Prediction of hot-fill-air-cool sterilization processes for tomato paste in glass jars

ELSEVIER

JoumalofFood Engineering23 (1994) 33-50 0 1994 Elsevier Science Limited

Printed in Great Britain. All rights reserved 0260-8774/94/$7.00

Prediction of Hot-Fill-Air-Cool Sterilization Processes for Tomato Paste in Glass Jars

A. J. Sandoval, J. A. Barreiro & S. Mendoza

Depto de Tecnologia de Procesos Biol6gicos y Bioquimicos, Universidad Sim6n Bolivar, Apdo 89000, Caracas 1080-A, Venezuela

(Received 1 March 1992; accepted 16 March 1993)

ABSTRACT

A mathematical model to predict heat transfer and integrated sterilization values during the hot-fill process of double concentrated tomato paste in glass jars was developed. The model was capable of predicting satisfactorily the time-temperature relationships during the air-cooling process following the hot-fill process. Integrated sterilization values after hot- filling were calculated as a function of the retention time. A hot-filling temperature of 85°C was not adequate to sterilize properly this product for any of the jar sizes studied and for the initial and final population levels established, for the target microorganism employed (B. coagulans). Hot- filling temperatures of at least 94, 92 and WC are recommended for jar sizes of 200, 500 and 4ooo cm3, respectively. As jar size increased, the hot- filling temperature and the retention time required to achieve the desired integrated sterilization value decreased. Larger retention times were obtained as the hot-filling temperatures decreased.

NOTATION

ZI Radius of the jar (cm)

B” Roots of the equation m,cot(A,) = A,, Parameter defined by eqn ( 10)

B” Roots of the equation m,J,( B,) = B,J, (B,) C Constant of eqn (2) D Decimal reduction time (min)

33

34

F h

HC

H,

i Jo J, k

K” 1

% mz n

L 4

t T

Ta T,

A. J. Sandoval, J. A. Barreiro, S. Mendoza

Lethality of the thermal process (min) Overall heat transfer coefficient (W mm2 K-l) Natural convection heat transfer coefficient for air in vertical cylindrical surfaces (W mP2 K-l) Radiative resistance created by the emissivity of the glass jar to the surroundings (W rnv2 K- ‘) Lag factor heating curve Bessel function of the first class of order zero Bessel function of the first class of first order Thermal conductivity (W m-l K- ‘) Thermal conductivity of glass (W m-2 K-l) Half height of the cylindrical jar (cm) ha/k hllk Constant of the eqn (2) Radial coordinate (cm) Rayleigh number Thermal resistance created by the glass wall of the jar (W-l m2 K) Time (s, min)

Temperature (K, “C) Air temperature (K, “C) Surface temperature (K, “C)

a T/&z Outward normal gradient of temperature (“C cm- ’ )

X” Thickness of the glass jar wall (cm) z Axial coordinate (cm) Z Reciprocal of the slope of the phantom thermal death time curve

(“C)

a Thermal diffusivity (cm” s- ‘) E Emissivity 0 Boltzmann constant (5.73 X lo-* W mP2 Km4)

Subscripts

f. Referred to the geometrical center of the jar Referred to any iso-j region in the jar

ref Reference temperature V Referred to the external temperature V Referred to glass properties

s, Integrated lethality Initial condition

Hot@-air-cool sterilization of tomato paste in glass jars 35

INTRODUCTION

Hot-fill methods are particularly useful and frequently utilized for the commercial sterilization of tomato paste. Other methods including aseptic filling and hot water processing are also employed (Goose & Binstead, 1973; Lopez, 1975).

In Venezuela, the most usual hot-fill process performed consists of processing the tomatoes followed by vacuum concentration of the juice in double effect evaporators. The tomato paste containing about 30% soluble solids, including added salt, is passed through a heat exchanger in order to elevate its temperature above 90°C. After reaching this temperature, the product is hot-filled into glass jars, closed, inverted in order to sterilize the lids and cooled in air for a given retention time in order to achieve the required sterilization lethality. After air-cooling, the jars are cooled with water at room temperature. During the retention time and cooling of jars in air, the packed hot product is subjected to a variable time-temperature relationship in which the microorganisms surviving the hot-filled process must be inactivated in order to guarantee commercial sterilization.

Various microorganisms have been reported to be of practical significance in the deterioration of thermally processed tomato products, especially spore forming saccharolytic and butyric anaerobes such as Clostridum pasteurianum and Clostridium butyricum (Hersom & Hulland, 1964). In the same way, spore-forming facultative anaerobes such as Bacillus coagulans have been related to such deterioration. Due to the higher thermal resistance of B. coagulans as compared to the saccharolytic and butyric spore-forming anaerobes, this microorganism is normally used as target in the design of thermal processes for the sterilization of tomato products (NCA, 1968; York et al., 1975; Rodrigo et al., 1990).

The microbiological evaluation of the hot-fill process in a Venezuelan tomato paste factory was accomplished by Sandoval et al. (1992). The flora surviving the heating process present at the moment of hot-filling the glass jars consisted of flat, sour, sporulated bacteria, isolated and identified as Bacillus coagulans. Other microorganisms of lower heat resistance such as molds, yeast, and butyric acid anaerobes were inactivated by the heating process.

The recommended values (F &oF ) for B. couguhs in products with pH 4.5 was O-7 min. York et al. (1975) determined integrated sterilizing values (F &oc) of 1.55 min for whole peeled tomatoes with pH14.3 1. Rodrigo et al. (1990) established an integrated sterilizing value (F,,,,.,)

36 A. J. Sandoval, J. A. Barreiro, S. Mendoza

for pureed and crushed tomatoes, with pH 4.5, of 159 min, using B. coagzdans (ATCC 8038) as target microorganisms.

The thermal resistance of B. coagulans in tomato products has been studied by various authors. Youland and Stumbo (1953) studied the heat resistance of B. coagulans (ATCC 8038), subjected to moist heat. Knock et al. (1959) determined D values of B. coagulans in South African tomato juice. York et al, (1975) determined the heat resistance of B. coagulans (ATCC 8038) in tomato juice and Rodrigo et al. (1990) characterized the thermal resistance of strain ATCC 8038 in pureed and crushed tomatoes. The thermal resistance of B. coagulant in double concentrated tomato paste (pH 4*0,3O”Brix and a, = 0.95 at 23”C, for an inoculum of 1.4 x lo4 spores ml- 1 of tomato paste), was reported to be D ,-,o”c = 3.5 min and Z= 9+5”C (Sandoval et al., 1992).

Modeling of thermal processing of foods in glass jars has received little attention in the literature. Merril (1948) developed equations for the calculation of heating rates in glass jars, considering the thermal resistance of the glass wall. Towsend et al. (1949) studied the heat transfer rate for bentonite suspensions packed in glass jars. Fagerson and Esselen (1950) investigated some factors influencing the heating rate in glass containers and presented time-temperature distribution patterns. Naveh et al. (1983) studied the application of finite element methods to simulate heat transfer in conductive products packed in glass jars, taking into account the geometry of the jar, the thickness of the glass wall at different locations (bottom, sides and neck), and the thermal properties of the jar and the food product. Air-cooling under natural convection conditions, such as those prevailing during the hot-filling-air-cooling retention process, were described and analyzed by the same method. The procedure developed was not subjected to experimental verifica- tion.

The thermal process of conductive products in glass jars is characterized by a finite surface thermal resistance composed of the glass jar wall and the natural convection heat transfer resistance of air. Various authors have determined and characterized the surface heat transfer resistance, taking into account the different resistances involved, as in the case of glass jars, retortable pouch processing, and pressurized hot water thermal processing of jars and cans (Adams et al., 1983; Naveh et al., 1983; Peterson & Adams, 1983; Naveh et al., 1984; Bhowmik & Tandon, 1987; Lebowitz & Bhowmik, 1989).

Because of the scarce information available for the hot-filling-air- cooling process of tomato paste packed in glass jars and the lack of simple models capable of being simulated in a personal computer, the objective of this research work was to develop and experimentally

Hot-fill-air-cool sterilization of tomato paste in glass jars 37

evaluate a mathematical model capable of predicting time-temperature relationships and sterilizing values for the hot-filling-air-cooling process of tomato paste in glass jars.

MATERIALS AND METHODS

Development of a mathematical model

Prediction of time-temperature relationships during the air-cooling process of tomato paste packed in glass jars The hot-filling-air-cooling sterilization process for tomato paste packed in glass jars was analyzed. Jars were approximated to the geometry of a finite cylinder of radius a and height 21, as indicated in Fig. 1. The global heat transfer coefficient (h in Fig. 1) takes into account the natural convection heat transfer coefficient for air (I&) in vertical cylindrical surfaces, the thermal resistance of the glass wall, and the radiative resist-

+I AIR

I

I

-1

i

To

a

c

,_

r

a h I I

AIR

T”

Fig. 1. Diagram of section r-z of a glass jar, assimilated to a finite cylinder.


ante created by the emissivity of the glass jar to the surroundings (H,), as indicated in eqn (1) (McAdams, 1954; Kreith, 1973):

h 1 =

+(x,10-z) 1

(H,+Hr) K”

(1)

The natural convection coefficient for air in vertical cylindrical surfaces can be calculated by eqn (2) (King, 1932; McAdams, 1954). This equation requires T, and T, in “F and 1 in ft, in such cases, H, units are Btu h-’ ft-2 “F-’ (t o convert H, to W mV2 K-l, multiply by 5.677):

H =,ux)” c

(2z)1-3” (2)

where: C= 0.19 and n= l/3 for 10y < R,< 1012

and: C= 0.29 and n= l/4 for lo4 < R$ 10y

The radiative resistance caused by the emissivity of hot glass to the surroundings can be estimated by eqn (3) (McAdams, 1954):

H =Eo(~+273)4-(T,+273)4 r

(T,- T,) (3)

The thermal resistance created by the glass walI of the jar (R,) can be estimated from eqn (4) as a function of the thermal conductivity of glass (K,) and the thickness of the jar waII (XV) (McAdams, 1954):

R,=XV10-2/K(, (4)

It is important to consider that in the system studied there are two convection heat transfer coefficients present: one associated with the cyhn- drical side and bottom of the jar that takes into account all the effects described above (eqns (l)-(4)), and another one for the top of the jar considering the metal cap and the headspace jointly with the other effects (eqns ( 1 )-( 3)).

Previous measures of the thickness of the glass wall at different locations of the jar including the neck, sides and bottom were indicative of a range from 0*31+_ 0.02 to 0.33 + 0.02 cm for the 200 cm3 jar, 0.26 f 0.04 to 0.36 f 0.01 cm for the 500 cm3 jar, and 0.27 + 0.03 to O-41+ 0.06 cm for the 4000 cm3 jar.

Temperature history at any point inside the container for a conductive heated food, during the air-cooling process following hot-fihing in the


glass jars, can be predicted by solving the heat equation in cylindrical coordinates (Carslaw & Jaeger, 1959):

a2T(r,z,t)+~ aT(r,z,r)+a2T(r,z,r)_l aT(r,z,t) a? r ar a22 -(x at (5)

with -I<z< +landOlr<a

with the following initial and boundary conditions prevailing during the process:

W,z,O)= G for t=O,OIr<aand -l<z< +I (6)

The initial temperature (To) of product in the jar is constant and uniform at any point. The following boundary condition also prevails:

aT h(T.+-T) -_= an k

for r=aandz= fl (7)

which considers the surface heat transfer coefficient as indicated above. Both the temperature of air surrounding the jar (TV) and the thermal conductivity of the product (k) remain constant during the air-cooling process.

Equation (5) was solved jointly with eqns (6) and (7) by the method of separation of variables, resulting in the following equation (Carslaw & Jaeger, 1959; Charm, 197 1):

T(r,z, t)- T, 4 t sin A,, cos [A/z/l]

To- TV =a.=, A,+sinA,cosA, x exp[ -A $at/Z’)]

(8)

The thermal diffusivity of double concentrated tomato paste was determined in a previous work (Sandoval, 1991): a = 0.00159 cm* s- ‘, and is considered to remain constant during the process.

Prediction of sterilization values (F,) in the hot-fill-air-cool process of tomato paste packed in glass jars The manual method of Barreiro et al. (1984) was employed to predict sterilization values during the air-cooling process of tomato paste packed in glass jars. This method was originally developed for conductive products packed in rectangular cans, but can also be applied to cylin-


drical containers due to the considerations implied in its development. These authors obtained the following equations to estimate the integrated lethality value in the volume of the container as a function of the lethality in the center of the container (F,) and in an iso-j region (FL), for which jJj, = l/3:

F,=FC-D,flog (0*143/B)(1-10-8)+ I 10-(O~998B+O~173)

(5*771B+ 1) 1 (9)

with

when jJj, = I/3

The values of F, and FL may be calculated method (Stumbo, 1973):

(10) (11)

employing the general

employing the time-temperature relationships in the center of the container and at any point of an iso-j region where jJjC = l/3, predicted with eqn (8). In this way:

T,, - T(O, 0, t) dt 2

and:

F =

L T,,- T(rL,zLd&

Z

(13)

(14)

t’ being the retention time during the air-cooling process following hot- filling of tomato paste in glass jars.

With the values calculated with eqns (13) and ( 14) and eqns (9)-( 1 l), the integrated sterilizing value F, associated to the air-cooling retention period, following hot-filling of tomato paste in glass jars, may be determined for a target microorganism characterized by thermal resistance parameters D, and Z.

A computer program was written in Basic language (HOTSTER.BAS) to calculate time-temperature relationships and the integrated sterilizing values F, for the hot-fill-air-cool, according to the model developed before. This program can be run in a personal computer and is available from the authors upon request.


Heat penetration studies

In order to calculate experimental time-temperature relationships to evaluate the model developed above, double concentrated tomato paste was packed in glass jars of 200 and 500 cm3, employing three hot-filling temperatures of 85,90 and 95”C, leaving a headspace of 0.4 and 1.1 cm for the 200 and 500 cm3 jars, respectively. The physical-chemical characteristics were determined in a previous work (Sandoval et al., 1992) (pH 3.98, aw= O-953 at 2O”C, 30.3”Brix).

The temperature of the packed product was stabilized in a water bath ( +_ 0.2”C) (Labconco-Mod. 213) at the previous indicated values, in order to have a uniform hot-fill temperature for the product. The jars were removed, quickly dried with a cloth and allowed to cool in stagnant air, with temperature ranging from 19 to 26°C.

Copper-constantan needle type thermocouples (Ellab-Mod. TC-67), provided with packing glands, were fixed at the geometrical center of the jars and in the air surrounding the jars during the air-cooling process. The temperature was recorded in a Leeds & Northrup (Speedomax W) recorder, previously calibrated against a mercury thermometer. A total of 18 heat penetration experiments (six by triplicates), with three filling temperatures and two jar sizes, were carried out.

Statistical analysis

Linear regression analysis between the experimental and predicted heat penetration values employing the model developed above were performed, utilizing a statistical package (Stratgraphics version 2.6).

RESULTS AND DISCUSSION

Experimental evaluation of the heat transfer model

The results obtained for the heat penetration studies for tomato paste, employing a hot-filling temperature of 95°C and glass jars of 200 and 500 cm3, respectively, are presented in Figs 2 and 3, along with the predicted temperature at the geometrical center of the jar utilizing the heat transfer model developed in this work. The theoretical model was capable of satisfactorily predicting the time-temperature profile during the air-cooling retention process, especially for temperatures above 85°C where the lethality of the target microorganisms is of practical significance. The results obtained for other hot-filling temperatures (85


52-

401 Time (mid

Fig. 2. Predicted and experimental time-temperature relationships for tomato paste, in the geometrical center of a 200 cm3 glass jar (T,, = 95°C and TV = 26°C).

V Experimental

o Predicted

and 90°C) were similar in nature. This fact may be explained by the assumption of a constant surface heat transfer coefficient during the air- cooling process, calculated at the beginning of the process. Actually this coefficient diminishes as cooling proceeds and therefore the prediction of temperature for long cooling times is expected to be lower than actual temperatures. This simplification is justified on the basis of the relatively small deviations between predicted and experimental data observed at long cooling times which had a nil effect in lethality of the target microorganism due to the temperature level involved when this deviation occurs. On the other hand, if a variable surface heat transfer coefficient were taken into account in the model, the mathematical development would have been more complex and computation time longer. In view of the experimental results obtained, this simplification was considered as valid.

For all the hot-filling processes studied, the correlation coefficients between the experimental and predicted temperature values were high (r> 0*99), with highly significant linear regression for all, according to the


66-

V Experimental

0 Predicted

62-

50 ( I I 0 36 72

Time (min)

Fig. 3. Predicted and experimental time-temperature relationships for tomato paste, in the geometrical center of a 500 cm3 glass jar ( To = 95°C and TV = 21°C).

analysis of variance practiced (p d O-0 1). Thus, the predictive capacity of the heat transfer model developed in this work was established.

Prediction of sterilization values for hot-filled tomato paste in glass jars

The integrated sterilization values (F,) for double concentrated tomato paste were calculated utilizing the model developed in this research work, as a function of the retention time, after hot-filling in glass jars. Three jar sizes of frequent use in industry were studied: 200, 500 and 4000 cm3. For the computer simulation, five hot-filling temperatures were selected (85,90,92,94 and 95”C), with an external air temperature during the retention period of 28°C. All these temperatures are in the usual range observed in industrial practice.

The integrated lethality curves determined (Figs 4-6), are general and independent of the initial and final populations of the target microorganism and of the lethality value required for the thermal process (F f, T,,,). This last value can be calculated by means of the linear semi-


logarithmic model (Pflug, 1987~):

Bacillus coagulam, characterized by DgOOc = 3.5 min and Z= 95°C in double concentrated tomato paste, was employed as target microorganism (Sandoval et al., 1992). Initial population values ranging from lo2 to 10’ spores per jar were selected. These values are representative of the usual concentration found in industrial practice (Sandoval, 199 1). A final population of 10 -2 spores per jar surviving the hot-fill process was utilized, since this value results in an actual probability of growth of thermophilic microorganisms from 10 - ’ to 10m6, if the product is to be stored at temperatures < 3O”C, below the optimal temperature range of the target microorganism (Stumbo, 1973; Pflug, 1987b). Mean storage temperatures below 30°C are frequently observed.

With the &$oc obtained, depending on the initial spore population reflecting product contamination and using the results presented in Figs 4-6, for various hot-fill temperatures and jar sizes, it is possible to calculate the retention time required to reach the sterilization value desired for the hot-fill process under study.

25

Retention time (min)

Fig. 4. Predicted integrated lethality values for the hot-fill-air-cool steriiization process for tomato paste packed in glass jars of 200 cm3 for diierent filling tempera-

tures, employing B. coagulans as target microorganism.


60

so-

QO-

2 E se-

e

20-

ICI

0 12 20 28 56 44


Fig. 5. Predicted and integrated Iethality values for the hot-fill-air-cool sterilization

process for tomato paste packed in glass jars of 500 cm3 for different filling tempera-

tures, employing B. c0agulan.s as target microorganism.

60.

.c_ E

ul IA 40.

20,

0 20 28


Fig. 6. Predicted integrated lethality values for the hot-f&air-cool sterilization

process for tomato paste packed in glass jars of 4000 cm3 for different filling tempera-

tures, employing B. coagulans as target microorganism.


Following the procedure previously indicated, the retention times required to reach the integrated lethality desired, after hot-filling at various temperatures for the jar sizes considered, are presented as a function of the initial concentration of the target microorganism in Tables l-3.

The results shown in Table 1 are indicative of the fact that in order to reach the integrated lethality desired for jars of 200 cm3, with an initial spore population per jar above 103, hot-filling temperatures above 94°C are required. For initial populations of lo2 spores per jar, the hot-filling temperature could be of at least 92°C.

Similar effects were observed for other jar sizes, where minimum hot- filling temperatures of 92 and 90°C for initial populations above lo3 and lo2 spores per jar, are required for the jar sizes of 500 and 4000 cm3, respectively. In the first case (500 cm3 jar), hot-filling at 90°C is possible if the initial population is equal or below lo2 spores per jar.

In all cases, a hot-filling temperature of 85°C was not adequate to sterilize properly this product for any of the jar sizes studied and for the initial and final population levels established, for the target microorganism utilized.

As a general observation, hot-filling temperatures of at least 94, 92 and 90°C are recommended for jar sizes of 200, 500 and 4000 cm3, respectively, unless the initial spore population levels are lower than lo2 spores per jar, where lower temperatures can be used and calculated employing the model.

In general, as the jar size increased, the hot-filling temperature and the retention time required to achieve the integrated sterilization value desired, decreased. On the other hand, larger retention times were obtained, as the hot-filling temperatures decreased. However, long time, low temperature, hot-filling processes could induce undesirable changes in the organoleptic properties and nutritive value of this product; thus, it is recommended to determine thermal processes capable of achieving commercial sterilization and the best quality attri- butes for this product, especially color, according to any suitable procedure (Barreiro et al., 1979; Lund, 1982).

CONCLUSIONS

A mathematical model to predict heat transfer and integrated sterilization values during the hot-fill process of double concentrated tomato paste in glass jars was developed.

tlot-fill-air-cool sterilization of tomuto paste in glass jars 47

TABLE1 Mention Time for Hot-Filled Tomato Paste in Glass Jars of 200 cm3 for Various Initial

Spore Populations of H. coqulrms

,y_i “( ‘L,

i\‘c~kwtion time (min)

‘N)“( 92 “C 94°C 95°C

j I, ?.I”? -_ to.2 12.9 10.0 l:! 21.0 - ‘0.2 11.2 8.8 If:’ 17.5 - 15.7 9.3 6.7 11): 144 __ ‘h+l 12.5 7.3 4.7

~_. ._~ ~_~____

-, Indicarc\ process is not capable of achieving commercial sterilization. I~?liiil, !k~,“?lr,~Lr.1KlI’r‘.


The model was capable of adequately predicting the time-temperature relationships during the air-cooling process following the hot-fill process, especially for temperatures above 85°C of practical significance for the target microorganism employed in the study: Bacillus couguluns. The heat transfer model was experimentally evaluated for various filling temperatures, ambient temperatures and jar sizes. The coefficient of correlation between the experimental and predicted temperatures during the retention period was high in all cases studied (r> 0*99), the linear regression being highly significant (p% O-01).

Integrated sterilization values (F,) after hot-filling in glass jars of double concentrated tomato paste were calculated utilizing the model developed in this research work, as a function of the retention time. Three jar sizes, five hot-filling and a single external air temperatures, normally found in the industrial practice were selected. The lethality value required for the thermal process (Ff T,,,), for the target microorganism involved (B. coaguhs), was calculated using the linear semilogarithmic model for initial population values ranging from lo* to lo5 spores per jar and final desired probability level of 10 -* spores per jar surviving the hot-fill process.

It was determined that a hot-filling temperature of 85°C was not adequate to sterilize properly this product for any of the jar sizes studied and for the initial and final population levels established, for the target microorganism employed. Hot-filling temperatures of at least 94,92 and 90°C are recommended for jar sizes of 200,500 and 4000 cm3, respectively. Retention times for these processes were calculated.

In general, as the jar size increased, the hot-filling temperature and the retention time required to achieve the integrated sterilization value desired decreased. On the other hand, larger retention times were obtained as the hot-filling temperatures decreased.

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Bhowmik, S. & Tandon, S. (1987). A method for thermal process evaluation of conduction heated foods in retortable pouches. J. Food Sci., 52,202-g.


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Fagerson, I. S. & Esselen, W. ( 1950). Heat transfer in commercial glass containers during thermal processing. Food Technol., 4,4 1 1 - 15.

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Peterson, W. R. & Adams, J. P. ( 1983). Water velocity effect on heat penetration parameters during institutional size retort pouch processing. J. Food Sci., 45, 848.

Pflug, I. J. (1987a). Using the straight-line semilogarithmic microbial destruction model as an engineering design model for determining the F-values for heat process. J. Food Prot., 50,342-51.

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Rodrigo, M., Martinez, A., San&is, J., Trama, J. & Giner, V. ( 1990). Determina- tion of hot-fill-hold-cool process specifications for crushed tomatoes. J. FoodSci., 55,1029-32,1038.

Sandoval, A. J. (1991). Estudio de1 Proceso de Esterilizacion por Llenado en Caliente de Pasta de Tomate Envasada en Vidrio. Tesis de Magister en Ciencia de 10s Alimentos, Universidad Simon Bolivar, Caracas, Venezuela.


Sandoval, A. J., Barreiro, J. A. & Mendoza, S. (1992). Thermal resistance of Bacillus coagulans in double concentrated tomato paste. J. Food Sci., 57, 1369.

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Townsend, C. T. et al. ( 1949). Comparative heat penetration studies in glass and cans. Food Technol., 3,213.

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Prediction of hot-fill-air-cool sterilization processes for tomato paste in glass jars

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