A mathematical model of heat transfer during tomato peeling using selected electric infrared emitters

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ScienceDirect journal homepage: www.elsevier.com/locate/issn/15375110

Research Paper

A mathematical model of heat transfer during tomato peeling using selected electric infrared emitters Sriram K. Vidyarthi a,b, Hamed M. El Mashad b,c, Ragab Khir b,d, Shrinivasa K. Upadhyaya b, Samrendra K. Singh b, Ruihong Zhang b, Rakhee Tiwari a, Zhongli Pan b,* a

The Morning Star Company, Woodland, CA, 95695, USA Department of Biological and Agricultural Engineering, University of California, Davis, One Shields Avenue, Davis, CA, 95616, USA c Department of Agricultural Engineering, Faculty of Agriculture, Mansoura University, P.O. Box 46, El-Mansoura, Egypt d Department of Agricultural Engineering, Faculty of Agriculture, Suez Canal University, Ismailia 41522, Egypt b

article info

A two-dimensional mathematical model of heat transfer was developed for heat transfer

Article history:

during the infrared (IR) peeling of tomato. The model was used to predict the temperatures

Received 8 May 2019

of tomato heated using selected electric IR emitters having different characteristics. The IR

Received in revised form

heating process was hypothesized as a mathematically gray-diffuse radiation problem

17 June 2019

based on the enclosure theory. The heat transfer model was solved in COMSOL using a

Accepted 4 July 2019

finite element scheme to predict the temperature of tomato during different heating times. The model was validated by comparing the predicted and measured temperatures of tomato surface that were presented in our accompanying study (Vidyarthi et al., 2019). The

Keywords:

predicted temperatures agreed well with the experimental data (R2 > 0.99). Simulation

Electric emitters

results indicated that IR heating for 25 s induced a dramatic temperature increase (>100
C)

Emissive power

on the tomato surface layers; limited to a maximum of 0.66 mm underneath the surface.

Infrared heating

There was no change in the temperature of tomato center (<28
C). The rapid increase of

Tomato peeling

tomato surface temperature and insignificant rise in interior temperature indicated a

Two-dimensional model

meager penetration capacity of IR radiation, causing insubstantial damage to tomato flesh

Heat transfer modeling

integrity, and consequently preserving the nutritional quality of peeled product. This study provides designing parameters of an efficient IR tomato peeling technology, ensuring a high peeling performance and product quality. © 2019 IAgrE. Published by Elsevier Ltd. All rights reserved.

* Corresponding author. Department of Biological and Agricultural Engineering, University of California, Davis, One Shields Ave., Davis, CA, 95616, USA. E-mail address: [email protected] (Z. Pan). https://doi.org/10.1016/j.biosystemseng.2019.07.001 1537-5110/© 2019 IAgrE. Published by Elsevier Ltd. All rights reserved.

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1.

Introduction

Infrared (IR) dry-peeling has been considered as a sustainable and alternative peeling method for tomato peeling process addressing the immediate needs of processors for meeting the long-term goals of water conservation, salinity management, and quality assurance of peeled tomato (Li et al. 2010, 2011; Pan, 2010; Pan, Li, Bingol, Mchugh, & Atungulu, 2009; Vidyarthi, Khir, & Pan, 2015; Vidyarthi, 2017; Vidyarthi et al., 2019). The performance of the IR dry-peeling process is influenced by several factors associated with the heat transfer phenomena involving radiation, conduction, and convection. In our accompanying study, tomato double-sided heated for 10e25 s using four different types of electric IR emitters with varying emissive powers could achieve successful peel removal while preserving the quality of peeled products (Vidyarthi, 2017; Vidyarthi et al., 2019). Execution of such controlled heating is challenging due to involvement of several factors, including emitter configuration, tomato size variation, surrounding air temperature, and overall heat loss during IR heating, which can contribute to under- or overheating of tomato, affecting the peeling performance and product quality. Therefore, an in-depth understanding of the heat transfer phenomena during IR dry peeling is vital to optimize tomato heating process and design an efficient industrial IR heating system for peeling process, ensuring high peeling performance and peeled product quality. Heat transfer modeling has been an effective and powerful tool for simulating different food processes (Erdogdu, Ferrua, Singh, & Singh, 2007; Singh, 2005; Singh & Heldman, 2010; Singh & Singh, 2008). Researchers often used different modeling techniques, including radiation exchange principle in an enclosure composed of diffuse-gray surfaces, hemicube method, and finite difference method to solve the model (Afzal & Abe, 1998; Cenkowski, Hong, Scanlon, & Arntfield, 2003; Cuccurullo, Giordano, & Metallo, 2017; Hebbar, Vishwanathan, & Ramesh, 2004; Jun & Irudayaraj, 2006; Li, 2012; Meeso et al., 2007; Shilton, Mallikarjunan, & Sheridan, 2002; Tanaka and Uchino, 2010; Turner & Mujumdar, 1996). Li et al. (2011) developed and validated a three-dimensional heat transfer model of IR heating of tomato using the computational software package COMSOL aiming at optimization of tomato peeling process. They adopted the hemicube method to compute the complex view factors between tomato and emitter for fast and accurate computations. Their sensitivity analysis indicated that emitter surface temperature, distance between emitters and tomato size had major effects on the heating rate of tomato. To date, all the studies have assumed either a finite penetration depth or zero penetration depth of IR radiation (Datta & Ni, 2002; Li & Pan, 2014a, 2014b; Prakash, 2012; Tanaka and Uchino, 2010). However, no significant temperature difference inside food materials has been found between these two assumptions when the IR penetration depth is small (<1 mm) (Prakash, 2012; Trivittayasil et al., 2011). This is most likely due to the limited penetration characteristics of the IR at food surface (Ginzburg, 1969). Accordingly, the present study assumes that all the IR energy is absorbed at tomato surface with zero penetration depth.

107

A heat transfer model can describe the impact of emissive power of the selected electric emitters on temperature profile of tomato surface and subsurface during IR heating, which is believed to cause peel loosening (Li, 2012; Vidyarthi et al., 2019). Moreover, it may also help in understanding the effect of shape, size, and configuration of the electric emitters on the temperature of tomato, which introduce additional challenges in designing an efficient IR peeling technology. In this study, the tomato is rotating in the radial direction along the longitudinal axis (stem-blossom axis) with a constant speed under the emitter enclosure. In addition, the purpose of the heat transfer modeling in this study was to predict the temperature profile of tomato in axis-symmetric radial direction. Both of these conditions make the modeling feasible in twodimension by neglecting the effect of horizontal direction. Therefore, the specific objectives were to: i) develop a twodimensional mathematical model of heat transfer to predict surface and undersurface temperatures of tomato during IR heating with four different electric emitters; and ii) validate the developed mathematical model by comparing the predicted and experimental tomato surface temperatures. The model results could provide a deeper understanding of the heat transfer in tomato during IR heating and be used to design and improve the IR peeling technology for tomato in the industrial applications.

2.

Materials and methods

2.1.

Heat transfer mathematical model development

A two-dimensional (2-D) mathematical model was developed to describe the heat transfer phenomena during IR heating of tomatoes. The model was applied to predict the performance of four electrical IR emitters on tomato peeling performance. The emitters included ceramic full trough element (CFTE), pillared quartz element (PQE), quartz tungsten medium (QTM), and quartz halogen medium (QHM) that were made by WECO International Inc. (Clio, Michigan, USA). The four emitters were described in details and the effect of their emissive powers and configurations on the tomato peeling performance was described in our accompanying study (Vidyarthi et al., 2019). Since two of the emitters (CFTE and PQE) were identical in shape and size and the other two (QTM and QHM) were of similar shape and size, overall two different types of heating set up were considered in the developed model. A schematic of the IR heating set-up for the heat transfer model is shown in Fig. 1. IR heat energy being applied to the surface of food mostly occurs by radiation, but also by convection and to a lesser extent by conduction. In this study, all the three modes of heat transfer (i.e., radiation, convection, and conduction) occur simultaneously at any given time during the IR heating of tomato. Temperature variations in tomatoes can be influenced by various processing factors, such as emissivity of emitters and tomato, thermo-physical properties of tomato, heating time and rotating speed of tomato, IR penetration on tomato surface, gap between emitter and tomato, view factor, heat exchanged with the surrounding air, and heat loss due to evaporation from tomato surface. IR heating of tomato, where

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Fig. 1 e A cross sectional view of the IR heating system in radial direction of tomato. Emitter configurations: a) CFTE and PQE were rectangular emitters; b) QTM and QHM were tubular emitters, (X and Y axes represent location, mm). heating period is very short (typically less than a minute), cannot be considered as an isothermal process. Conduction is the dominant heat transfer mechanism mode within the tomato interior. Therefore, the internal temperature profiles are affected by the thermal properties of tomatoes. At tomato surface, the skin is exposed to the radiation from emitters and natural convection from the surrounding hot air. Accordingly, the developed model included conduction heat transfer inside tomato and radiation-convection heat transfer at tomato surface. Latent heat of evaporation is another factor that was considered in developing the model because when the surface temperature of a tomato reaches the water boiling point, evaporation of free water can alter the final surface temperature distribution.

2.1.1.

iii.

iv.

v.

Model assumptions

Heat transfer modeling in a tomato IR heating is complicated due to the non-linear exchange among different radiative surfaces. For simplicity and reduction in computational times, several assumptions were made in the development of the heat transfer model. Such assumptions have frequently been used by researchers to develop heat transfer models of the IR heating of food (Krishnamurthy, Khurana, Soojin, Irudayaraj, & Demirci, 2008; Li, 2012; Prakash, 2012; Togrul, 2005):

vi. vii.

viii. ix.

i. Tomato used in this study was longer in the longitudinal direction (stem-blossom end) than the radial direction (Generally, roma tomatoes have these configurations and are processing varieties) as shown in Fig. 2A. Moreover, the diameter of tomatoes used in this study were relatively uniform (50e53 mm). Since three tomatoes could fit in the emitter when they were lined up in the longitudinal direction, the long row of tomatoes could be considered as an infinitely long cylinder (i.e., the variation in the diameter of tomatoes over its longitudinal direction was neglected). This assumption made it possible to use a 2-D model for tomatoes with a circular cross-sectional area in cylindrical coordinates (r, q). ii. Tomato was opaque to thermal radiation (no transmission) and all the incident energy was absorbed at tomato surface with a small reflectivity (approximately 5%) of incident energy (Li, 2012). The tomato

x.

xi.

absorptivity was assumed same for the entire tomato surface. The emissivity of tomato was assumed independent of temperature and a constant value of 0.95 was used in the model (Hellebrand, Beuche, & Linke, 2002; Li, 2012). All participating radiating surfaces were diffusedgray surfaces based on the enclosure theory, which means that each participating object could emit to and absorb radiation from each other. Hot air between emitter and tomato was transparent and did not interact with the IR radiation passing through it. In other words, the proposed model involved heat transfer with surface to surface radiation among diffused surfaces through nonparticipating medium. Tomato flesh and peel materials were homogeneous, isotropic, and had similar thermal properties. Heat transfer at tomato surface occurred by radiation between radiating surfaces (emitter enclosure) and tomato and convection between air and tomato. Air temperature (T∞ ) remained constant. Heat transfer within the tomato occurred only by conduction. All radiation heat was incident on tomato surface only (i.e., zero penetration depth). Heat generation due to respiration was very small compared to total thermal energy received by tomato during IR heating and thus neglected (i.e., Aresp ¼ 0) Tomato skin had no stomata openings for gas exchange and was covered with heavily cutinized epicular waxes (Kalloo, 1993; Ray & Ward, 2006), which could serve as a water vapor barrier (Showalter, 1993; Vogg et al., 2004). Overall, in this study, moisture loss during IR heating of tomatoes was less than 3% of initial weight of tomato, probably due to the short heating period (25 s) of tomato and high degree of impermeability of tomato skin. Therefore, heat transfer due to evaporation (qevap) was assumed to be zero ðqevap ¼ 0).

Roles of different modes of heat transfer on tomato during IR heating are described in detail in the following section.

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Fig. 2 e A) Parts of electric IR heating set up, and B) A representative picture of tomato heating with PQE.

2.1.2.

Radiation heat transfer

The tomato was surrounded by an enclosure that consisted of two emitters, reflectors, aluminum cover, and air contained in the enclosure. Heat transfer due to surface-tosurface radiation depends on the surface temperatures, surface properties, and view factors between participating materials (heating and receiving materials). View or shape factor accounts for the fraction of the radiation emitted by high-temperature surfaces that are not intercepted by lowtemperature objects (Singh et al., 2010). The view factor depends on the object geometry (Howell, Siegel, & Menguc, 2011). Although emitters were the predominant source of radiation towards the tomato surface, other surfaces, such as reflectors and aluminum foils, were considered as additional sources of radiation. When the IR energy primarily emitted by emitters is absorbed by objects (e.g., tomato and enclosure surfaces), they then re-emit radiation based on their emissivity. This exchange process continues until the driving force of the deduced IR radiation (i.e., the temperature difference between the emitting/absorbing surfaces) hypothetically attenuates to zero. The enclosure theory suggests that radiative heat flux at any place on the object surface should include the radiation arriving at that place from all surrounding directions (Howell et al., 2011). The surrounding temperature was considered constant with a zero reflectivity. In this model, the tomato surface was subdivided into infinitesimal areas, and temperature at each area could be considered isothermal (Howell et al., 2011). Each element (dA2) on the tomato surface received integrated amount of radiations from each element (dA1) of the emitter (Fig. 3). The heat flux from top emitter which was intercepted by tomato surface element dA2 could be written as: qA1 /dA2 ¼

sε1 T41 dA2 A1

I

 ðCos 41 Cos 42 ÞdA1 r2 ðW m2 Þ

  qA1 /dA2

absorbed

i h ¼ qA1 /dA2 r2 ðW m2 Þ

(Eq. 2)

where r2 is the absorptivity of tomato surface (dimensionless), T1 is the absolute temperature of top emitter (K), s is the Stefan-Boltzman Constant (5.6703  108 (W m2 K4), dA1 is the element area on emitter surface (m2), dA2 is the element area on tomato surface (m2), 41 is the angle between the surface normal of dA1 and the ray to dA2 (
), 42 is the angle between the surface normal of dA2 and the ray to dA1 (
), r is the distance between dA1 and dA2 (m), ðCos 41 Cos 42 dA2 Þ =r2 is the view factor from surface element of emitter dA1 to surface element of tomato dA2, and ε1 is the emissivity of top IR emitter (0  ε1  1) (assumed constant for whole emitter).

(Eq. 1)

A1

The average flux of the IR radiation absorbed by a surface element of tomato from top emitter could be written as:

Fig. 3 e Representation of radiative heat transfer between surface element of emitter (dA1) and surface element of tomato (dA2). Symboles are defined below.

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According to the Kirchhoff's law, since tomato is assumed to be a grey diffuse surface, its emissivity (ε2) and absorptivity (r2) will be equal (i.e., r2 ¼ ε2). Radiosity (J) of tomato surface element is the total outgoing heat flux from tomato surface element (dA2), which is the sum of emitted and reflected fluxes and was computed as: JdA2 ¼ qdA2 /emitted þqdA2 /reflected ðW m2 Þ

(Eq. 3)

where qdA2 /emitted ¼ ðqA1 /dA2 Þ absorbed ¼ ½qA1 /dA2 ε2 ðW m2 Þ, qdA2 /reflected ¼ a2 ðqA1 /dA2 $dA2 Þ and ðW m2 Þ, ε2 is the emissivity of tomato surface (dimensionless), and a2 is the reflectivity of tomato surface (a2 ¼ 1 e r2 ¼ 1 e ε2) (dimensionless). A fraction of the tomato radiosity will be absorbed by emitter and then emitted back to tomato. Considering a view factor from the tomato surface element dA2 to the emitter as FdA2 /1 and absorptivity of emitter as r1 , the fraction ðqr ) of this thermal radiation reflected by emitter and absorbed by the surface element area of tomato could be written as:     qr ¼ JdA2 :r1 F1/dA2 ε1 r2 W m2

(Eq. 4)

where, r1 ¼ ε1 ¼ 1  a1 and r2 ¼ ε2 ¼ 1  a2 (applying the Kirchoff's law for emitter and tomato). This will further continue to be reflected and absorbed albeit becoming smaller in the magnitude with each step. Considering the view factor, emissivity and absorptivity of both surfaces, fraction of thermal radiation emitted from tomato to emitter and then received back to tomato surface would be so small so that it could be assumed negligible (i.e., qr ¼ 0). Therefore, the net radiosity on the surface element of tomato due to the top emitter could be written as: JdA2

net

¼ JdA2 þ qr ¼ JdA2 ðqr ¼ 0Þ ðW m2 Þ

(Eq. 5)

The net radiation at the surface element of tomato due to the top emitter could be written as the difference between incoming and outgoing fluxes: qdA2

net

¼ qA1 /dA2  JdA2 ðW m2 Þ

(Eq. 6)

Finally, the net radiative flux at the whole tomato surface due to top emitter could be computed by integrating Eq. (5) over the surface area (A2) of tomato as follows: I qdA2 net ðW m2 Þ (Eq. 7) qnet emitter1 ¼ A2

Similarly, the net radiation flux on tomato from the emitter located at the bottom and other parts of enclosure, such as reflectors and aluminum covers can be computed. Due to the symmetrical nature of the enclosure, the overall radiative heat flux on tomato surface will be the sum of all radiative fluxes on tomato:   qnet rad ¼ qnetemitters þ qnetreflectors þ qnetalum I   I ¼2 qdA2 þ qdA2 emitter

net

A2

þ

I

qdA2

net

A2

where,

 alum cover

net



covers

refletor

A2

ðW m2 Þ

(Eq. 8)

ðqnet Þrad ¼ Net radiation flux on tomato surface (W m2)  H qdA2 ¼ Net radiation flux on qnet emitters ¼ 2 net

A2

emitter

tomato surface from both emitters (W m2)  H qdA2 ¼ Net radiation flux on qnet reflectors ¼ 2 net

A2

refletor

tomato surface from both reflectors (W m2)  H qdA2 ¼ Net radiation qnet Alum covers ¼ 2 A2

net

alum cover

flux on tomato surface from both aluminum covers (W m2) The radiative heat transfer problem was solved by integrating Eq. (7) numerically applying ‘Heat Transfer with Surfaceto-Surface Radiation’ module using a computational software COMSOL (COMSOL Multiphysics-5.2a, 2016). Based on the shape and dimensions of the participating surfaces, the built-in hemicube feature in COMSOL automatically calculated and implemented the view factor while solving the radiation model.

2.1.3. Convective heat transfer between the enclosed air and tomato Convective heat transfer between tomato and air is another major heat transfer occurring at tomato surface during the IR heating of tomato. The temperature of air in the IR enclosure was measured at ten points using a direct contact thermometer (HH147U, Omega Data Logger Thermometer, Omega Engineering Inc., Stamford, CT, USA) connected to K-type thermocouples. The surrounding air temperature ranged between 40 and 50
C, which was lower than that of tomato surface after tested heating period (25 s). Therefore, a heat loss from tomato to air could occur. Heat flux on tomato surface due to convection could be calculated using the Newton's law of cooling as follows (Singh et al., 2010): qconv ¼ hðTs  T∞ Þ

(Eq. 9)

where qconv is the heat flux due to convection at tomato surface (W m2), Ts is the temperature of tomato surface (K), T∞ is the temperature of enclosed air between emitter and tomato (K), and h is the convective heat transfer coefficient (W m2 K1)

2.1.3.1. Estimation of convective heat transfer coefficient (h). During tomato heating experiments, tomatoes were rotated slowly at a rotational speed of 12 rpm. Moreover, air surrounding tomato was not forced by any mechanical means. Therefore, the heat exchange between the tomato surface and surrounding air was natural convection. The value of the natural convection heat transfer coefficient depends on object geometry, airflow velocity, air properties, and instantaneous temperature difference between the air and the object (Alhamdan, Sastry, & Blaisdell, 1990; Alhamdan & Sastry, 1990; Debnath, Vidyarthi, & Singh, 2010; Verboven, Datta, Anh, Scheerlinck, & Nicolar, 2003). The convective heat transfer coefficient was computed by applying the suitable Nusselt number correlation formula for the laminar flow. The calculation of Nusselt number was based on cylindrical tomato rotating vertically along the horizontal traverse axis (stem-blossom end). The average convective heat transfer coefficient for a horizontal cylinder was computed as follows (Singh & Heldman, 2010):

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k h ¼ Nu : ¼ Dc

"

0:387 Ra1=6

#2

0:60 þ n o8=27 1 þ ð0:559=PrÞ9=16

:

k Dc

(Eq. 10)

where Nu is the average Nusselt number (dimensionless), Ra is the Rayleigh number (Ra ¼ Gr x Pr) (dimensionless), Pr is the Prandtl number (Pr ¼ m cp/k) (dimensionless), Gr is the Grashof 3 2 number (Gr ¼ Dc r mg2 b DT (dimensionless), Dc is the characteristic diameter of a cylinder (m), ɡ is the acceleration due to gravity (9.8 m s2), DT is the temperature difference between ambient air and tomato surface (K), ?? is the air density (kg m3), b is the coefficient of volumetric expansion of air (K1), cp is the specific heat capacity of air (J kg1 K1), m is the air viscosity (Pa.s), k is the thermal conductivity of air (W m1 K1) The dimensionless numbers, Grashof, Rayleigh, Prandtl, and Nusselt were evaluated at the film temperature Tf ¼ Ttom sur2 þ Tair based upon the above-mentioned physical properties of air at the film temperature. In this study, considering surrounding air and tomato surface temperatures of 40 and 109
C, respectively, the average convective heat transfer coefficient (h) was estimated to be 6.35 W m2 K1, which falls within the range (2e25 W m2 K1) of typical values of heat transfer coefficient for natural convection (Cengel and Ghajar, 2011).

2.1.4.

Heat transfer due to conduction inside tomato

Based on the assumptions stated above, the conductive heat flux at a surface element area from the inside of tomatoes could be written as follows: qcond

tom

¼ n$ ð  kVTÞ

(Eq. 11)

where qcond tom is the conductive heat flux at surface element form inside of tomato (W m2), n is the normal vector on the surface element (outside), V is the divergence operator, VT is the temperature gradient at tomato surface (K), and k is the thermal conductivity of tomato (W m 1 K-1).

2.1.4.1. Thermophysical properties of processing tomato. Thermophysical properties of tomato depend on the thermophysical properties of its chemical components, which are functions of temperatures (Singh & Heldman, 2010). A linear Eq. for thermophysical properties of processing tomato with respect to temperature was generated from the data of Li (2012) as shown in Table 1. Tomato density, specific heat, and thermal conductivity of tomato were assumed homogenous and isothermal in nature.

2.1.5.

Conductive heat transfer within tomato

The governing Fourier Eq. for general transient conductive heat transfer within the tomato in the 2-D Cartesian coordinate system is given as follows: Table 1 e Thermophysical properties of processing tomato with respect to temperature (Singh & Heldman, 2010; Li., 2012). Thermophysical Properties Thermal conductivity (k) Specific heat capacity (Cp) Bulk density (r)

Equation k ¼ 0.0009 T þ 0.5495 (W/m
C) Cp ¼ 0.6024 T þ 4020.5 (J/kg
C) r ¼ 0.4266 T þ 976.59 (kg/m3)

rCp

vT ðx; y; tÞ ¼  V$ðkVTÞðx; vt

y; tÞ

þ Q vol ðx; yÞ

(Eq. 12)

where r is the tomato density (kg m3), Cp is the specific heat of tomato (J kg1 ºC1), T is the tomato temperature (ºC), t is the time (s), k is the thermal conductivity of tomato (W m1 ºC1), ðx; yÞ is the axes of Cartesian coordinate system, and Qvol is the volumetric heat generation in tomato (W m3) Volumetric heat generation in tomato is very small compared to the total energy absorbed from the IR heating and therefore can be neglected (Qvol ¼ 0). Eq. (12) could be expressed as: rCp

vT ðx; y; tÞ ¼  V$ðkVTÞðx; vt

(Eq. 13)

y; tÞ

2.1.5.1. Boundary conditions. At tomato surface, the total heat flux is composed of IR thermal radiation (qrad) and natural convection. The latter follows the Newton's law of cooling. Hence, the first boundary condition could be given as:   n $ðkVTÞ ¼ qnet rad þ qconv

(Eq. 14)

At the center of tomato (x ¼ 0, y ¼ 0 and z ¼ 0), heat gradient is zero due to the symmetrical boundary condition. Therefore, the boundary condition at the center could be written as: n $ ð  kVTÞ ¼ 0

(Eq. 15)

2.1.5.2. Initial conditions. The experiment of tomato heating was conducted once the temperature of IR enclosure achieved a steady state condition. The emitters required some preheating time of about 15 min to reach the steady state. The temperatures of emitters, reflectors, and aluminum covers upon 15-minute of IR heating simulation were considered to be equal to the initial temperatures of IR enclosure for tomato heating. TinitialIRenclosure ¼ Tpreheatemitter ; Tpreheatreflector ; Tpreheat

al cover

At t

¼ 15 min (Eq. 16) o

The initial temperature (Tinitial, C) of the tomato was assumed uniform and constant (i:e:; Tinitial tomato ¼ 300 K).

2.1.5.3. Meshing and numerical solution. A finite element scheme was used to solve the 2-D transient heat transfer model Eq.s to obtain the temperature distribution profile of the cross-section of tomato in radial direction with respect to time. This numerical procedure was implemented in COMSOL Multiphysics software (COMSOL Inc., Palo Alto, CA, version 5.2a). A default physics-controlled mesh consisting of triangular area elements was generated for the simulations. Fine meshes were used for all the domains in the model. A representative mesh distribution for tomato and IR enclosure for all four types of emitters are shown in Fig. 4. A complete mesh consisted of 1902 domain elements and 1078 boundary elements. These numbers of elements were considered sufficient because increasing their numbers above 2000 significantly increased the computational time without improving the

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prediction accuracy. The input parameters, such as thermophysical properties of each domain and rotational speed of tomato were kept constant for all simulations. The heating duration (25 s) was determined from the experiments in our accompanying studies (Vidyarthi, 2017; Vidyarthi et al., 2019). An implicit time-stepping scheme was used to solve the transient heat transfer problem. Each time step of 1 s included solution of the nonlinear system by an arbitrary COMSOL linear system solver using Newton-Rapson iteration (Li, 2012).

resulting in higher firmness loss of the peeled product. In this study, a predicted tomato temperature of 100
C was considered as a reference point to evaluate the firmness loss. Interior distance from tomato surface on the radial axis up to the predicted reference temperature (100
C) was measured from the model. A shorter distance was considered to cause a lower disintegration underneath tomato surface, meaning a lower loss in firmness.

2.1.6.

3.

Model validation

The model results were validated by comparing the predicted and measured temperatures of the surface of radial crosssection of tomato. The details of the experimental procedures were explained in our accompanying study (Vidyarthi, 2017; Vidyarthi et al., 2019). A linear regression analysis between predicted and measured temperature profiles at different heating time was performed and Standard Error of Estimates (SEE) was evaluated for different emitters. The coefficient of determination (R2) was used to assess the goodness of model prediction. The Standard Error of Estimate (SEE) is defined as: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Pn  1 Tpre  Texp SEE ¼ n

(Eq. 17)

where Tpre is the predicted temperature of tomato surface (
C), Texp is the experimental or measured temperature of tomato surface (
C), and n is the number of observations. SEE provided a direct estimation of how well the predicted temperature profiles from the model match with the measured temperature profiles. A smaller SEE value indicates a better fit of the model. The quality of the final product after peeling was correlated in terms of loss of firmness with respect to the predicted temperature profile of tomato interior layers. Our accompanying study showed a significant effect (a ¼ 0.05) of IR heating time on tomato firmness. The relationship between tomato interior temperature profile at different heating times and respective firmness loss of peeled tomato may provide an indication of the penetration depth of IR radiation. A higher predicted temperature beneath tomato surface could lead to a higher degradation of cellular networks beyond exocarp,

Results and discussion

3.1. Predicted and measured temperatures of tomato surface Figure 5 shows the predicted maximum temperature of tomato surface along the circumference at different residence times during the IR heating of tomato with different emitters. The results reveal that the rate of rise in tomato surface temperature was more rapid in the initial stage up to the first 5 s; then it slowed down. In general, at any heating time, emitters with higher emissive power led to higher temperatures of tomato surface. Validation of the model was performed by comparing the predicted and measured temperature profiles of tomato surface approximately closest to the emitter during 25 s of the IR heating. The predicted temperature profiles of tomato surface matched closely with the measured temperature profiles

Fig. 5 e Predicted temperatures of tomato surface at different times during IR heating.

Fig. 4 e Physics-controlled finite element mesh on circular cross section of tomato under emitter enclosure shapes: a) rectangular; and b) tube.

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(R2 > 0.99) as shown in Fig. 6 and Table 2. Although the overall predicted temperature profiles in general agreed well with the measured temperature profiles, the difference between predicted and measured temperatures was large (approximately 15
C) at 10 s of tomato heating in the case of PQE (Fig. 6). This could be attributed to the instant drop of tomato surface temperature due to the internal vapor release with consistent skin cracking during tomato heating under PQE. Throughout the experiments, tomato skin started cracking at approximately 8 s during heating under PQE, whereas skin-cracking was not consistent in the case of other emitters. A general theory to deal with peel loosening and cracking due to the IR heating is still lacking. However, it was presumed that IR heating caused a dramatic temperature increase of tomato surface and water underneath the epidermal layers, which resulted in vaporization of water. When the vapor pressure increases enough, it damages several layers of tomato epidermal cells, causing cracking of peel (Li et al., 2014). It is believed that peel cracking induced a sudden release of steam from the epidermal cells into the atmosphere which might act like a heat shock at tomato surface with a sudden increase in the surface temperature momentarily. Since the first measurement of tomato surface temperature was carried out at 10 s during the IR heating experiments, the measured temperature was unexpectedly higher than the predicted temperature at 10 s of tomato heating (right after peel-cracking) under PQE. Once the heat dissipated in atmosphere after cracking, the rise of tomato surface temperature might normalize again like prior to peel-cracking. Similar pattern was noticed when peel-cracking occurred during the IR heating of tomatoes with QTM and QHM. However, the difference between the predicted and the measured temperatures was smaller than that of PQE. In addition, the assumed heat transfer coefficient used in this study might be higher than the effective time-averaged value and this could result in a greater difference between predicted and measured temperatures. In future studies, considering a temperature

Table 2 e SEE and determination coefficients (R2) of predcited and measured surface temperatures of tomato undergoing IR heating with different electric emitters. Emitter CFTE PQE QTM QHM

SEE (
C)

R2

1.77 8.30 4.80 2.99

0.995 0.999 0.991 0.993

variable heat transfer coefficient could used to adjust the predicted results more accurately. A sharp increase of the tomato surface temperature and consistent peel cracking under PQE may be due to the greater heating uniformity of tomato with a higher IR intensity. The view factor between tomato and emitter may have a significant impact on surface heating uniformity. In other words, the ratio of tomato to emitter surface areas may significantly affect the uniformity of tomato surface temperature. Under the same heating configuration, a higher ratio of emitter-to-tomato surface areas might result in more uniform surface heating. CFTE and PQE were of rectangular shape with a larger width than tomato diameter, contributing to a higher emitter-to-tomato surface area ratio. Whereas, QTM and QHM were tubular in shape with significantly smaller diameter than tomato, causing a smaller emitter-to-tomato surface area during the IR heating. Consequently, CFTE and PQE could provide more uniform heating to tomato than QTM and QHM. Despite similar ratio, PQE had a larger emissive power than CFTE, providing considerably higher thermal energy during the IR heating than CFTE. In fact, CFTE had the lowest emissive power among all the emitters and thus tomato received small amount of IR energy to crack the peel, even in 25 s of heating time. In contrast, PQE had the highest emissive power among all the tested emitters and a high surface-to-surface area ratio with tomato, providing adequate thermal energy at tomato surface to achieve latent heat of evaporation of

Fig. 6 e Predicted vs measured surface temperatures of tomato undergoing the IR heating with different electric emitters (Error bars are the standard deviations of triplicated measurements of temperature).

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water, contained under tomato peel, in as little as 8e10 s of IR heating, which prompted peel cracking. This whole scenario of the IR heating of tomato also reveals an important point that increasing emitter temperature or emissive power might enhance the heating rate but not improve heating uniformity, which is crucial for achieving acceptable peeling performance. In a similar study using catalytic IR radiation, Li et al. (2014) carried out sensitivity analysis for evaluating the effects of different design parameters, including emitter configurations, tomato size, and initial tomato temperature on the heating rate and uniformity using a dimensionless number, Surface Temperature Uniformity Index (STUI). The sensitivity analysis indicated that emitter surface temperature, distance between emitters and tomato size had major effects on the heating rate of tomato. The SEE and determination coefficients (R2) are shown in Table 2. Both SEE and R2 values indicated that the simulated surface temperatures well agreed with the measured values (R2 > 0.99). The average SEE for the emitters and conditions (except PQE at 10 s of heating) in this study was 4.47
C, which were in agreement with the results of Li et al. (2014) who studied tomato peeling under catalytic IR heating and the SEE in their study varied between 1.1 and 5.2
C with an average of 2.6
C. The SEE value for PQE (8.3
C) was higher than that of other emitters (1.8e4.8
C), which was due to the higher difference in predicted and measured temperatures of tomato surface at 10 s of heating time with the PQE as explained above.

Fig. 7 e Temperature profile inside tomato during the IR heating for 25 s with different electic emitters.

3.2. Macroscopic and microscopic interpretation of product quality and temperature profile inside tomato 3.2.1.

Macroscopic interpretation

Radiation heat transfer is the principal cause of skin disintegration during IR dry-peeling process. Theoretically, IR radiation first impinges tomato surface and then the heat penetrates inside tomato tissues through conductive heat transfer. A sudden temperature increase in the epidermic cells causes vaporization of cell fluids and accumulation of vapor pressure, which reduces the strength of cell walls (Li et al., 2014). Despite the rapid increase of the skin temperature, the predicted temperatures of tomato interior remained low in all cases as shown in Figs. 7 and 8, which was mainly due to the lower thermal conductivity of tomato. The core center of tomato exhibited no change in temperature over the entire heating period. The interior location closer to tomato surface had the largest temperature gradient, whereas majority of interior locations (about up to 17 mm from tomato center) experienced minor or negligible temperature gradient (Fig. 8). Temperature accelerated slowly from 17 to 20 mm and then moderately from 20 to 23 mm from tomato center. Finally, a rapid increase in temperature occurred as the tomato surface approached (Table 3). Overall, predicted temperatures 100
C were located only up to 0.66 mm underneath the tomato surface during the 25 s of heating time. The temperature profile was further analyzed by plotting the average predicted temperatures of the interior of modeled tomato along radial axis (“line temperature” of tomato interior) with respect to the heating time (Fig. 9). As can be seen that the interior temperature of tomato increased slowly in the beginning

Fig. 8 e Predicted tomato temperature profile along the minor axis with increasing the distance from the centre to surface of tomato after 25 s of IR heating with different electric emitters.

and rose gradually as the heating time increased. However, the average line (i.e., the radial axis connecting surface to center of tomato) temperature remained below 37
C. These phenomena indicated that IR heating contributed a dramatic thermal shock to the skin, which induced a sudden increase in the surface temperature, whereas temperature inside the tomato flesh remained low. Macroscopically, the minor rise in interior temperature indicated that tomato flesh remained almost integral and the tomato quality was preserved, which presents values to

Table 3 e Maximum rate of temperature change of interior tomato during the IR heating of tomato with different electric emitters. Distance from center of tomato (mm) 0e17 17e20 20e23 23e25

Maximum rate of change of temperature (
C/mm) 0.002 0.88 9.8 34.5

b i o s y s t e m s e n g i n e e r i n g 1 8 6 ( 2 0 1 9 ) 1 0 6 e1 1 7

Fig. 9 e Predicted average line temperature of the tomato interior along radial axis during IR heating with different emitters.

the tomato industry (Vidyarthi et al., 2019; Vidyarthi & Evans, 2019). In summary, the overall predicted temperature profile of tomato clearly showed that a rapid surface heating could be readily achieved with the IR heating technology while leaving the edible inner part of the fruit mostly intact with a minimum change in texture.

3.2.2.

Microscopic interpretation

In our previous studies, it was noticed that the surface temperature of tomato during the IR heating had a great influence on tomato peeling performance and product quality. The best condition to achieve a desirable peeling performance and product quality was evaluated mainly on the basis of primary indicators, such as peeling easiness, peelability and skin burn, as these solely depend on the changes in skin properties due to local thermal stress generated by IR radiation (Li et al., 2014; Vidyarthi et al., 2019). Whereas, other indicators, such as peeling and firmness losses, may be affected by not only changes in the properties of skin but also inner parts of tomatoes, including flesh. For example, an increase in emissive power resulted in better peeling easiness and peelability but might not guarantee a lower peeling loss or loss in firmness. The later may be a result of comprehensive changes in the properties of the whole tomato, including exocarp (peel), pericarp, and mesocarp. Since thermal energy absorbed by tomato surface is the major contributor to skin separation, affecting peeling easiness or peelability during IR heating of tomatoes, a transport of thermal energy inside tomato may be a reason for peeling loss and loss of firmness. Although macroscopically, the temperature rise in tomato interior was small in general and other factors may be the primary reason for peeling loss and loss in firmness. Nonetheless, it is worth analyzing the effect of temperature profile of tomato interior on peeling loss and loss of firmness microscopically. In our accompanying study (Vidyarthi, 2017; Vidyarthi et al., 2019), the peeling and firmness losses of tomato significantly increased (a ¼ 0.05) with the increase in residence time during the IR heating under a constant emissive power. However, at a constant heating time, emissive power had no significant (a ¼ 0.05) effect on peeling loss and loss of firmness. The predicted average temperature of tomato interior increased with the increase in heating time for all the studied

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emitters (Fig. 5). Theoretically, the rise in the internal temperature was a result of conductive heat transfer from the IR heat absorbed by tomato surface to the inner layers. A longer exposure of tomato to an emitter resulted in a higher heat energy absorbed by tomato surface, and hence a higher surface temperature over time. This could cause a more conductive heat transfer inside tomato, leading to a rise of the average interior temperature. This would consequently adversely impact the peeling loss and loss of firmness. On the other hand, the average predicted temperatures of tomato interior increased minutely at a given heating time under different emissive powers as shown in Fig. 9. For example, the largest difference in the interior temperature of tomato for different emissive powers was merely 2.5
C at the longest heating time (i.e., 25 s). At other heating times (<25 s), the differences were even lower, which may result in an insignificant change in peeling loss and loss of firmness. In conclusion, even though the average predicted temperature of tomato interior had no significant change during IR heating tests macroscopically, the rate of temperature rise was more rapid with respect to time compared to emissive power microscopically. Therefore, the predicted temperature profile of tomato interior validates that, for the tested range of heating times and emissive powers, peeling loss and loss of firmness were significantly affected by different heating times under a fixed emissive power but not by different emissive powers at a fixed heating time.

4. Recommendations for model improvement In this study, rigorous sorting was conducted to obtain tomatoes with nearly uniform shapes and sizes. However, the industrial peeling processing receive different varieties of tomatoes varying in shapes and sizes. Although it is extremely challenging to define a real shape of processing tomato of peeling varieties due to variations in their shapes and sizes, a 3-D tomato model with a shape as close as possible to a processing tomato may improve model predictions. Moreover, it would be valuable to develop a 3-D mathematical heat transfer model of this study and compare the simulation results obtained from the 2-D model studied here. The current model revealed that not only emissive power but also the ratio of emitter-to-tomato surface areas is important to achieve a desirable peeling performance in short heating times. With increasing loading rates, the view factors between flat emitters and tomatoes would become smaller, resulting in lower heating uniformity. Curved shaped emitters could be used to provide uniform heating of tomatoes. Hence, developing a heat transfer model featuring curved emitter with the same emissive power as of the flat emitter and then comparing the respective predicted results can help in further improvement of the design of IR tomato peeling system. In addition, a sensitivity analysis could be useful to compare the impact of different parameters, such as emissive power and emitter configuration on tomato peeling performance in the current model. The current model assumed a natural convection between air and tomato. The convective heat transfer coefficient would vary not only over time, but also across different surface areas

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of the tomato when a non-uniform tomato shape is considered. A calculation of the convective heat transfer coefficient would become even more complex when multiple tomatoes with different shapes would be included in the simulation. Nonetheless, the current heat transfer model could be improved by calculating the more accurate heat transfer coefficient by simulating the exact airflow pattern inside the IR heating system. Additionally, in the current model, lumped thermal properties of tomato were used without differentiating between skin and flesh. Future improvement of the model may include a distinction between the thermal properties of tomato skin and flesh. Moreover, analysing the tomato firmness with respect to the interior temperature of the tomato due to IR heating could provide valuable information about the effect of IR heating on the final product quality.

5.

Conclusion

A 2-D heat transfer model was developed to predict the temperature of tomato during the IR heating using four types of electric emitters. The model was validated with experimental results. The model results help in understanding the temperature profile of tomato and correlate with tomato peeling performance and product quality. A good agreement between predicted and measured temperatures of tomato surface was observed. The radiative heat transfer between tomato and emitter enclosure was the dominant source of thermal energy for tomato peel loosening. The average predicted temperature of tomato interior remained very low (<37
C). The emissive power and configuration of emitters had major effects on tomato heating rate, peeling performance, and product quality. The overall predicted temperature profile of tomato revealed that a rapid tomato surface heating can be achieved with the IR heating technology. The insignificant rise in the temperature of the tomato interior indicated a higher integrity of tomato flesh and a better quality of peeled product. Further improvements of the model may include developing a 3-D model that should include tomato shape as close as possible to a processing tomato cultivar for peeling, differentiating the thermal properties of tomato skin and flesh, use of curved shaped emitters, and incorporating the industrial washing process of tomatoes prior to introducing them to IR peeling.

Acknowledgement We would like to express our gratitude to The Morning Star Company, Woodland and Pacific Coast Producers, Woodland, CA for providing tomato samples throughout this research.

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