absorbed by the tortilla chips during the cooling period.Investigation of the cooling process is very important to

I

II

I

CoteI

I

x!o x=U2x=-U2

Figu~e 1. Tortilla chip undergoing frying.

fully understand the frying mechanism. This is not thesubject of this paper and the reader should refer to Moreiraand Barrufet15for a detailed description of oil absorptionmechanism during cooling.

Assumptions

The assumptions made in this study were the following:

(1) The tortilla chip is considered to be initially isotropicand isothermal. The initial moisture and temperaturedistributions in the chip are uniform.(2) Because the thickness of the tortilla chip is smaller thanthe other dimensions, an infinite slab model was assumed inthe study. A one dimensional heat and mass transfer modelwas considered.(3) The heat required for chemical reactions (i.e., starchgelatinization, protein denaturation) is small compared tothe heat required to evaporate the water.(4) Changes in the length of tortilla chip is negligiblecompared to changes in thickness during frying. Tortillachips puff during frying (i.e., become thicker)lO.(5) Thermal and physical properties are functions of localtemperature and moisture content during the frying process.(6) A 'microscopically uniform' porous medium is formedafter frying. The surface of the chip is covered with auniform layer of oil after frying and most of the oil diffusesinto the chip after frying during the cooling period.(7) In this study, the volumeof frying oil in the fryer kettle tothe volume of chips ratio was around 15, i.e., around 20-50chips were placed in a 5x 10-4m3basket and then into a fryerkettle containing 7.5x 10-3m3 of oil. It was observed thatonly the oil that was in direct contact with the chips (inbetween the chips) was affected by the chips moisture lossduring frying,whereasthe changein temperatureof the rest ofthe oil in the kettle was negligible.Therefore, it was assumedthat the fryer consistedof two oil zones, and the exchange ofenergybetween these two zoneswasby convectiononly. Thiswould not be true for the case of continuous frying or if thevolume oil/volume chips ratio was small.

Governing Equations

Because of its symmetry, the computational domain maybe simplified to a half section of a tortilla chip. Thetemperature (0), moisture content (M), and oil content (F) in

Batch fryer with tortilla chips

, tortilla chips temperature,8(X,t)'oilat varying temperature, T(t)

Figure 2. Batch fryer of tortilla chips.

Trans IChemE, Vol 75, Part C, September 1997

.L

Oil

F-

Crust

q

:I Oil-F-

Crust

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

a batch of tortilla chips as well as the oil temperature (T)change dramatically during frying. Energy and massbalances were written on a differential volume located atan arbitrary position in a batch fryer containing tortilla chips(see Figure 2). The basic one dimensional heat and massdiffusion equations were employed. Thus, these fourbalances result in four equations.

(I) The governing differential equation describing thetemperature change in the product during frying is,

~ (/}O)_ a(rCpwO) = a(PbCpO)ax ax ax at

The second term in the left side of the equation representsthe heat transfer caused by diffusion of water vapour, wherer is the water vapour flux,

r = _ a(PbDwM)ax(2) Fick's Law of diffusion was used to calculate the masstransfer rate in the product in two different directions:moisture (water vapour) diffuses from the chip to the oil andthe oil diffuses from the surface to the centre of the chip,

~ (D aM)= a(PbM) (3)ax wPbax at

~ (D aF)= a(PbF) (4)ax 'fPbax at

(3) The temperature of the oil will decrease significantlyduring the first seconds of frying when tortilla chips aredropped into the fryer. The change in enthalpy of the oilwith respect to time in the void space (between tortillachips) is equal to the sum of energy required for heating theproduct, for evaporating water from the chips, for heatingthe water vapour evaporated from the chips, and forexchanging energy to the surrounding oil. The equationfor calculating the changes in the temperature of the oil is,

aT

[

ao a(PbM)Poi/Cpoi/at= -k ax + hfgDw~

+ rCpw(Osur - T)] (I ~ cf»

+ hsS(Tfo- T) (5)

Equations (I) to (5) are used to describe temperature andmoisture changes at all points in the chip (i.e. core andcrust). Inside the crust there is an evapouration zone thatmoves towards the centre of the product. In the evapourationzone, the temperature is constant, and the energy is mainlyused to evaporate the water. The duration of this constantperiod depends on the water content in that location. As thewater content is reduced at the level corresponding to Me,the temperature increases rapidly and this part of the productbecomes part of the crust. Different thermal properties wereused in this study (equations (11)-( 17)) for the two differentzones in the product. When the temperature of the chip washigher than the boiling temperature of water, the propertiesof vapour instead of liquid water were used to predicttemperature and moisture changes in the product. The crusthas thermal and physical properties of an insulatingmaterial. Its low 'thermal conductivity and porosity


183

(I)

(equations (13) and (15)) slow the rate of heat transfer andtherefore the rate at which the product cooks and watervapourizes.

Two boundary conditions and one initial condition areneeded for each governing equation. The first boundarycondition is a symmetric condition at the centreline of theslab (equation 6). The second boundary condition is aconvection surface condition (equations (7)-(9)).

At x = 0 (centreline) for any time, no temperature,moisture, or oil gradient exists at the centre of tortilla chips,

ao = 0; aM= 0; aF = 0 (6)ax ax axAt x = :t U2 (surface) for any time, the energy

transferred by convection from the oil to the chip's surfaceis equal to the sum of energy required for transferring heat tothe centre of the product by conduction, for evapouratingwater from the chips, and for heating the water vapourevaporated from the chips at temperature 0 to the oiltemperature T,

aoh(Osur- T) = -k ax + hfgr + rCpw(Osur- T) (7a)

. The second term at the right side of equation (7a) iseliminated when the temperature of the chip is above theboiling point of water,

aoh(Osur- T) = -k ax+ rCpw(Osur- T) (7b)

withtwo masstransferboundaryconditions,

kdPb(Msur- M_) = -r (8)where M_ = Me= 0, i.e. the moisture content of thesurrounding oil. And,

a(F)kf(Fsur - F_) = -Dfax (9)

where F_ = Fe = 1, i.e. oil content of the surrounding oil.The mass transfer coefficients (kf and kd) should be a

function of the mass flux of water leaving the chip. The useof constant values are a limitation to the model; however, atpresent these data are not available and further work willprovide the necessary information on the coefficients.

The initial conditions for any location x in the chip at timezero are the following,

O(x,O) = 00; M(x, 0) = Mo;

F(x,O) = Fo;T(x, 0) = Tfo (10)

The above four governing equations and 10 boundaryconditions can be solved simultaneously by using finitedifference technique. Heat and mass transfer equations arecoupled by the transport properties and thermal propertieswhich are functions of moisture content and temperature.Equation (5) is used to calculate the temperature of the oilbetween the chips at each time step and this value is thenused in equations (1)-(4) to obtain the temperature,moisture content and oil content profiles in the chipduring batch frying process.

(2)

Solution of the Mathematical Model

This study employed a control-volume formulation todiscretize the governing equations, initial conditions and


boundary conditions. The continuous physical space(infinite slab) was divided into a number of non-overlappingcontrol volumes in the x-direction so that one controlvolume surrounded each node. The differential equationswere integrated over each control volume, and the controlvolume formulation method obtained the finite-differenceequation by applying conservation of energy to a controlvolume around each node. The most attractive feature ofthis method is the resulting solution would imply that theintegral conservation of energy is exactly satisfied over anygroup of control volumes and over the whole calculationdomain.

After the discretization of heat and mass transferequations for every node, a set of simultaneous algebraicrelationships were obtained and solved to obtain thetransient temperature, moisture content, and oil content ateach node. The flowchart for the computational procedureof the frying process is shown in Figure 3.

Grid Sensitivity and Stability

From the mathematical point of view, the development ofthe mathematical model could not be ended at this step.Even when the finite difference equations have beenproperly formulated and solved, the results might stillrepresent a coarse approximation to the exact solution. Anumerical simulation enables determination of the tempera-ture at only discrete points which represents the averagevalue of the surrounding region.

However, the finite difference approximations could bemade more accurate as the nodal network was refined. Thecost is that the computer takes longer CPU time to completethe iterations. A grid sensitivity study was performed to

Figure 3. Row diagram of the computer program.

define when the computed results no longer depended on thechoice of.::lx and tJ..t.

Explicit finite difference technique was used in this study.The temperature, moisture content, and oil content of anynode at t+tJ..t was calculated from the knowledge oftemperatures, moisture contents, and oil contents at thesame and neighboring nodes for the preceding time t.Hence, the determination of a nodal temperature andmoisture/oil content at one time is independent oftemperatures and moisture/oil content at other nodes ofthe same time. In this method, the choice of.::lxis based on acompromise between accuracy and computational timerequirements, as mentioned above. Once this selection hasbeen made, however, the value of tJ..tmay not be chosenindependently. It is, instead, determined by stabilityrequirements. For a one-dimensional node, the followingcriterion was used to select the maximum allowable value ofFo, and hence dt, to be used in the calculation:

Fo(1 + Bi) :S! (11)

where Fo = Fourier number, Fo = at/P; a = thermaldiffusivity, a = k/pCp [m2/s-I]; I = half of the thickness[m]; t = time,s, andBi = Biotnumber,Bi = hl/k.

A series of tests were conducted for the model todetermine the effect of time and distance grid size (.::lx,tJ..t)on the output of the program. The output was thetemperature at the surface and the centre, average moisturecontent, and average oil content. The following tests andresults, as shown in Table I, were accomplished with aconstant frying oil temperature of 190°Cand frying time of80 seconds.

The temperature outputs were almost identical but Test 2and Test 3 required longer computation time. To minimizethe time required for processing and yet give the maximumaccuracy, a time step of 0.01 s and distance step of 0.1 mmwere chosen and further tests were done to test theconvergence and stability of the program. For a time stepof 0.01 s, the program was still convergent if.::lxchanged ina certain range. But Test 4 could hardly satisfy the accuracyrequirement. The output of Test 6 was also not satisfied andTest 7 failed to converge because equation (II) was notsatisfied.

Therefore, all computations were performed with a PC-mM (Pentium 90, 8MB Ram), with time step of 0.01 sanddistance step 0.1 mm16.The computer program to solve theabove problem was written using MATLAB (The Math-Works, Natick, Ma).

Thermal and Physical Properties Used in the Model

The mathematical model requires physical and thermalproperty data of the material to be fried and the processconditions used. While most property data were obtainedfrom values reported in the literature, some of the propertieswere analysed and determined in this study.

Thermal conductivity, k, of the tortilla chip during fryingwas found to have the following correlationsI?:for ():S lOO°C(R2 = 0.98)

k[W/m°C] = 0.1085 + 0.OO9986()

- 5.203 x lO-6()2 (12)


MODELLING OF A BATCH DEEP-FAT FRYING PROCESS FOR TORTILLA CHIPS 185

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

for (» 100°C (R2= 0.99)

k[W/m°C] = 0.06938 + 9.997 x 1O-5()

+ 6.327 x 1O-8()2 (13)

Changes in the tortilla chips specific heat (Cp) withtemperature were small compared to changes with moisturecontent. The effect of moisture content on the tortilla chip'sspecific heat was calculated as17,

Cp[kJkg-10C] = 2.506 + 2.503Md - 1.557MJ (14)

where Md is moisture content in decimal (db) for1.22<Md<0.01 (R2 = 0.99).

Bulk density, Pb,of the tortilla chips changes significantlyduring frying. The following relationship was obtained bycorrelating the experimental data presented by Moreira etal.17. It was found that the bulk density had a strongerrelationship with moisture than with temperature or oilcontent,

pb[kgm-3] = 587.287 + 1017.34M (15)

where M is moisture content in decimal (wb) for0.55<M<0.01 (R2= 0.93)

The moisture diffusion coefficient was assumed to beconstant during frying but a function of different fryingconditions, such as oil temperature and chip's initialmoisture content,

(16)

where [MC is the initial moisture content (decimal, wb)before frying and Tabs is the absolute temperature, K2(R = 0.94) .

Oil diffusion during frying increases as the initialmoisture content of the tortilla chip increases18(R2 = 0.99),

(17)

the diffusion coefficients (Df and Dw) should be a functionof the x and local moisture content; however, at presentthese data are not available and futher work will provide thenecessary information on these coefficients.

Other property data used in the program are given inTable 2. Symbols explanation is in the nomenclaturesection. The mathematical model was then used to


determine the effect of process parameters and productinitial conditions on the frying process of tortilla chips.

MATERIALS AND METHODS

The model was designed to predict temperature, moistureand oil profile of tortilla chips during the frying process. Themodel can be used to analyse the effect of different processvariables and initial product conditions on the final qualityof frying products.

Tortilla Chip Preparation

All the tortilla chips were prepared at the Texas A&MCereal Quality Pilot Plant. One kilogram of nixtamalizedcom masa flour (Masa Mixta for tortilla chips, Valley GrainProducts, Muleshoe, TX) was mixed with one kilogram ofdistilled water at ambient temperature for 4 minutes at thelowest speed of a Hobart mixer (Model A200, Troy, OH).The resulting masa was fed through a sheeter/former (ModelCH4-STM, Superior Food Machinery Incorporated, PicoRivera, CA), and then baked in a three-stage moving tiergas-fired oven (Model OPOl004-02,Lawtence Equipment,EI Monte, CA) to form the tortilla. The oven temperaturewas controlled at 343°C, 190°C, and 190°C for the top,middle, and bottom tiers, respectively. The residence timeof the tortilla in the three-stage oven was 45 seconds. Thechip thickness was controlled by adjusting the roller gap ofthe sheeter/former. Mter baking, the tortilla pieces werecooled down at room temperature for about 20 minutes andthen fried in a 7.5-L batch fryer (Hobart, model HK3-2,Troy, OH) using fresh soybean oil (Lau Ana, Lau AnaFoods, Inc. Opelousas, LA) as the frying medium. The

Table 2. Parameters used in the simulation of a batch of tortilla chips friedat 190°C for 80 s.

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 4.12 0.05 0.0025 185.08 6.5 3.13 0.025 0.001 185.87 6.3 2.84 0.1 0.02 186.36 6.7 4.15 0.1 0.005 183.86 7 4.16 0.2 O.oI 181.41 8.1 7.47 0.05 O.oI error error error

Parameter Value Source

kd 0.00128ms-1 Moreira and SunlSh 285Wm-2K-1 Moreira and SunlS

kf 1.3 x 10-6 ms-I Chenl6

hfg 2250kJk -I Moreira and SunlShs 12ooWm-K-l Chenl6CPw 4.2kJkg-lK-1 Chenl6CPv 2.0kJkg-lK-1 Chenl6

CPf 2.2kJkg-1K-l Choi and OkOS21S 0.0459 m2m-3 Chenl6cf> 0.5 Chenl6A 0.00276m2m-3 Chenl6


tortilla chips were then cooled down, sealed in zippedplastic bags and stored in a desiccator for further analysis.

Tortilla chips with different initial conditions anddifferent process conditions were prepared for variouspurposes:

1) Tortilla chip thickness-two levels: 1.6mm and 2.6mm.The thickness was obtained by adjusting the roller gap of thesheeter/former.2) Baking time of the tortilla chips-three levels: no baking(0 second), 45 seconds, and 90 seconds. This test wasdesigned to obtain tortilla chips with different initialmoisture contents before frying.3) Temperature of the frying oil-three levels: 190°C,160°C,and 130°C. The frying time was 60 seconds for the1.6mm thick tortilla chips and 80 seconds for tortilla chipwith thickness of 2.6 mm. The temperature history at thecentre of the chip (thickness of 2.6 mm) was measured byinserting a thin thermocouple (Type E,-0.25 mm) in thecentre of the chips. The temperature of the frying oil wasmeasured with a thermocouple (Type E,-0.81 mm). At leastthree measurements were made for each test condition.4) Batch frying and single chip frying were compared byfrying one chip at a time and a batch of chips (20 to 50) at atime using the same fryer.

Moisture and Oil Content Measurements

Moisture contents at different frying times were measured.Approximately 10 pieces of each sample were ground in ahouseholdgrinder (Regal,Model 7450, China). The moisturecontent was determined by weight loss after drying theground sample 24 hours at 103-105°C in a forced air oven19.Oil contents at different frying and cooling times weredeterminedwith the petroleum ether extraction method19in aSoxhlet apparatus (Model HTl043, Tecator, Sweden).

All the measurements in this study were made at least intriplicate.

RESULTS AND DISCUSSION

Using the thermal and physical properties specified in theprevious section, computer simulations were conducted tocompare the mathematical model with the experimentalresults.

200

180

160

~ 140

'Q; 120:;OJ100Q;~ 80Q)

I- 60- Predicteddata:t: Experimentaldata

40

20

oo w ~ ~ ~ W ~ ro M 00

Time[s]

Figure 4. Predicted and experimental results of tortilla chip's centretemperature during frying (oil temperature = 190°C; initial moisturecontent = 48.8% wb; chip thickness = 2.6mm; single chip frying).

Temperature Changes During Frying

The temperatures at the centre of the tortilla chip duringfrying predicted by the model and obtained experimentallyare shown in Figures 4 and 5 for single and batch processes,respectively. As it was expected, the temperature at thecentre of the chip increased to the boiling point of water,remained constant until all water vapourized (10-15 s), thencontinued to rise and reached the oil temperature.

In both cases, single and batch, the model was able topredict the temperature profile behaviour of the chips duringthe process very well. The difference, however, between thepredicted and observed temperature data for both processescould have been caused by the difficulty to accurately locateand maintain the thermocouple at the centre of the chips,especially during the batch frying process when the chipsare continuously in motion. This factor also resulted in arelatively large standard deviation (see error bar in Figures 4and 5) in the temperature measurements.

For a single chip frying process, the temperature of the oilis almost constant during the entire frying process.However, for batch frying, the oil temperature dropssubstantially and then increases gradually to the fryersetting temperature. Figure 6 shows the predicted andobserved results of the frying oil temperature change duringa batch frying process for tortilla chips. Good agreementwas obtained between the model and the experimentalresults with the exception of the first five seconds of frying.This could be caused by lack of uniformity in the oil bathtemperature before the batch of chips was placed into thefryer. As the frying proceeded, however, the chips spreaduniformly in the basket so the temperature distributionbecame more uniform and better agreement betweenexperimental and predicted data was obtained.

Both experimental and predicted results indicate that thetemperature of the oil changes greatly during the initialseconds in batch frying process. The study of this process isvery important for industrial practice.

Moisture Content Changes During Frying

The average moisture content was calculated in thecomputer program by numerically integrating the moistureprofile at each time step. This average moisture content was

200

180

160

~1~

~ 120.a~ 100Q)c.E 80Q)

I- 60

- Predicteddata:t: Experimental data

40

20

oo 10 20 30 ~ 50 60 70 80

Time[s]

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



200

190

180

~ 170

';' 160:;m 150Q;~ 140'"t- 130

120

Predicted

:t: Experimental

110

100.20 .10 0 10 20 30 40 50 60 70 80 90 100

Tlme[s)

Figure 6. Oil temperature change during batch frying process (settling

temperature of the oil = 190°C; chip thickness = 2.6 mm; initial moisture

content = 48.8% wb; batch frying of 50 chips).

then compared with the experimental data. As expected, themoisture content decreased greatly at the beginning of thefrying process and then reached equilibrium at the end of thefrying process (see Figure 7). Moisture loss reachedequilibrium in 60 s of frying for tortilla chips fried at190°C oil temperature, requiring longer time for tortillasfried at lower temperature (see Figure 8). The predicted datawere in good agreement with the experimental data.

Oil Content Changes During Frying

The average oil content during the frying process wasdetermined by numerically integrating the oil profile at eachtime step in the computer program. Only the average oilcontent was calculated during the cooling process and thisaverage value was then compared with experimental data asshown in Figure 9. Both the experimental and the simulationresults indicated that the diffusion of oil is very slow duringthe frying process.

Analysis of the Frying Process

The good agreement between the predicted and theexperimentaldata confirmedthe validity of the mathematical

0.6

0.5- IMC = 0.54 w.b.- - IMC = 0.44 w.b.. . . . IMC = 0.27 w.b.i 0'4

~

\- \~ \

g 0.3 "\.~ . \.:; ".',- . "-.!!20.2 '. "-o "........

~ . .,~~~0.1-1 . .....

0.0o 10 20 30 40

Time [s)

50 60

Figure 7. Predicted and experimental results of tortilla chip's averagemoisture content during frying as affected by tortilla chip's initial moisturecontent (oil temperature = 190°C;chipthickness= 1.6mm,batchfryingof 20chips). .


187

- T=130.C- - T=160.C

. . . T=190.C

0.0o 20 30 40

Tlme[s)

Figure 8. Predicted and experimental results of tortilla chip's averagemoisture content during frying as affected by frying oil temperature (initialmoisture content = 44% wb; chip thickness = 1.6mm, batch frying of 20chips).

10 50 60

model developed and verified the frying and coolingmechanisms proposed by this study. The followingsensitivity analysis was conducted to analyse the effect ofdifferent processing parameters on the frying and coolingprocesses of tortilla chips.

Convection heat transfer coefficientIn this study, the convection heat transfer coefficient (h)

value of 285 W m-2K-l 17was used throughout the fryingprocess. During the deep-fat frying process, the watervapour bubbles escaping the surface of food would causeturbulence in the oil and increase the convection heattransfer coefficient between the oil and the chips. Theconvection heat transfer coefficient is also enhanced due tothe movement of the chips during the batch process. Asensitivity test was performed by increasing the h value of285 W m-2K-l by 25 percent and 50 percent (356 and427 W m-2K-1, respectively), to examine the effect of thisparameter on the frying process of tortilla chips. The centretemperature of the chip during batch frying process did notchange significantly even when the convection heat transfercoefficient was 50 percent higher (see Figure 10). As thecentre temperature of the chip is not affected by the value ofthe convection heat transfer coefficient, it is concluded that

0.12

0.10

. experimental- predicted

:c 0.08.! .

0.02

20 30 40Tlme[s]

Figure 9. Predicted and experimental results of tortilla chip's average oilcontent during frying (oil temperature = 190°C; initial moisture con-tent =44% wb; chip thickness = 1.6 mm).

50 6010

0.5

0.4

:c.!

0.3E8

0.2I .

u;'0 .

0.1

E.$ 0.06c:0u

5 0.04

188

200

CHEN and MOREIRA

180

_.-'~ ~,.., ~ ~.~ ,/./.-

,,/."/.

/./.

/."/.:

/..:

160

~ 140

~ 120~~ 100E~ 80

60 - h 3 285 W/m2K.. h. 356 W/m2K

-- h=427W/m2K40

20o 10 20 30 40 50

Tlme[s]

60 70 80

Figure 10. The effect of convection heat transfer coefficient on the centretemperature of tortilla chips during batch frying process (oiltemperature = 190°C; initial moisture content = 48.8% wb; chip thick-

ness = 2.6 mm; batch frying of 50 chips).

the frying process and the quality of the final frying productsare not sensitive to changes in the convection heat transfercoefficient. This result indicates that the convection heattransfer is of minor importance during frying because themain resistance to heat transfer is inside the product, asobserved by Hallstrom2o.

Frying oil temperatureThe fryingoil temperatureisan importantparameterin frying

because the oil serves as a heating medium in the process.Differentoil temperatureswereusedin themodelto analysetheeffecton temperatureand moisturecontent of the chips.

Figure 11 shows the temperature history at the centre ofthe chip using different frying oil temperature (160°C and190°C). The temperature of the chip increased up to theboiling point of water at the same rate regardless of thetemperature of the frying oil. It was observed that the centretemperature in the chip increased much faster for the chipfried in the oil at 190°C than fried in the oil at 160°C.However, in both cases the temperature of the chips reachedthe temperature of the frying oil after 60 seconds of frying.A similar phenomenon was observed by Farkas et al.12,whosuggested that the temperature profile in the crust regionwas mainly a function of oil temperature while the

0.010 20 30 40 50 60 70 80 90

Time Is]

Figure 11. The effect of oil temperature on the centre temperature andaverage moisture content of tortilla chips during frying (initial moisturecontent = 44%; chip thickness = 1.6 mm, batch frying of 20 chips).

200 0.5

.ci~

0.3 'ECD'Eo(.)

2!0.2 ~en

'0:::;;

0.1

180--

.-"., f-0.4-"

/../. thickness= 1.6 mm/./ =Thickness=2.6mm/

...>::/ /

"~~

160

~ 140

~ 120e~ 100E~ 80

60

40

20 I I r I" I I . I ' . , I I I' . I 10.0o 10 20 30 40 50 60 70 80 90 100 110

Time[s]

Figure 12. The effect of thickness on the temperature and average moisture

content of tortilla chips during frying (oil temperature = 190°C; initialmoisture content = 44% wb; chip thickness = 1.6 mm; batch frying of 20chips).

temperature profile in the core region was unaffected bythe oil temperature.

The average moisture content of the chips decreasedfaster when the oil temperature was higher, as expected (seeFigure 11). The higher the oil temperature, the higher thediffusion coefficient and thus the higher mass transfer ofwater vapour. To achieve the same final moisture content(2% wb), chips fried at 190°Coil temperature only needed60 seconds of frying while 90 seconds was required to frythe chips in the frying oil maintained at 160°C.

It was observed17that as the water evaporates from thechip, during the first 10s of frying, the product becomesharder (crust formation) due to faster water evapourationresulting in the formation of a structure with a number ofsmall pores. As frying continues, the pore starts to enlarge(due to vapour expansion), the material expands andbecomes crispier (decreased hardness). In the last stage offrying (30-60 s), the pore stops expanding due to theincrease in the matrix complex viscosity since the amount ofplasticizing water has been greatly reduced. Similary todrying, it is believed that the average Tg of the materialelevates above the frying temperature thus stoppingexpansion rates and increasing porosity. The bulk porosityis then formed only at the end of the frying process.

200] fo.6- IMC=0.27wb

180 -- IMC=O.54wb __160

0.060

0.5

~ 140CD:; 120e~looE~ 80

.ci0.4 ~

'ECD

0.3 g(.)CD

:;0.2 .!io

:::;;60

0.140

20o 10 20 30 40

Time [s]

Figure 13. The effect of initial moisture content on the temperature andaverage moisture content of tortilla chips during frying (oiltemperature = 190°C;chip thickness = 1.6mm; batch frying of 20 chips).

50


200 0.5

180

160 0.4

.ci140

2! 0.3 'E120 CD::J 'Ee 8CD 100Co

0.2E80 en

'060 :::;;

r---0.1

40


200

180 .........

160

""",""""'-,,' /

,;. ./

~ 140CD5 120~~ 100E{!!. 80

- One chip30chips

- - 60 chips

60

40

20o 10 20 30 40

Time[s]

Figure 14. The effect of batch frying process on the centre temperature of

the tortilla chips during frying (oil temperature = 190°C; chip thick-ness = 1.6mm; initial moisture content = 44% wb).

50 60

Tortilla chip thicknessFigure 12 shows the effect of chip thickness on the centre

temperature. As expected, the thinner chip reached a highertemperature faster than the thicker chip. The plateau for thethicker chip was much longer because the thermal resistanceincreased significantly due to the low thermal conductivityof the frying product.

Moisture removal rate was slower for the chips with athickness of 2.6mm than for the chips with 1.6mm (seeFigure 12).More than 1()(}seconds were required for the thickerchips to reach the equilibrium moisture content (2% wb).

Thicker chips result in a fried product with a lower oilcontent. A previous study also suggested that highersurface-to-mass ratio of the food increases oil absorption 7.

Initial moisture contentThe effect of initial moisture content on the frying

process was studied by frying tortillas with initial moisturecontents of 54% wb and 27% wb. Figure 13 shows thetemperature at the centre of the tortilla chip. Thetemperature of the chip with higher initial moisture (54%wb) content was a little lower at the beginning of the fryingprocess and soon reached the same temperature of the chipwith lower initial moisture content (27% wb). Thetemperature profile was not greatly affected by the chip'sinitial moisture content during frying. The higher the initialmoisture content, the higher the diffusion coefficient andthus, the higher mass transfer of water vapour.

Moisture loss rate was faster for the tortilla chips with ahigher initial moisture content (see Figure 13). Theequilibrium moisture content was reached in 50 secondsof frying for both cases.

It is known from a previous study5 that chips with ahigher initial moisture content will have a higher final oilcontent. This is related to the effective porosity of the chip.Chips with a higher initial moisture content have more spaceavailable for oil absorption after the moisture is removedduring frying.

Batch frying processAs described before, batch frying is quite different from

single chip frying process. It is very important to study batchfrying because this is the process actually used by the foodindustry. For a single chip frying, the temperature of the oilis assumed to be constant while for a batch process, changes


189

200

190

180

1

\'..170 I.,

U I~ 160 \e \~ 150 \Q)

~14OQ)

I- 130

-"""",,""""----

120- One chip

30chips- - 60chips110

100o 20 30 40

Time [s]

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

10 50 60

in temperature of the oil depend on how many chips arefried at the same time. The temperature of the oil decreasesgreatly at the moment the chips are placed into the oil, thenincreases gradually to the setting temperature as observed inFigure 6.

Figure 14 shows the centre temperature of the chipsduring a batch frying process. The temperature of the chipincreased slowly when more chips (around 60) were fried atthe same time. The temperature of the oil dropped moredramatically (volume of oiVvolume chips decreased) whenmore chips were fried at the same time, as shown inFigure 15.

CONCLUSIONS

A predictive mathematical model based on the funda-mental principles of heat and mass transfer was developedto simulate the temperature, moisture content, and oilcontent during the frying process of tortilla chips. Thismodel can be used to analyse processes for a single chip anda batch of chips.

To validate the model, experiments were also conducted.Temperature at the centre of the chip during both the fryingand cooling processes, temperature of the oil during thefrying process, moisture and oil contents of the chip atdifferent frying times were measured.

Good agreement was obtained between the model and theexperimental results. This agreement also validates thefrying mechanism proposed in this study. Batch frying isquite different from a single chip frying process because thetemperature of the oil changes significantly during the batchfrying process. Analysis of this process is very important forindustrial practice.

NOMENCLATURE

A tortilla chip surface area per unit bed volume, m2m-3Bi Biot number

Cp specific heat of chip, Jkg-1K-1Cpf specific heat of the oil, J kg-I K-1Cpw specific heat of water vapour, J kg-I K-1Df mass diffusivity of oil, m2S-IDw mass diffusivity of moisture, m2S-IF oil content of the tortilla chip in wet basis, defined as: (kg oil

absorbed)f(kg product), wb


Fe final oil content at surface interface between batch and the bath oils,wbFourier number

oil content of the surrounding oil, decimal, wbinitial value of oil content of the chip, decimal, wbsurface oil content of the chip, decimal, wbinitial moisture content, decimal, wb

convection heat transfer coefficient between the oil and the chip,Wm-2K-1

convection mass transfer coefficient of water vapour, m S-Iconvection mass transfer coefficient of oil at the surface of chips,ms-1

latent heat of vapourization, J kg-Iconvection heat transfer coefficient between frying oil andsurrounding oil, Wm-2K-1thermal conductivity, W mK-1half thickness of product, mmoisture content of the tortilla chip in wet basis, defined as: (kgwater evaporated)/(kg product), wb

moisture content of the tortilla chip in dry basis, defined as: (kgwater evaporated)/(kg product - evaporated water), dbequilibrium moisture content, wbmoisture content of the surrounding oil, wbinitial value of moisture content, wb

surface moisture content of the chip, wbsurface area of the frying oil per unit volume of oil, m2m-3time, s

temperature of the frying oil between the chips, °Cabsolute temperature of the frying oil between the chips, Kset temperature of the frying oil, °Cinitial value of oil temperature, °Cproduct thickness, mthermal diffusivity, m2 S-Iporosity of the bed of tortilla chips,water/vapour flux, kgm-2s-1temperature of the chip, °Cinitial values of temperature, °Csurface temperature of the chip, °Cbulk density of the chip, kg m-3density of the oil, kg m-3

Fo

F~FoFsurIMCh

kIM

REFERENCES

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 infrying, in Frying of Food, Principles, Changes, New Approaches,Varela, G., Bender, A. E., and Morton, I. D. (ed) (VCH Publishers,Chichester, England) .

3. Pravisani, C. I. and Calvelo, A., 1986, Minimum cooking time forpotato strip frying, J Food Sci, 51: 614-617.

4. Gamble, M. H., Rice, P., and Selman, J. D., 1987, Relationshipbetween oil uptake and moisture loss during frying of potato slicesfrom c.v. Record U.K. tubers, Inti J Food Sci Technol, 22: 233-241.

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6. Gamble, M. H. and Rice, P., 1987, Effect of pre-fry drying of oil uptakeand distribution in potato crispy manufacture, Inti J Food Sci Technol,22: 535-548.

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8. Pinthus, E. 1., Weinberg, P., and Saguy, I. S., 1995, Oil uptake in deep-fat frying as affected by porosity, J Food Sci, 60: 767-772.

9. Pinthus, E. 1. and Saguy, I. S., 1994, Initial interfacial tension and oiluptake by deep-fat fried foods, J Food Sci, 59(4): 804-807.

10. Moreira, R G., Palau, J. E., and Sun, X., 1995a, Deep-fat frying oftortilla chips: an engineering approach, Food Technol, 49(4): 146-152.

II. Farkas, B. E., Singh, R P. and Rumsey, T. R, 1996, Modeling heat andmass transfer in immersion frying. I: model development, J FoodEngineering, 29: 211-226.

12. Farkas, B. E., Singh, R. P. and Rumsey, T. R., 1996, Modeling heat andmass transfer in immersion frying. II: solution and verification, J FoodEngineering, 29: 227-248.

13. Ateba, P. and Mittal, G. S., 1994b, Modelling the deep-fat frying ofbeef meatballs, Int J Food Sci and Tech, 29: 429-440.

14. Benson, C. K., Caridis, A. A. and Klein, L. F., 1992, Continuous foodprocessing methods, United States Patent number 5,/37,740.

15. Moreira, R. G. and Barrufet, M. A., 1997, A new approach to describeoil absorption in fried foods: a simulation study, submitted to theJournal of Food Engineering.

16. Chen, Y., 1996, Simulation of a deep-fat frying process for tortillachips, Master Thesis, (Department of Agricultural Engineering, TexasA&M University, USA).

17. Moreira, R. G., Palau, J. E., Sweat, V. E., and Sun, X., 1995b, Thermaland physical properties of tortilla chips as a function of frying time, JFood Proc Preserv, 19: 175-189.

18. Moreira, R G. and Sun, X., 1997, Snack foods: tortilla chipsprocessing, in Deep fat frying, Blumenthal and Pokorny, (ed)(Chapman & Hall, New York) in press.

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20. Hallstrom, B., 1979, Heat and mass transfer in industrial cooking, inFood Process Engineering, Linko, P., Malkki, Y., Olkku, 1., andLarinkari, J., (eds) vol. I, (Applied Science Publishers Ltd., London)pp. 457-465.

21. Choi, Y. and Okos, M., 1986, Thermal properties of liquid foods-review, in: Physical and Chemical Properties of Food, Okos R M.,(ed) (ASAE Publication, St. Joseph, MI).

ADDRESS

Correspondence concerning this paper should be addressed to ProfessorR G. Moreira, Department of Agricultural Engineering, Texas A&MUniversity, 201 Scoates Hall, College Station, Texas 77843-2117, USA.

The manuscript was received 21 January 1997 and accepted forpublication after revision 5 June 1997.


modelling of a batch deep-fat frying process for tortilla chips

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