vol1no4-5_KannanA

Engineering Applications of Computational Fluid Mechanics Vol. 1, No.4, pp. 288303 (2007)

Received: 15 Apr. 2007; Revised: 12 Jun. 2007; Accepted: 13 Jun. 2007

288

ESTIMATION OF ENERGY CONSUMPTION IN THERMAL STERILIZATION OF CANNED LIQUID FOODS IN STILL RETORTS

Kannan A* and Koribilli Neeharika

Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600 036, INDIA * E-Mail: [email protected] (Corresponding Author)

ABSTRACT: Thermal sterilization of canned liquid foods using saturated steam is dominated by natural convective heat transfer. The temperature in the can is strongly influenced by the velocity patterns and varies both with position and time thereby making estimations of heat transfer rates and energy consumption difficult. Computational Fluid Dynamics (CFD) simulations are carried out to determine the temperature-time history in cans of different aspect ratios and food media thermal conductivities. Correlations are developed for the variation of the volume averaged temperature and heat transfer flux with time during different phases of the heating period. Integrating the heat transfer expressions over the entire duration of the heating period, closed form solutions of energy consumption are developed. These expressions for heat transfer rate and energy consumption may be incorporated into various process design, operation and optimization strategies in batch still retort operations.

Keywords: thermal sterilization of liquid food, natural convection, heat transfer rates, energy consumption

1. INTRODUCTION

Liquid food materials such as in-packaged heat pasteurized beer, evaporated milk, thin soups and broth, fruits in syrup or water, fruit juices and vegetable soups are often sterilized in still retorts with steam flowing around the surface of the can (Datta and Teixeira, 1988; Kumar, Bhattacharya and Blaylock, 1990). The important issue in thermal food sterilization is the preservation of food nutritive values and appearance while ensuring the deactivation of the harmful microorganisms. Most of the earlier studies have only been restricted to conduction heat transfer in solid foods. In sterilization of liquid foods, the heat transfer rates are enhanced by natural convection currents. However in such cases, the governing transport equations are considerably more complex than the heat conduction equation. Numerous Computational Fluid Dynamics (CFD) based studies in literature have analyzed the natural convection heating. They have reported on natural convection induced temperature-velocity fields and location of the slowest heating zone as a function of time. However, information in estimating the actual heat transfer rates and energy consumption involved in the thermal sterilization process of liquid foods is scarce. This work focuses on the estimation of energy consumption from the CFD simulation of

the heating cycle of the thermal sterilization process. Simple expressions are developed for the temperature driving forces and heat transfer fluxes which may be integrated to yield closed form expressions for the total energy consumption.

2. BACKGROUND AND SCOPE

Numerical simulations have been carried out to analyze the convective heat transfer involved in canned liquid food sterilization (Datta and Teixeira 1988; Kumar, Bhattacharya and Blaylock, 1990; Kumar and Bhattacharya, 1991; Engelman and Sani 1983). Computational fluid dynamics studies using commercial software for thermal sterilization analyses have become popular in recent times (Ghani et al., 1999; Ghani, Farid and Chen, 2002ac; Varma and Kannan, 2005 & 2006). Varma and Kannan (2005 & 2006) investigated the effects of geometry modifications and orientation on the rate of thermal sterilization of pseudoplastic food can from CFD simulations. Numerical simulations are preferred since accurate measurement of temperatures inside the can is complicated by the interference of the probes with the temperature-velocity fields. In addition, the slowest heating zone is not fixed to one location (Teixeira et al. 1969). Hence, mathematical modeling approach has been extensively applied to

Engineering Applications of Computational Fluid Mechanics Vol. 1, No. 4 (2007)

289

predict the temperature patterns in the thermal sterilization process (Naveh, Kopelman and Pflug, 1983; Datta and Teixeira 1987; Nicolai et al. 1998; Marra and Romano, 2003; Ghani and Farid 2004). Even in the relatively simpler conductive heat transfer study using wireless temperature sensors, Marra and Romano (2003) observed that the sensor presence, location and size relative to the can dimensions influenced the estimated cold spot temperature evolution and sterility values. They further noted that the sterility time calculations should incorporate a safety factor when wireless temperature sensors were used especially in small cans. Optimization and control of food retort processes is an important and emerging field in thermal food processing as is evident from numerous papers published in recent times. The highly model-driven formulations for food sterilization optimization are still mostly based on the conduction approach (Banga et al., 1991; Balsa-Canto, Alonso and Banga, 2002; Baucour, Cronin and Stynes, 2003; Garca et al. 2006). Rao and Anantheswaran (1988) have earlier reported the complexities due to natural convective effects on canned food sterilization. Silva, Oliveira and Hendrickx (1993) in their review on canned food sterilization optimization observed that the lack of research was more noticeable for convection-heated foods. They observed that all research carried out in this area dealt with conduction heating foods owing to poor understanding of the heat transfer processes involved in prepackaged convective heated foods. The convective heat transfer rates determine the temperatures and their distribution in the domain, which is critical to the foods microbial destruction, nutrients retention and process energy consumption. Even the transient three-dimensional conduction model may be simplistic and inaccurate for convection heated liquid foods. Adopting various conduction model-based optimum policies for operation and control of liquid food sterilization may lead to unacceptable extent of processing. Bermudez and Martinez (1994) applied optimal control methods to minimize degradation of nutrients and energy consumed while satisfying the constraint of acceptable reduction in microbial concentration. However, a conduction model was adopted in this work to track the temperature with time. A constant heat transfer coefficient based heat flux model was used as the boundary condition.

For natural convection heating of liquid food, part of the difficulty arises in getting accurate estimates of the heat transfer coefficients. Farid and Ghani (2004) proposed a technique for calculating sterilization times which was based on numerical data generated from CFD simulations. In this work, a heat transfer coefficient correlation that was developed earlier for the parallel vertical walls maintained at different but constant temperatures (Catton, 1978) was applied. Dincer, Varlik and Gun (1995) emphasized the need to determine the total heat transfer coefficient of a cylindrically shaped canned food subjected to sterilization for process heat transfer analysis and energy optimization. They commented on the difficulties in measuring the total heat transfer coefficients accurately for isothermal conditions, especially when there was a large variation along a curved surface. In their study, they had considered heat transfer by conduction in the food medium and by convection to the can walls by steam. In the actual thermal sterilization process, isothermal boundary conditions are commonly applied owing to the condensing steam with a high heat transfer coefficient. The heat transfer resistance (taken usually as inverse of the heat transfer coefficient) would be actually from the interior can food contents. The resistance would increase inside the food can with time because of the reduction in the thermal driving force. Hence, the thermal driving force between the can wall and the bulk food contents has to be properly quantified. In a recent study, Kannan and Gourisankar (under review) defined the thermal driving force for convective heat transfer in terms of the difference between the constant can wall temperature and the time varying volume averaged temperature in the domain. Once the heat transfer coefficients and the temperature driving forces are quantified, the heat transfer fluxes and energy consumption rates may then be estimated. There is scope for further work on the determination of heat transfer rates and energy consumption during the heating of the canned liquid food undergoing thermal sterilization. Simpson et al. (2007) observed that the transient energy consumption was an important factor in deciding retort scheduling, minimizing energy costs and process times and maximizing nutrient retention. They further observed that batch processing with a battery of individual retorts was a common mode of operation in many food-canning plants (canneries). Although high speed processing


290

with continuous rotary or hydrostatic retort systems can be found in very large canning factories (where they are cost-justified by high volume of throughput), such systems are not economically feasible in the majority of small- to medium-sized canneries. In their recent work, Ghani and Farid (2006) observed that the still retort was used in large canning plants for metal and glass packed products. In the present work, the methodology for estimating the heat transfer rates and energy consumption in a still retort from the CFD simulation results is presented. While CFD simulations of transient multidimensional conservation equations are useful for a rigorous analysis of the thermal sterilization process giving time and location dependent temperature-velocity profiles, they are numerically expensive and take considerable time to converge. Incorporation of CFD simulations in liquid food sterilization optimization calculations has not been carried out so far to our knowledge and may prove to be complex. Balsa-Canto, Alsonso and Banga (2002) observed that complex first principle models involving nonlinear partial differential equations were computationally expensive to solve. Hence it is difficult to apply them in real-time tasks and model predictive control. Instead, simple closed form expressions are proposed for dynamic sterilization temperatures, heat fluxes, heat transfer rates and total energy consumption based on CFD simulation data. These expressions can be directly integrated into retort design, operation, control and optimization calculations involved in liquid food sterilization treatment. This study focuses on the heating cycle of the sterilization process where the

energy consumption is expected to be higher. In their recent work, Ghani and Farid (2006) used CFD simulations to analyze the cooling cycle of food sterilization in a food pouch. While food pouches are becoming increasingly reliable and popular, the present work focuses on the standard geometrical shape of the popular cylindrical food can.

3. DETAILS OF FOOD SYSTEM AND CAN GEOMETRY

The pseudo plastic fluid involving 0.85% w/w CMC solution in water was taken as the test system. The properties of this system are given in Table 1. Steffe, Mohamed and Ford (1986) suggested that this model was applicable to tomato puree, carrot puree, green bean puree, applesauce, apricot and banana purees, which are regularly canned and preserved usually by heating. The different cylindrical can geometries studied in this work are illustrated in Fig. 1 and their geometric parameters are given in Table 2. Three categories of cans labeled small (S), medium (M) and long (L) with different food medium thermal conductivities (0.351.4 W/m. oC) are explored. To explore the effect of thermal penetration into the can, seven categories of the food can were defined and simulated based on the thermal conductivity of the food contents contained (Table 2). The small and medium cans correspond to the standard dimensions documented by the Can Manufacturers Institute, Washington while the long cans have been included for parametric analyses.

Fig. 1 Cylindrical can geometries investigated.

S

M L


291

Tabl

e 1

Prop

ertie

s of t

he c

anne

d fo

od sy

stem

(0.8

5 %

(w/w

) CM

C) (

Kum

ar a

nd B

hatta

char

ya, 1

991)

.

Syst

em P

rope

rtie

s V

alue

/Exp

ress

ion

Uni

ts

Vis

cosi

ty (

) 1

exp

=

n . )T

Ra

nE (o

Pa.s

Con

sist

ency

inde

x (

o)

0.00

2232

Pa

.sn

Cha

ract

eris

tic v

isco

sity

(re

f) 13

.57

Pa.s

Act

ivat

ion

ener

gy (E

a) 30

.74e

+03

J/g

mol

e

Shea

r rat

e (

. )

If b

elow

0.0

1 s-

1 ta

ken

to b

e 0.

01(K

umar

and

Bha

ttach

arya

, 199

1)

s-1

Para

met

er fo

r she

ar ra

te, n

0.

57

-

Spec

ific

heat

(Cp)

41

00

J/kg

. K

Ther

mal

con

duct

ivity

(k)

0.7

W/ m

. K

Den

sity

()

950

Kg/

m3

Coe

ffic

ient

of v

olum

e ex

pans

ion

()

0.00

02

K-1

Tabl

e 2

Tota

l ene

rgy

cons

umed

for d

iffer

ent c

ateg

orie

s of c

ans. E

nerg

y C

onsu

med

(MJ)

C

ateg

ory

For

at

2589

s k

(W/m

o C)

L

(mm

) R

(m

m)

x

107

(m

2 /s )

S (-)

Tot

al su

rfac

e ar

ea(m

2 )

x104

Vol

ume

(ml)

0 1)

= 428.0

8145.0696.0exp1S

Fo rsuper

(14)

The fits of these correlations to the CFD data is illustrated in Fig. 5. For easier analysis, is defined as 1- so that

( )( )W

W o

T T

T T < >

=

(15)

It is desirable to have a small value of as it would imply that the volume averaged temperature would be close to the wall temperature. Re-expressing Eqs. (13) and (14), the following are obtained.

0.575

0.225

0.628exp rsub

Fo

S

=

(16)

= 428.0

8145.0696.0expS

Fo- rsuper (17)

For the supercritical regime, the AARD from the fit for the dimensionless temperature was found to be 2.08%. Combining both the subcritical and supercritical regimes, the AARD from the fit was 1.78%. From the above equations, it may be inferred that the approach to wall temperature is closer at higher Fourier numbers and smaller aspect ratios. The thermal penetration time as given by For will be higher at increasing times and/or higher thermal conductivities. Further, a smaller aspect

ratio cylinder will entail faster dynamics leading to closer approach to the wall temperature.

5.3 Correlations for heat transfer flux The heat transfer flux (q) was earlier defined according to Eq. (11). Earlier analyses by Kannan and Gourisankar (under review) revealed that the heat flux contribution from the curved surface was in good comparison with the total heat flux. In the conduction region, the heat flux contributions were uniform from the top, curved and bottom walls (Fig. 3). In the convection regime, the higher heat flux contribution from the lower surface was negated by the lower heat flux from the top walls, where the temperature gradients were smaller (Fig. 4). Further, the curved surface, owing to its higher contribution to the total surface area will dominate the heat transfer. The heat transfer coefficient may be interpreted in terms of the Nusselt number and a characteristic dimension (l) relevant to the appropriate heat transfer regime prevalent in the cylinder. Hence Eq. (11) may be given as follows.

( )TTlkNuq wl =

(18)

Expressing in terms of dimensionless temperature ( ) , Eq. (18) given above may be written as:

( )TTlkNuq wl 0=

(19)

The heat transfer rate (.

Q ) may then be estimated as the product of the heat flux and the total surface area of the cylinder as shown below.

( )TTAlkNuQ wl

.

0=

(20)

Due to the heat supply from the walls, the temperature within the domain increases with time. This leads to a higher volume averaged temperature and a consequent decrease in the thermal driving force (Tw - ). The temperature gradients at the wall also decrease leading to a decrease in the heat transfer coefficient with time. In the convection regime, the length of the cylinder relative to the diameter, i.e., the aspect ratio, will determine the distance that has to be traveled by the natural convection currents transporting thermal energy. Hence, the Nusselt number as well as the volume averaged temperature may be functions of


297

the Fourier number and aspect ratio. The model equations for the Nusselt number and may be expressed as follows.

( )11 nrm Fo,SNuNu = (21) ( )22 nrm Fo,S = (22)

Here, n1 is the exponent for the Fourier number associated with the Nusselt number while n2 is the corresponding exponent associated with the dimensionless temperature . Correspondingly, m1 and m2 are exponents for the aspect ratio in the two regimes. These models may be incorporated in Eq. (20) and integrated to yield the total energy consumption. The integrations for total energy consumption are carried out with respect to time (or equivalently, the Fourier number) and the aspect ratio is constant. The exponents for the Fourier number is adjusted such that:

21 n1n = (23) While it may be argued that such an adjustment may lead to suboptimal fit with the CFD data, it has to be viewed from the perspective of the utility of the resulting expressions. If the values recommended by the original regression fit had been used, the resulting expression for heat transfer rate would have not been amenable for analytical integration. The resulting expressions will entail numerical integration leading to numerical errors as well as reduced utility for thermal processing applications. The analytical solutions on the other hand will be in convenient closed form expressed in terms of the Fourier number, aspect ratio, geometric and thermal properties of the food can. It also ensured that the resulting fits to the CFD data were satisfactory as will be shown in subsequent discussions.

5.3.1 Subcritical regime In the subcritical regime the characteristic dimension for the Nusselt number is chosen as the diameter, as the heat transfer occurs predominantly from the vertical curved walls towards the fluid in the radial direction. In the Nusselt number modeling for this regime, the analysis revealed only a Fourier number dependency. After substituting for the dimensionless temperature in Eq. (18) and fitting a conformable expression for the Nusselt number, the following expression for the heat flux was obtained. The fits are given as follows.

0.575

0.425 0.225

9.53 ( ) 0.628expW o r

r

k T T Foq

DFo S

= (24)

The Nusselt number in the conduction regime with can diameter as the characteristic dimension is the pre-exponential term as shown by Eq. (25).

425.0534.9

rD Fok

hDNu ==

(25)

The AARD of the heat flux fit from the CFD data was 5.9%.

5.3.2 Supercritical regime (For 1) Due to the onset of convection in the supercritical regime, the length (L) of the cylinder is the more appropriate dimension. This is due to the convection of heat in the upward direction by the convection currents along the walls and in the downward direction along the core. This convective heat transfer in the core distorts the temperature contours as shown in Fig. 4. For ensuring more accurate correlation predictions of the heat flux and the heat transfer rate, a further distinction of the supercritical regime was made in the Fourier number range between 1 and 2. In this regime, the following expression for heat flux was found suitable.

y Supercritical with 1 For 2

+= 428.0

8145.0

1855.0

8145.0816.0692.0 696.0)298.0595.0(S84.12

SFoexp

FoFo)T(T

Lkq r

r

row (26)

In this range the AARD for the fit was found to be 3.6%. The effective Nusselt number in this regime is given by:

1855.0

8145.0

184.0

692.0 )298.0595.0(84.12r

rL Fo

FokS

khLNu +== (27)


298

y Supercritical with For >2

( ) ( )

+= 428.0

8145.0

1855.0

8145.097.084.0 696.0107.0914.034.12

SFoexp

FoFoTT

LkSq r

r

row

(28)

The effective Nusselt number in this regime is given by:

( )1855.0

8145.0

03.0

84.0 107.0914.034.12r

rL Fo

FokSNu += (29)

The AARD for the correlation fit was 21.70%. This may be attributed to the data near the end of the heating period. Here, the volume averaged temperature approaches the wall temperature (Tw) as indicated in Fig. 5. Even though the predicted from correlation was close to the actual CFD value, even a small error value in caused a larger error value in the thermal driving force calculation as a result of subtraction of two nearly equal quantities. However, these occurred near the end of the heating period and hence have only an insignificant effect on the total heat flux. The correlated heat fluxes are compared with the CFD-based heat fluxes in a parity plot (Fig. 9) and a reasonable fit may be observed. The representative variation of heat flux over the entire heating period is illustrated in Fig. 10 for the S7 category data. As is evident from this figure, the heat fluxes vary by over nearly three orders of magnitudes in this heating period. The variation of heat flux in the different Fourier number ranges is analyzed next. Typical trends of heat flux in these regions as a function of aspect ratio are shown in figures 68. In the subcritical region, the heat fluxes may be seen to drop rapidly by an order of magnitude. This may be attributed to an increasing thermal boundary layer thickness which decreases the rate of conductive heat transfer. Further, the thermal driving force is also decreasing as the temperature in the interior regions is increasing.

1000

10000

100000

0 0.2 0.4 0.6 0.8 1

Fo r

q(W

/m2 )

S35 S7 S14 Fig. 6 Heat flux variation in the subcritical region.

1000

10000

100000

1 1.2 1.4 1.6 1.8 2

Fo r

q(W

/m2 )

S35 S7 S14 Fig. 7 Heat flux variation in the region of 1


299

0

10000

20000

30000

40000

50000

0 10000 20000 30000 40000 50000

q CFD (W/m2)

q pre

d. (W

/m2 )

S7 M7 L7 L35 S14 S35 M14 +10% -10%

0

1000

2000

3000

0 1000 2000 3000

10

100

1000

10000

100000

0 2 4 6 8 10 12

Fo r (-)

q (W

/m2 )

Correlation CFD

Fig. 9 Parity plot of heat flux from CFD estimations and correlation predictions. (Inset: Parity plot within 20% CFD estimation for lower range of heat fluxes.)

Fig. 10 Typical plot of comparison of wall heat flux from CFD estimation and correlation prediction (for S7 category).

It may be seen from equations (24), (26) and (28) that the heat flux is strongly influenced by the thermal conductivity of the food medium in all the three regimes. Higher the thermal conductivity, higher is the heat flux at a given Fourier number. If the thermal conductivity is low, as for the S35 case, more time is required for reaching a given Fourier number value when compared to the higher thermal conductivity case (Eq. (9)). Hence the heat flux for the S35 case will be lower as with increasing time, the temperature driving force and heat transfer coefficients decline. This trend is also seen in the other Fourier number ranges (figures 7 and 8). In Fig. 8, the heat flux curve for the S35 case is shorter as the maximum simulation time of 2589 s will correspond to a reduced Fourier number of about 5 while the S14 case will correspond to a For of nearly 20. However, in the range of 1


300

Upon integrating this expression, the following function of For is obtained.

( )

= 225.0

575.0225.0 628.01184.0

SFoexpSDTTACQ rowpI (33)

Using the upper limit of For as unity in the subcritical regime, this equation reduces to:

( )

= 225.0

225.0 628.01184.0S

expSDTTACQ owpI (34)

5.4.2 Supercritical regime (1 < For < 2) Substituting the expression from Eq. (27) for Nul and Eq. (17) in Eq. (31), the following result is obtained.

( )=

+

=

2

14280

81450

18550

814502

1840

6920 6960298059500280

48412

rFo

r.

.r

.r

.r

owp

.

.

II dFoSFo.

expFo

Fo..TT.

DCALk

S.Q

(35)

After integrating, the result expressed as a function of For becomes

( )

( ) ( )

++

+

=

4280814504280

814504280

4280

21840

121

428029059506960

428089306960

1580

..r.

.r.

.

pow.

.

II

S.Fo..S

Fo.expS..

S.exp

CDATTkLS.Q

(36)

Applying the upper limit for For of 2, we get

( )

( ) ( )

+

+

=

42804280

42804280

21840

121

4280120212231428089306960

1580

..

..

pow.

.

II

S..S.expS..

S.exp

CDATTkLS.Q

(37)

5.4.3 Supercritical regime (For >2) Substituting the expression from Eq. (29) for Nul and Eq. (17) in Eq. (31), the following result is obtained.

( ) rFo

.

.r

.r

.r

owp.

.III dFoSFo.

expFo

Fo..TT.

DCAS

kL.Q

r

+

=

24280

81450

18550

814502840

0290

6960107091400280

43412 (38)

After integrating, the result expressed as a function of For becomes

( )

( ) ( )

++

+

=

4280814504280

814504280

4280

20280

271

1520106091406960

15201021231

15240

..r.

.r.

.

pow.

.

III

S.Fo..S

Fo.expS..

S.exp

CDATTkLS.Q

(39)

In this integration, the upper limit for For will be decided as shown in Eq. (9), based on the product of individual food mediums thermal diffusivity, radius of the food can and the maximum sterilization time (2589 s) The variation of energy consumption with time during the sterilization process is given in Fig. 11. The total time for the sterilization process was fixed at 2589 s for all simulations for the sake of

comparison between different cans that were simulated. It may be observed from this figure that the energy consumption is more sensitive to the aspect ratio of the cylinder than the thermal diffusivity of the food medium. In the conduction regime, it may be observed from Eq. (34) that the energy consumption is independent of the thermal conductivity of the food medium. The results are summarized in Table 2. The contribution to the total


301

energy consumption in the three regimes (For


302

Q heat transfer rate (W) Q energy consumed (J) r radial coordinate (m) R radius of the can (m) R universal gas constant (J/mol. o C) S aspect ratio, ratio of length to diameter of

the food can (-) t time of heating (s) T temperature (o C) T0 initial temperature (o C) volume averaged temperature (o C) Twall temperature at the wall of the can (o C) V velocity vector Vr velocity in the radial direction (m/s) Vz velocity in the axial direction (m/s) z axial coordinate (m)

Greek Symbols

thermal diffusivity (m/s2) dimensionless volume average temperature,

( )( )oW

o

TTTT

><

dimensionless volume average temperature, ( )

( )oWW

TTTT

>


303

17. Ghani AGA, Farid MM and Chen XD (2002b). Theoretical and experimental investigation of the thermal destruction of vitamin C in food pouches. Computers and Electronics in Agriculture 34(13):129143.

18. Ghani AGA, Farid MM and Chen XD (2002c). Numerical simulation of transient temperature and velocity profiles in a horizontal can during sterilization using computational fluid dynamics. Journal of Food Engineering 51(1):7783.

19. Ghani AGA, Farid MM, Chen XD and Richards P (1999). An investigation of deactivation of bacteria in a canned liquid food during sterilization using computational fluid dynamics (CFD). Journal of Food Engineering 42(4):207214.

20. Gourisankar SPCh (2006). Heat Transfer Analysis in Canned Food Sterilization. M. Tech. thesis, Indian Institute of Technology Madras.

21. Kannan A and Gourisankar SPCh (under review). Heat Transfer Analysis of Canned Food Sterilization in a Still Retort.

22. Kumar A and Bhattacharya M (1991). Transient temperature and velocity profiles in a canned non-Newtonian liquid food during sterilization in a still-cook retort. International Journal of Heat and Mass Transfer 34(45):10831096.

23. Kumar A, Bhattacharya M and Blaylock J (1990). Numerical simulation of natural convection heating of canned thick viscous liquid food product. Journal of Food Science 55(5):14031411.

24. Marra F and Romano V (2003). A mathematical model to study the influence of wireless temperature sensor during assessment of canned food sterilization. Journal of Food Engineering 59(23):245252.

25. Naveh D, Kopelman IJ and Pflug IJ (1983). The finite element method in thermal processing of foods. Journal of Food Science 48:1086.

26. Nicolai BM, Verboven B, Scheerlinck N and De Baerdemacker J (1998). Numerical analysis of the propagation of random parameter fluctuations in time and space during thermal food processes. Journal of Food Engineering 38:259278.

27. Rao MA and Anantheswaran RC (1988). Convective heat transfer to fluid Foods in cans. Advanced Food Research 32:3984.

28. Rhie CM and Chow WL (1983). Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J. 21:15271532.

29. Silva CLM, Oliveira FAR and Hendrickx M (1993). Modeling optimum processing conditions for the sterilization of prepackaged foods. Food Control 4(2):6778.

30. Simpson R, Figueroa I, Llanos D and Teixeira A (2007). Preliminary validation of on-line correction of process deviations without extending process time in batch retorting: any low-acid canned foods. Food Control 18(8):983987.

31. Steffe JF, Mohamed IO and Ford EW (1986). Rheological properties of fluid foods: data compilation. In Physical and chemical properties of foods. Ed. Okos MR. American Society of Agricultural Engineering, St. Joseph, MI.

32. Teixeira AA, Dixon JR, Zahradnik JW and Zinsmeister GE (1969). Computer optimization of nutrient retention in thermal processing of conduction-heated foods. Food Technology 23(6):134140.

33. Varma MN and Kannan A (2005). Enhanced food sterilization through inclination of the container walls and geometry modifications. International Journal of Heat and Mass Transfer 48(18):37533762.

34. Varma MN and Kannan A (2006). CFD studies on natural convective heating of canned food in conical and cylindrical containers. Journal of Food Engineering 77(4):10241036.

List of FiguresFig. 1 Cylindrical can geometries investigated.Fig. 2 Section of the computational mesh for the smallcylinder with fine mesh near the wall and coarse mesh near the core.Fig. 3 Temperature contours in the subcritical conduction regime for cylinders of different aspect ratios (For = 0.4).Fig. 4 Temperature contours in the convective supercritical regime for cylinders of different aspect ratios (For = 5.0).Fig. 5 Dimensionless temperature in the cylindrical domain as a function of m.Fig. 6 Heat flux variation in the subcritical region.Fig. 7 Heat flux variation in the region of 1

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