R.G. Moreira Department of Biological and Agricultural Engineering, Texas A&M University, College Station, TX, USA.

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1 CHAPTER 7 Deep-fat frying R.G. Moreira Department of Biological and Agricultural Engineering, Texas A&M University, College Station, TX, USA. Abstract Frying models can be very complex. Comprehensive models associate energy, mass, and momentum transport equations with all the thermodynamically interactive fluxes. Food materials are typically hygroscopic in which some water is tightly bound to the solid matrix, causing shrinkage when frying. Oil absorption is a complex phenomenon that still requires investigation. The models presented here show the most used approaches to simulate the frying of a single product or a batch of products. These models require a series of input parameters that sometimes are not available in the literature. Numerical solutions are required to solve these models because the nonlinearity of the developed partial differential equations. 1 Introduction Frying is one of the most popular unit operations to process foods. Frying makes food more palatable, it is fast, and fried products keep better. There is a large economical potential for development of innovative and improved frying processes. Typical examples of frying technology still evolving include improving oil quality, the mechanism of oil absorption, and engineering considerations of residence time and design [1]. Deep-fat frying, or immersions frying, is defined as the process of cooking and dehydration of foods by immersing them in hot oil, typically, at C. During this time, various chemical and physical changes occur. Chemical structural changes occur in the form of starch gelatinization, protein denaturation, and flavor development. Physical changes are manifested as a decrease in moisture content, increase in product temperature, oil content, and crust formation. doi: / /07

2 210 Heat Transfer in Food Processing Fried products absorb oil during frying and as they cool. Changes taking place during frying are difficult to model since there are a number of interrelated factors that have to be taken into account. It is important to identify the structure changes during the different stages of the process to understand better the quality changes that occur during frying. The porosity of the product formed during frying plays an important role in the subsequent oil uptake. When a crust begins to form at the surface of potato chips, for example, there is an excessive pressure buildup and the product expands and puffs. Therefore, a better understanding of the transport processes and their relationship to various parameters should provide ways to optimize the frying process, and thus control oil pickup. Mathematical models of various complexities have been developed. These models deal with frying of individual products assuming constant physical properties. A large number of models have been based on simple diffusion of energy and mass transfer, with various approximations accounting for evaporation or ignoring it altogether, and not including the oil phase transport [2]. The single-piece frying models can be divided into two types, namely, heat and mass balance (semi-empirical) and differential equation (DE) models. The first type is treated, partially, for its historic interests and partly to place it in content of a more general model. A number of DE models, one for chips (all crust) and one for French fries (crust and core), is presented and given a much more detailed treatment in view of greater accuracy and applicability over a wide range of frying problems. 2 Mathematical models 2.1 Heat and mass balances models the semi-empirical models For a crustless model (e.g. bread croutons, extruder puffed snacks, soy protein), moisture content during frying is proportional to the square root of frying time and the difference between oil temperature and boiling temperature of water. For crust-forming products (French fries), an ordinary DE similar to Plank s equation for freezing is used to predict the crust thickness of the product during frying [3]. The limitations of these models are as follows: (1) physical and thermal properties are assumed constant; (2) oil absorption is neglected; (3) sensible heating is neglected in the core and in the crust; (4) do not address the transient temperature and moisture profiles in the core. 2.2 DE models the deterministic models DE models of frying are based on the laws of heat and mass transfer and lead to rather complicated systems of equations. The models can be solved only with the aid of digital computers. This model describes the frying process as illustrated in Fig. 1. During frying, heat is transferred by convection from the oil to the surface of the product (i.e. chips or French fries), and then transferred into the center of the product by conduction. There is, however, a certain transfer of heat coupled to the transfer of water vapor,

3 Deep-Fat Frying 211 Figure 1: Schematic of an infinite slab undergoing frying. which is the energy carried by the water/vapor. Most of the water escapes from the product in the form of vapor during frying. The moisture content decreases, oil content increases, and the chip becomes more porous during frying. Two regions, crust and core, exist during frying. The crust/core interface moves toward the center of the food during frying. In the interface, the temperature remains at the boiling point for a short period of time to allow for the water present in that region to evaporate. The assumptions to this model include: (1) the product is initially isotropic and isothermal; (2) the initial moisture and temperature distributions in the product are uniform; (3) the heat required for chemical reactions (i.e. starch gelatinization, protein denaturation) is small compared to the heat required to evaporate the water; (4) thermal and physical properties are functions of local temperature and moisture content during the frying process; (5) a microscopically uniform porous medium is formed after frying; (6) the surface of the product is covered with a uniform layer of oil after frying, and (7) most of the oil diffuses into the chip after frying during the cooling period DE model for all crust products (chips) Governing equations for temperature change in the product (k T p ) (N w c pv T p ) = (ρ pc p T p ) t (1)

4 212 Heat Transfer in Food Processing The second term on the left side of eqn (1) represents the heat transfer caused by diffusion of water vapor, where N w is the water vapor flux, N w = ( ρ p D w M ) (2) where ρ p is the product density, M the product moisture content, D w the mass diffusivity of water vapor, k the thermal conductivity of the product, c p the specific heat of the chip, T p the product temperature, and c pv the specific heat of the water vapor Governing equations for mass change in the product Fick s law of diffusion is used to calculate the mass transfer rate in the product in two different directions: moisture (water vapor) diffuses from the chip to the oil and the oil diffuses from the surface to the center of the chip, (D v ρ p M ) = (ρ pm ) t (D f ρ p F) = (ρ pf) t where D f is the mass diffusivity of oil, F the oil content. Equations (1) (4) are used to describe temperature and moisture changes at all points in the chip (i.e. core and crust). Inside the crust, there is an evaporation zone that moves toward the center of the product. In the evaporation zone, the temperature is constant, and the energy is mainly used to evaporate the water. The duration of this constant period depends on the water content in that location. As the water content is reduced at the level corresponding to M e (equilibrium moisture content), the temperature increases rapidly and this part of the product becomes part of the crust. Different thermal properties are used for the two different zones in the product. When the temperature of the chip is higher than the boiling temperature of water, the properties of vapor instead of liquid water are used to predict temperature and moisture changes in the product. The crust has thermal and physical properties of an insulating material. Its low thermal conductivity and porosity slow down the rate of heat transfer and therefore the rate at which the product cooks and water vaporizes. In the case that the ratio of the volume of product to the volume of oil in the frying vat is large (batch process), the temperature of oil will decrease significantly during the first seconds of frying when the products are dropped into the fryer. The change in enthalpy of the oil with respect to time in the spaces between the products is equal to the sum of energy required for heating the product, for evaporating water from the chips, for heating the water vapor evaporated from the chips, and for exchanging energy to the surrounding oil, (3) (4) m fat c pfat T fat t = [ h T p + h fg D w ρ b M + N w c pv (T p sur T fat ] (1 ) + h A o (T fo T fat ) (5) A p

5 Deep-Fat Frying 213 where h is the convective heat transfer coefficient between frying oil (in the bed of products) and surrounding oil, A p is the chip specific surface area (batch of chips), A o the oil specific surface area (surface area of the frying oil per unit volume of oil), and is the porosity of the batch of products Initial and boundary conditions At the onset of the frying process, the temperature and moisture content of the product are uniform. The initial conditions in equation form are thus, T p n,t=0 = T po and M n,t=0 = M o (6) The mathematical domain is bounded by the product surface and the center of the stack of products. Because of the symmetry, there is no temperature or moisture concentration gradient at the product s center (n = 0); therefore, at this boundary the following conditions exist, M n = 0 n=0,t F n = 0 n=0,t and T n = 0 (7) n=0,t At the surface (n = L) for any time, the energy transferred by convection from the oil to the chip s surface is equal to the sum of energy required for transferring heat to the center of the product by conduction, for evaporating water from the chips, and for heating the water vapor evaporated from the chips at temperature T p to the oil temperature T fat [4]: h(t p sur T fat ) = k θ n + N w[h fg + c pv (T p sur T fat )] (8a) where n represents the normal to the surface, h the convective heat transfer coefficient, and h fg the latent heat of vaporization. The second term on the right side of the eqn (6a) is eliminated when the temperature of the chip is above the boiling point of water, h(t p sur T fat ) = k θ n + N wc pv (T p sur T fat ) (8b) with two mass transfer boundary conditions, k d ρ p (M sur M ) = N w (9) where M = M e = 0, i.e. the moisture content of the surrounding oil, and, k d ρ p (F sur F ) = D f F n (10) where F = M e = 1, i.e. the oil content of the surrounding oil.

6 214 Heat Transfer in Food Processing Input parameters The mathematical model requires physical and thermal property data of the material to be fried and the process. While most property data are obtained from values reported in the literature, some of the properties will need to be analyzed and determined for the product being fried DE model for crust and core products (French fries) The main differences with the previous approach are (1) the process is viewed as a moving boundary problem similar to the freeze-drying situations; (2) the product is divided into crust (free of liquid water and above the boiling point) and core (vapor free and below the boiling temperature, but not saturated) and mass and energy equations are developed for each region (Fig. 1); (3) the vapor moves in the crust region due to pressure differences; and (4) the mass fraction of oil in the fried product is assumed negligible with negligible effect on other mass and energy fluxes [5, 6] Governing equations for temperature change in the product Core region 0 < x < X(t) Crust region X(t) < x < L k II ( 2 T p ) N βx c pβ ( T p ) = (ε β ρ β + ε σ ρ σ c ρσ ) T p t (11) (ε γ ρ β c pγ + ε σ ρ σ c ρσ ) T p t = k I ( 2 T p ) + N γx c pγ ( T p ) (12) where subscripts β, γ, and σ refer to liquid water, water vapor, and solid, respectively; superscripts I and II are crust and core regions, X(t) the position of crust/core interface, and ε the volume fraction Governing equations for mass change in the product Core region 0 < x < X(t) C β = D βσ 2 C β (13) t Crust region X(t) < x < L (ρ γ P γ ) = 0 (14) where C is the concentration Initial and boundary conditions Sets of eight boundary conditions and three initial conditions are specified to solve these equations. The boundary condition at the crust-core interface is defined as k I ( T p ) + k II ( T p ) ρ γk γ µ γ ( P γ )(h β H γ ) = [(ε σ ρ σ (h I σ hii σ ) + ε γρ γ (H γ h γ )] dx dt (15)

7 where the interfacial mass balance is dx dt Deep-Fat Frying 215 = N βx N γx ε γ ρ γ ε β ρ β (16) N βx = D βσ 2 c β and N γx = ρ γk γ µ γ ( P γ ) (17) K the permeability, µ the viscosity, and P the pressure. The final mass transfer boundary condition relates the pressure of the vapor, P γ,at the crust/core interface to the temperature through the Clausius Clapeon equation: at x = X(t), t > 0 P γ T = h fg T(V γ V β ) [ ] hfg P γ = exp RT + B (18) (19) Input parameters There are several physical properties and transport parameters that are required to solve the DEs describing the models. These include the heat transfer coefficient, the mass diffusion coefficient, the crust and core thermal properties, and densities Solution of the equations As frying is a simultaneous heat and mass transfer process, correlation of moisture and temperature changes in the product involves solution of coupled DEs. Generally, the equations are not linear (the parameters involved in the equations are functions of moisture or temperature) and must be solved through numerical methods. 2.3 Multiphase porous media models the mechanistic model The deterministic models developed for deep-fat frying are based on scientific principles such as the conservation of mass, momentum, and energy. Mechanistic models include kinetic, thermodynamic equilibrium, and mass transport models. Both models lead to complex theoretical equations that can be solved only with the aid of digital computers. Simplifying assumptions are generally made in order to solve these models. These include the use of simplified geometry, homogeneity, and idealized initial and boundary conditions. Parameter estimates (i.e. reaction rates, mass transfer coefficients) have a critical role in mechanistic modeling, and are often based on empirical equations and physical models. The drying and frying processes are very similar and many models have been developed to describe and predict the two systems. The basic energy and mass governing equations are very much the same. The differences in the models usually come in the system which the model is describing. In each case, assumptions,

8 216 Heat Transfer in Food Processing boundary conditions, transport mechanisms, and physical properties for each system will vary. Food materials are considered hygroscopic and consist of bound water. During frying, the removal of bound water causes shrinkage of the material. There are several assumptions that have been widely used for drying processes. These include: (1) the phases of solid, liquid, and gas are continuous; (2) local thermal equilibrium is valid, which means that the temperatures in the three phases are equal; (3) sorption isotherm is valid in describing the vapor pressure as a function of temperature and the moisture content; (4) gas phase consists of a binary mixture of air and vapor; (5) Darcy s law is valid in describing the convective flow of liquid and gases; (6) liquid transport is due to the capillary and convective flow, and gas transport is due to convective flow and molecular (Knudsen) diffusion; and (7) heat conduction in the porous media is described in terms of effective thermal conductivity and is proportional to the mass content of each phase. For the frying of chips, the following assumptions are also included: (8) the latent heat of vaporization cools the region during evaporation keeping the local temperature near the boiling point, (8) local temperature remains at boiling point until very low water saturation is reached, (9) heat transfer coefficient is a function of frying temperature and temperature gradient between the surface and the oil, (10) shrinkage is due to bound water removal, and (11) puffing is due to air and vapor expansion. During the frying of a porous media, the following transport phenomena will take place: diffusive transport of vapor and air, capillarity driven transport of liquid (water and oil), and total pressure driven flow of liquid, vapor, and air. The following rate equations are derived in similar fashion to Ni and Datta [7]. Combining the diffusive and convective fluxes, the total flux of air and vapor becomes: n a = ρ a K i K gr µ g P C2 ρ g M a M v D eff,g x a (20) n v = ρ v K i K gr µ g P C2 ρ g M a M v D eff,g x v (21) where K i is the intrinsic permeability, K gr the air relative permeability, K vr the water vapor relative permeability, M the molecular weight, D eff the effective mass diffusivity, and x the molar fraction. The liquid flux of water and oil based on the total cross-sectional area can be derived as n w = ρ w K i K wr µ w P a m S w δ T T (22) n o = ρ o K i K or µ o P a mo S o δ To T (23)

9 Deep-Fat Frying 217 where S w is the water saturation (pore volume fractions occupied by water), S o the oil saturation, K wr the water relative permeability, and K or the oil relative permeability. The coefficients a m, δ T, a mo, and δ To, are given below: a m = ρ w K i K wr µ w p c S w a mo = ρ o K i K or µ o p c S o K i K wr p c δ T = ρ w µ w T K i K or p c δ To = ρ o µ o T where the capillary pressure p c is a function of S w and T Governing equations The conservative equations for vapor, liquid water, air, and energy in the porous medium are written, respectively as follows Mass conservation of vapor and liquid water ( ) pv M v S g φ + t RT t (ρ wφs w ) = ( n v + n w ) (24) where M is the molecular weight, φ the porosity, p the partial pressure, and R the gas constant Mass conservation of air ( ) pa M a S g φ = ( n a ) (25) t RT Mass conservation of oil t (ρ oφs o ) = ( n o ) (26) Energy conservation (ρc p ) eff T t (h fg φρ w ) S w t (h fg φρ o ) S o t = ( n v c pv + n a c pa + n w c pw + n o c po ) T + [( a m h fg ) S w ] + [( a mo h fg ) S o ] + [( k eff (δ To δ T )) T] [ ( Ki K wr + ρ w + K ) ] ik or ρ o h fg P µ w µ o where k eff is the effective thermal conductivity of the product. (27) Initial and boundary conditions The product is assumed to be at equilibrium prior to frying and has uniform S w, S o, T, and P. The initial conditions include S w = S wi, S o = 0; T = T i, P = P amb. The boundary conditions are given below.

10 218 Heat Transfer in Food Processing Closed boundary Assuming symmetric geometry, the closed boundary yields the following mass and energy equations n w + n v = 0 (28) n o = 0 (29) n a = 0 (30) k eff T = 0 (31) Open boundary Mass transfer on the surface is assumed to be in equilibrium with the surrounding. Regardless of volumetric evaporation present inside, surface evaporation occurs simultaneously which means that there is liquid flux crossing the boundary and vaporizing instantly [7]. Therefore, the surface evaporation only affects the boundary mass and heat flux. At the surface, oil saturation is assumed constant. For the open boundary, the following mass and energy equations are ( ) n v + pv n w = φ(s g + S w ) R v T ρ v0 h mv (32) S o = S o1 (33) P = P amb (34) k eff T = h(t T amb ) + n w h fg (35) Oil absorption during cooling The majority of the fat content in products such as tortilla chips results from the absorption of oil during the cooling process [8]. The only transport phenomenon during cooling is oil absorption, which is assumed to be a function of the capillary pressure. In solving the sets of partial DEs for the cooling process, eqns (24) (27) are followed with several additional assumptions. First, there is no moisture transfer and, second, there is rapid oil transfer due to the capillary pressure difference. The initial conditions during cooling are S w = S ii, S o = S o1 ; T = T amb, P = P amb. The closed boundary conditions are the same as eqns (28) (31) and the open boundary conditions are the same as eqns (32), (34), and (35), but eqn (33) is modified to include the oil flux, K i K or p c n o = ρ o (36) µ o S o Structural changes The basis of this model is to account for the structural changes during the frying process. Experimental data on shrinkage and expansion are required to model the structural changes during the process [2]. Realistically, a microscopic model may have to be developed to represent each individual pore expansion.

11 Deep-Fat Frying Input parameters This model also needs a large number of input parameters. Some are physically measurable while others are quite difficult and are not available for food systems. These parameters are porosity, thermal conductivity, density, specific heat, capillary diffusivity, molecular diffusivity, vapor and liquid permeability, and moisture isotherms Implementation case study: deep-fat frying of tortilla chips The 2-D model of Yamsaengsung and Moreira [1] will be used to illustrate the application of the described mechanistic model. This model was developed to predict the heat and mass transfer during the frying and cooling process of tortilla chips. Since symmetry is assumed, the diagram shown in Fig. 2 illustrates only the top right section of the tortilla chip viewed from the side. The tortilla chip is then divided into four sections. Only the upper right section was considered for model development. Figure 3 shows the transport mechanisms involved in the frying process. There is no mass or energy transfer from the bottom and left sides, while there Figure 2: Schematic of the 2-D model for a tortilla chip. Figure 3: Transport mechanism for the 2-D frying process of a tortilla chip (showing the top right section of the chip).

12 220 Heat Transfer in Food Processing Figure 4: Model of thickness expansion due to puffing. Upper slice of the tortilla chip. are diffusional and convective fluxes occurring at the top and the right side of the tortilla chip. Experimental data on shrinkage and expansion obtained from Kawas and Moreira [9] were used to develop empirical equations of shrinkage and expansion factors as a function of the average water saturation of the tortilla chip. Following Achanta s puffing algorithm [10], more thickness expansion was assigned toward the center of the chip and progressively less expansion was assigned moving toward the edges. This is to account for a higher gas pressure expansion toward the center of the product. Figure 4 shows the model of thickness expansion due to puffing Numerical solution The finite element formulation for solving the set of coupled partial DEs is taken from Lewis et al. [11]. Lee s three level time-stepping scheme was applied to produce a series of algebraic equations D model To obtain the distribution of water saturation, S w, oil saturation, S o, temperature, T, and pressure, P, in the radial (x-direction) and y-direction, a 2-D analysis of the problem was completed. The assembly of elements method was used with each element being four-noded quadrilateral elements. Quadrilateral elements are useful when considering shrinkage and expansion, when the elements become nonrectangular. The Gauss Legendre method [12] was used for the numerical integration of each of the integrals. Each of the input parameters was updated locally and applied to that particular element. The system of nonlinear equations (including contributions from all elements) was solved using FORTRAN [2] Boundaries Figure 5 depicts the setup of the open and closed boundaries. Oil transfer at the surface by capillary pressure, eqn (36), was applied to the boundary only during the cooling process. The moisture content and the structure of the tortilla chip were assumed to remain constant during cooling, while the pressure and temperature were assumed to decrease toward the ambient conditions. Therefore, moisture transport at the boundary was zero during cooling, and T amb for eqn (35) was equal to T cooling. Moreover, the mesh was assigned to be more concentrated near the surface where there was a rapid change in S w, S o, T, and P Structural changes Equations (37) (40) were used to recalculate the diameter and thickness (in the y-direction) of the tortilla chip as a function of

13 Deep-Fat Frying 221 Figure 5: Symmetric portion of tortilla chip with open and closed boundaries. Approximated drawing of actual mesh distribution. the water saturation after each time step [9], S factor = S 3 w S2 w S w (37) where S factor = d(t) d(o) (38) and d(t) is the diameter of the tortilla chip at time t and d(o) is the initial diameter. Ex factor = S 3 w S2 w S w (S w < 0.20) (39) where Ex factor = w(t) w(o) (40) and w(t) is the thickness of the tortilla chip at time t and w(o) is the initial thickness. The shrinkage factor was applied to approximately the outer 13% of the tortilla chip, with the rest of the internal nodes (x-coordinates) fixed at the same coordinates. This was done to increase stability of the internal nodes (maintain small S w, S o, T, and P) as the program proceeded from one time step to the next. For the expansion process, the factor was used for S w < 0.20, because there was no puffing observed until the corresponding water saturation (less than 14% moisture content w.b.) [2] Input parameters The input parameters are vital in yielding an accurate predictive model. For different products, the input parameters will vary, thus reliable experiments must be conducted. For food products, relatively little data, such as the

14 222 Heat Transfer in Food Processing permeability of liquids and gases, the sorption isotherms, and the capillary pressure curve, are available. Equation (40) gives the sorption isotherm used in this model. The equation is taken from Kawas [9] who fitted experimental data for the frying of tortilla chips with the Chung and Pfost [13] model. The k 1 and k 2 values are kg-mol/kj and 17.91, T is in kelvin, and M is moisture content (d.b.), ( ) pv ln = k 1 RT exp ( k 2 M ) (41) p s Since no permeability data for tortilla chips have been collected, values for the intrinsic and relative permeabilities follow those used by Ni and Datta [7]. To account for the convective flow of liquid and gas due to capillary pressure, several correlations were studied. In this model, the Spolek and Plumb [14] equation was modified (eqn (42)) and it gave good results. The equation gives the capillary pressure as a function of water saturation. In further research, experiments must be conducted to obtain true capillary pressure curves for tortilla chips, p c = S 0.23 w (42) The effective heat capacity, which includes the contribution of all the components in the tortilla chip, is given in eqn (43), (ρc p ) eff = ρ s c ps (1 φ) + ρ w c pw φs w + ρ o c po φs o + ρ g c pg φ(1 S w S o ) (43) Changes in the tortilla chips specific heat (c ps ) with temperature were small compared to changes with moisture content [4]. The heat capacities of the tortilla chip solid fraction along with the rest of its components are shown in Tables 1 and 2. The unit of specific heat is J/kg K. From Table 1, M is the moisture content in decimal (d.b.), M a is the molecular weight (m.w.) of air (28.85 g/gmol), and M v is the m.w. of vapor (18.02 g/gmol). Table 1: Heat capacity values used in this model [2]. Parameter Values (J/kg K) Solid c ps = ( W 1.557M 2 ) 10 3 Water c pw = 4180 at 15 C Oil c po = 2223 O 2 (J/mol K) c po2 = (a O2 + b O2 T + c O2 T 2 + d O2 T 3 ) N 2 (J/mol K) c pn2 = (a N2 + b N2 T + c N2 T 2 + d N2 T 3 ) ( ) 1 Air c pa = (0.21C po C pn2 ) 10 3 M a Water vapor c pv = (a v + b v T + c v T 2 + d v T 3 ) 10 3 ( 1 M v )

15 Deep-Fat Frying 223 Table 2: Coefficients for determining c po2, c pn2, and c pv from Table 3. Component a b c d O N Water vapor Table 3: Thermal conductivity values used in this model. Parameter Values (W/m K) Water k w = 0.64 Gas k g = Oil k o = 0.17 The effective thermal conductivity (in W/m K), which includes the contribution of all the components in the tortilla chip, is given in eqn (44): k eff = k s (1 φ) + k w φs w + k o φs o + k g φ(1 S w S o ) (44) The thermal conductivity of solid fraction of the tortilla chip is taken from the following correlations [4]: k s = T T 2 for T 100 C (45) k s = T T 2 for T > 100 C (46) where T is the temperature of the tortilla chip. The rest of the thermal conductivity values are shown in Table 3. In addition, the heat and mass transfer coefficients are important parameters that are also very hard to determine for food materials. Farkas and Hubbard [15] found the convective heat transfer coefficients, h, to be a dynamic property ranging from 300 to 1100 W/m 2 K and to be coupled with the movement of oil. For this study, it was assumed that the temperature of the product does not increase until very low moisture content due to large latent heat of vaporization compare to the rate of heat transfer from the oil to the surface. Thus, the convective heat transfer term is neglected during this period. Once the water saturation of the product has dropped below 0.20, the convective heat transfer term is added back on. This water saturation limit is used based on experimental observations [9]. Furthermore, the mass transfer coefficient is assumed to be a function of the moisture gradient and the frying temperature. As the water saturation decreases, h mv decreases, and as the frying temperature increases the initial h mv increases.

16 224 Heat Transfer in Food Processing Convergence and mesh refinement Mesh refinement is used to check for convergence of the numerical results. The input parameters used in this simulation are shown in Tables 4 and 5. The input data are for 1.27 mm thick tortilla chips fried at 190 C. The number of nodes that were analyzed included 80, 96, 120, and 144 nodes. It takes 100 s per time step for the 144 nodes setup while it takes only 12 s Table 4: Input parameters for the 2-D frying model for tortilla chips [2]. Parameter Symbol Value Units Latent heat of vaporization h fg J/kg True density ρ s kg/m 3 Water density ρ w kg/m 3 Oil density ρ o kg/m 3 Vapor density ρ v kg/m 3 Air density ρ a 1.30 kg/m 3 Bulk density ρ eff M kg/m 3 Water intrinsic permeability k wi m 2 Gas intrinsic permeability k ai m 2 Oil intrinsic permeability K oi 0.05(k wi ) m 2 Irreducible water saturation S ir Vapor diffusivity in air D va m 2 Water thermal conductivity k a 0.64 W/m K Oil thermal conductivity k o 0.17 W/m K Gas thermal conductivity k a W/m K Heat capacity c p Tables 3 and 4 J/kg K Water viscosity µ w Pa s Vapor viscosity µ v Pa s Gas viscosity µ a Pa s Oil viscosity µ o µ ref exp [E a /RT] Pa s Heat transfer coefficient h 285 W/m 2 K Mass transfer coefficient h mv m/s Table 5: Input parameters for cooling. Parameter Symbol Value Units Surface oil saturation for 25 C So Surface oil saturation for 80 C So Oil relative permeability k or 0.01 Oil intrinsic permeability for 25 C k ir k wi 0.18 m 2 Oil intrinsic permeability for 80 C k ir k wi m 2 Heat transfer coefficient for air h 25 W/m 2 K

17 Deep-Fat Frying 225 per time step for the 80 nodes setup. Based on the agreement between experimental and predicted results, it is sufficient to use just 80 nodes for the calculations of the 1.27 mm thick chips [2] Validation Several frying conditions were set according to the experiments performed by Kawas and Moreira [9] and Chen and Moreira [4]. All moisture contents are in wet basis (w.b.) unless specified During frying Figure 6a shows the water saturation profile of a 1.27-mm thick tortilla chip with an initial moisture content (IMC) of 42% fried at 190 C. The figure shows good agreement between the predicted model and the experimental data. The predicted curve resembles typical drying curves. Most of the water is lost during about the first s of frying. This period is described by a falling rate period in which the rate of moisture loss decreases and the slope of the drying curve decreases. Finally, once the equilibrium is reached, the slope is nearly zero. Figure 6: Model validation: (a) water saturation during frying (T = 190 C, IMC = 42%, thickness 1.27 mm), (b) chip s temperature during frying (IMC = 42%, T = 190 C, thickness = 2.60 mm); (c) oil saturation during cooling (T = 25 C, chip thickness = 1.60 mm, IMC = 44% w.b., frying temperature = 190 C), and (d) chip s temperature during cooling (IMC = 42%, thickness = 2.60 mm, T = 25 C).

18 226 Heat Transfer in Food Processing The experimental temperature profile is shown along with the predictive profile in Fig. 6b. It indicates a short sensible heating period until the product temperature reaches the boiling point of water (approximately 100 C). Following the sensible heating period, the sample enters a constant temperature period in which all of the heat is used to evaporate water from the product (i.e. latent heat). After water has been removed to nearly equilibrium, the temperature at that particular region begins to increase up to the temperature of the oil bath (approximately 190 C). While the temperature at the center of the product may still be in the proximity of 100 C, the temperature near the edges (crust) is already above 100 C. This edge region is the crust region, which contains very little moisture and has physical properties much different than the high moisture core region. As frying proceeds, the crust region increases in thickness and moves toward the center of the product During cooling During the cooling process, when the chips are removed from the fryer, the oil content increases sharply, reaching a maximum value at about 160 seconds, i.e. when the chips temperature is reduced to the ambient temperature [16]. Since nearly 64% of the oil is absorbed during cooling, the mechanism of oil absorption may be related to the capillary pressure difference and the interfacial tension between the oil and the gas within the pores [16]. Hence, the oil transport due to capillary pressure term is included during the cooling process. From previous experiments [4], it has been shown that less oil absorption occurs when the ambient temperature is closer to the temperature of the product at the instant it has been removed from the fryer (i.e. 190 C). Figure 6d compares the predicted and experimental results for cooling at 27 C. To make a comparison with the experimental data, the original oil content was set at 8.0% w.b., or an oil saturation value of Oil saturation was uniformly distributed for this particular case. For tortilla chips fried at 190 C, the amount of oil absorption predicted during frying alone was around The total amount of oil absorbed after cooling was about 27% w.b. or about 0.28 oil saturation. The temperature history of the tortilla chips during the cooling process was compared with data from Chen [4] at 27 C. Figure 6d shows that even after 160 s, the temperature of the tortilla chip still does not reach the ambient temperature. This is due to the thickness of the tortilla chip. Further cooling would force the product temperature toward the ambient temperature. The temperature drops rapidly during the first part of the cooling process with the chip cooling at a lower temperature having a less dramatic temperature drop. This rapid decrease in temperature also leads to a rapid decrease in the internal pressure of the tortilla chip resulting in about 0.28 oil saturation (27% OC w.b.) Structural changes During frying, the tortilla chip undergoes both shrinkage in the radial direction and expansion in the thickness due to gas bubble expansion inside the tortilla chip. Figure 7 shows the thickness (y) at each radial position (x) of the chip during frying. Most of the shrinkage occurs after 5 s of frying and most of the expansion occurs after 20 s of frying, or at very low water saturation. Expansion was occurring at about the time the crust was forming.

19 Deep-Fat Frying 227 Figure 7: Shrinkage and expansion of tortilla chips during frying (IMC = 42%w.b. and oil temperature 190 C). The formation of the crust greatly reduces the rate of moisture transfer and causes an increase in pressure inside the chips. Thus, this pressure buildup leads to an expansion of the pores, which results in a crispy final product. When the expansion factor was not included, the pressure increased even more dramatically and the solution sometimes diverged Sensitivity analysis After obtaining reasonable agreement with the experimental data, a sensitivity analysis was performed to study the effects of the frying and cooling temperatures, the IMC, and the tortilla thickness on the water saturation, oil saturation, temperature, and pressure profiles During frying Several factors affect the water saturation, oil saturation, temperature, and pressure profiles during the frying process. The frying temperatures that were examined included 130 C, 160 C, and 190 C. In addition to the IMC of 42%, values of 27% and 48% w.b. were studied. Finally, the thickness of the tortilla chip was considered. The values used were 1.27 and 2.60 mm. Effect of frying temperature Figure 8 presents the plots of the water saturation, oil saturation, temperature, and pressure profiles along the center of the tortilla chip fried at 130 C and 190 C. The values are plotted as a function of the thickness coordinate of the tortilla chips at 10, 20, and 60 s of frying. After 60 s of frying, there is a much larger water saturation gradient from the center to the surface for the chips fried at lower temperature, since the temperature of the chip increases much slower than for the 190 C chip. The profiles also illustrate that oil saturation gradient for the chip fried at higher temperature is much more significant, because it has lower oil content in the center and lower average oil content.

20 228 Heat Transfer in Food Processing Figure 8: Effect of frying temperature on the water saturation, oil saturation, temperature, and pressure profiles at 10, 20, and 60 s of frying. IMC, 42% w.b.; chip thickness, 1.27 mm; frying temperature, 130 C and 190 C. In addition, the temperature profiles show that a significant temperature gradient develops from the center to the surface of the chip after only 20 s of frying for the 190 C chip, while the gradient is only evident after 60 s of frying for the 130 C chip. Finally, the pressure profiles for the two frying temperatures are very similar; however, the pressure value is much higher for the 190 C chip. Effect of IMC Figure 9 shows the profiles along the thickness of the tortilla chip for chips fried at 27% and 42% IMC. The frying temperature was 190 C and the chip thickness was 1.27 mm. The values are plotted at 10, 20, and 60 s of frying. The water saturation profiles indicate that after 60 s of frying, there was no gradient from the center to the surface of the chip with 27% IMC, while there is still a slight gradient for the 42% IMC chip. The oil saturation profiles show that the 42% IMC chip absorbs more oil than the 27% IMC chip, as discussed previously, and there is a much larger gradient from the center to the surface of the chip for the 27% IMC chip because of its lower oil saturation value. The temperature profiles show that there is a large temperature gradient from the center to the surface of the chip after only 10 s of frying for the 27% IMC, while it takes over 20 s for a temperature gradient to be evident in the 42% IMC case. Finally, the pressure profile along the thickness of the chip is fairly flat, indicating little significant difference in pressure values from the center to the surface of the chip. Still, the pressure value for the 27% IMC chip after only 30 s of frying is much higher than that of the 42% IMC chip. Effect of tortilla thickness Figure 10 shows the profiles along the thickness of the tortilla chip for the 2.60-mm thickness chip fried at 190 C. The values are plotted

21 Deep-Fat Frying 229 Figure 9: Effect of the initial moisture content on the water saturation, oil saturation, temperature, and pressure profiles at 10, 20, and 60 s of frying. Chip thickness, 1.27 mm; IMC, 27% and 42% w.b.; frying temperature, 190 C. Figure 10: Effect of the tortilla thickness on the water saturation, oil saturation, temperature, and pressure profiles at 10, 20, and 60 s of frying. Chip thickness, 2.60 mm; IMC, 44% w.b.; frying temperature, 190 C.

22 230 Heat Transfer in Food Processing at 10, 20, and 60 s of frying and the IMC was 44%. The water saturation profile from the center to the surface of the chip is fairly flat at 10 and 20 s of frying; however, after 60 s of frying, there was a large gradient that developed. Once the crust begins to form along the surface, the rate of water transfer from the center to the surface decreases and a gradient is formed. From the oil saturation profiles, as time progresses and more oil is absorbed into the tortilla chip, oil saturation at the center gradually increases and the oil gradient from the center to the surface of the chip decreases. After 60 s of frying, the oil saturation value at the center of the 2.60-mm chip was approximately 0.065, while the value was about for the 1.27-mm chip [2]. This indicates that more oil is absorbed in the thinner chip possibly due to its larger surface area. From the temperature profile, compared to the 1.27-mm thickness chip, the 2.60 mm chip has a slight temperature gradient from the center to the surface of the chip after 60 s of frying, while there was no gradient for the thinner chip. Since there is still a significant amount of water left toward the center of the thicker chip, the center temperature remains slightly lower than the surface temperature. Finally, the pressure profile of the 2.60-mm chip remains near 1.0 atm after 60 s of frying, while the pressure profile of the 1.27-mm chip approached 3.0 atm (Figure 9) During cooling During the cooling process, water saturation remains constant while oil is absorbed due to the capillary pressure difference. Cooling temperatures of 25 C, 55 C, and 80 C were studied. The cooling temperature affects the rate of heat transfer and consequently the change in the capillary pressure between the environment and the tortilla. The IMC affects the amount of oil absorbed during the frying process and the porosity of the tortilla chip after frying. The porosity in turn affects the amount of oil that is absorbed during cooling. Finally, the effect of the tortilla chip thickness on oil absorption was also studied. The values for the IMC and the chip thickness are 27%, 42%, and 54% w.b. and 1.60 and 2.60 mm, respectively. The 1.60-mm thick tortilla chip was used because previous experimental data on cooling [4] was for this chip thickness. Since the pressure inside the tortilla chip increases above 1 atm during frying, the initial pressure of the tortilla chip after frying was assumed to be approximately 1.49 atm or kpa. This is merely an arbitrary value, but a safe approximation. For example, tortilla chips fried at 190 C may have pores pressure above 2 atm; however, at the instant that they leave the fryer, there will be an instantaneous pressure drop. Pressure measurements will have to be made in order to study the pressure profile more accurately. Effect of cooling temperature Figure 11 shows the profiles along the thickness of the tortilla chip for the 1.60-mm thickness chip cooled at 25 C and 80 C. The IMC was 42% and the frying temperature was 190 C. The values for the water saturation and oil saturation profiles are plotted at 0, 20, and 120 s of cooling, while the values for the temperature and pressure profiles are plotted at 5, 20, and 120 s of cooling. Since the water saturation of the chip was assumed to be constant during cooling, the profiles do not change with time. For the oil saturation profiles, after 20 s of cooling, there was a significant gradient from the center to the surface of the

23 Deep-Fat Frying 231 Figure 11: Effect of the cooling temperature on the water saturation, oil saturation, temperature, and pressure profiles. Values are at 0, 20, and 120 s of cooling for the water saturation and oil saturation profiles, and at 5, 20, and 120 s of cooling for the temperature and pressure profiles. Chip thickness, 1.60 mm; IMC, 42% w.b.; frying temperature, 190 C. tortilla chip in both the 25 C and 80 C cases, with the 25 C chip having a much larger increase in oil saturation. After 120 s of cooling, more oil is absorbed in the 25 C case with much higher saturation occurring along the surface of the chip. In addition, the temperature profile shows a gradual gradient from the center of the chip to the surface for both cases; however, the 25 C chip cooled much faster as expected. Moreover, the rapid temperature decrease for the 25 C chip also correlates to the pressure profile, which decreases in value faster than the 80 C chip. This large pressure difference between the chip and the cooling environment may be responsible for the higher oil absorption for the 25 C chip. Effect of IMC Figure 12 shows the profiles along the thickness of the tortilla chip for the 1.60-mm thickness chip cooled at 25 C. The IMC was 27% and 42% and the frying temperature was 190 C. The values for the water saturation and oil saturation profiles are plotted at 0, 20, and 120 s of cooling, whereas the values for the temperature and pressure profiles are plotted at 5, 20, and 120 s of cooling. Once again, the water saturation profile is constant for both cases. The oil saturation profile also shows a significant gradient from the center to the surface of the chip with a large amount of oil saturation occurring along the surface. Since the 27% IMC chip had much lower oil saturation after frying, it absorbs less oil during cooling. In addition, since both the 27% and 42% IMC chips are cooled at the same temperature, the temperature and the pressure profiles are nearly identical. Thus, with about the same capillary pressure difference, oil absorption for the two cases

24 232 Heat Transfer in Food Processing Figure 12: Effect of the initial moisture content on the water saturation, oil saturation, temperature, and pressure profiles. Values are at 0, 20, and 120 s of cooling for the water saturation and oil saturation profiles, and at 5, 20, and 120 s of cooling for the temperature and pressure profiles. Chip thickness, 1.60 mm; cooling temperature, 25 C; frying temperature, 190 C; IMC in w.b. begins to slow down at about the same cooling time and the oil saturation profiles appear to have the same gradient from the center to the surface. Effect of tortilla thickness Figure 13 shows the profiles along the thickness of the tortilla chip for the 2.60-mm thickness chip cooled at 25 C. The IMC 44% and the frying temperature was 190 C. The values for the water saturation and oil saturation profiles are plotted at 0, 20, and 160 s of cooling, while the values for the temperature and pressure profiles are plotted at 5, 20, and 160 s of cooling. The water saturation profile remains constant whereas the oil saturation profile shows a large gradient as it approaches the surface of the chip. Compared to the 1.60-mm chip, the 2.60 mm absorbed less oil (Fig. 12). As mentioned previously, this may be due to the larger surface area of the thinner chip. The profiles for the two cases are very similar at the final cooling time, because both are cooled at the same temperature. The temperature profiles illustrate the gradual temperature decrease from the center to the surface as the surface is exposed to the cooling environment. Finally, the pressure profiles are flat showing that the pressure inside the chip decreases at about the same rate throughout Crust formation The formation of the crust is important in giving the fried product its color, flavor, and its crispy texture. Moreover, it has been noted

25 Deep-Fat Frying 233 Figure 13: Effect of the tortilla chip thickness on the water saturation, oil saturation, temperature, and pressure profiles for the 2.60-mm chip. Values are at 0, 20, and 160 s of cooling for the water saturation and oil saturation profiles, and at 5, 20, and 160 s of cooling for the temperature and pressure profiles. Cooling temperature, 25 C; IMC, 44% w.b.; frying temperature, 190 C. Table 6: Physical and thermal properties of the crust and the core regions. Characteristics Crust region Core region Temperature >100 C Approximately 100 C Moisture content <0.05 M w.b. Highly saturated Type of water Zone I and zone II Zone III Type of diffusion Capillary Capillary and convective Thermal conductivity Eqn (45) Eqn (44) that most of the oil absorbed lies in the crust layer. The crust limits water diffusion from the center of the tortilla leading to a pressure buildup inside the tortilla chip and to pore expansion. These air pockets give the chips the crunchy sound when bitten into. Table 6 compares the characteristics of each of these regions. The water present in the crust region is from the immobile bound water of zone I and a small amount of multilayer water is from zone II [2]. Thus, this water is what remains at equilibrium. In addition, since water in the crust region is in vapor form, the type of mass diffusion here is only from capillary diffusion.

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