## Abstract

Throughout this chapter we will explore the computational applications that can help us in the evaluation, calculation and simulation of the thermal treatment of canned foods. Although some basic principles of microbial death kinetics will be recalled, the course is basically focused on the exploration and use of computational applications to evaluate and simulate the heat treatment of low-acid foods, considering C. botulinum as the reference microorganism. I hope that this book chapter will be useful for you and that you will be able to explore all the contents that are planned to be developed: General and technical aspects of the heat treatment of canned foods, heat penetration studies of canned foods, heat treatment evaluation General method, calculation and prediction of heat treatment by Ball’s Method, heat treatment modeling and simulation, and optimization of heat treatment.

### Keywords

- canned food
- heat penetration study
- general method
- Ball’s Formula Method
- simulation
- F-value

## 1. Introduction

Heat treatment is a process of utmost importance to ensure food safety. If the product, a canned food, for example, does not receive an adequate heat treatment, it might cause intoxication and even death of the consumer [1]. The treatment must be designed correctly to guarantee efficient results, reducing the negative impact on the food, caused by the use of high temperatures [2]. For this, in order to optimize the process, it is necessary to know the thermal properties of the food, the kinetics of the changes in its quality, in addition to the quantitative and qualitative characteristics of the microbial load and/or enzymes [3].

To evaluate and simulate a thermal treatment, there are computational tools that use techniques that have been designed to evaluate the time of a process, or its F-value and/or simulate a thermal process.

In order to evaluate a thermal process there are two groups of methods, the Formula Methods and the General Methods. The Figure 1 shows that there are several Formula methods to evaluate a heat treatment. The classic Formula Methods are those of Charles Olin Ball and Charles Raymond Stumbo, which are called Ball’s Formula Method [4, 5, 6], and Stumbo’s Formula Method [7, 8, 9, 10], respectively. There are other Formula Methods such as the one proposed by Kan-Ichi Hayakawa and the Formula Method developed by Quang Tuan Pham. These Formula Methods are called Hayakawa’s Formula Method [11, 12, 13], and Pham’s Formula Method [9, 13, 14, 15].

General methods can also be used to evaluate a packaged food. There are three General Methods (Figure 2). The Original General Method (OGM) was plated by Willard Dell Bigelow and his team in 1920 [15, 16]. The Improved General Method (IGM) was proposed by Charles Olin Ball after 1923 [15, 17, 18, 19, 20].

The Combined General Method (CGM) was proposed by William R. Miranda-Zamora, and Arthur A. Teixeira in 2012, as its name says it is a combination of the two previous General Methods [2, 15].

Both General Methods and Formula Methods can be solved using software or computer applications [21, 22, 23].

The simulation of the heat treatment of packaged foods can be done using the finite difference method or using the finite element method [24, 25, 26, 27, 28, 29].

## 2. General and technical aspects of the heat treatment of canned foods

Knowing the acidity of the food is crucial to determine the severity of the heat treatment. If the food has a pH < 4.6, as in the case of apple nectar, canned mango, pickles, citrus fruit juices, jam, sauerkraut, some sauces, etc.; in this case, the acidic medium will inhibit the proliferation of sporulated bacteria such as * C. botulinum* and, therefore, severe heat treatment (<100°C) will not be required. In contrast, if the food has low acidity (pH > 4.6), such as canned asparagus, milk, among other meat products, seafood and canned vegetables, it is essential to use high temperatures >100°C [8, 14], which guarantee the sterilization of the food, increasing its shelf life. There are particular cases such as, for example, although milk has an almost neutral pH, being susceptible to microbiological spoilage, a mild pasteurization is applied to preserve its nutritional characteristics, in addition to the fact that milk is a product with a short shelf life; however, in many cases a high temperature-short time (HTST) pasteurization is applied and, being for a few seconds, the impact on the quality of the product is considerably avoided [2, 15].

Thermal treatment is based on two aspects: the biological (or microbiological) and the physical. The biological aspect refers to the microorganism, as the reference microorganism or target microorganism. The important thing is the number of decimal log reductions, n, [30, 31, 32, 33], which is defined as:

where N_{0} = the number of spores of the target microorganism, and N = the number of spores of the target microorganism that remains after heat treatment.

For example, if we start with a load of 1000 spores of * C. sporogenes*, and after heat treatment it is reduced to 1 spore. Therefore, the number of decimal log reductions will be 3 according to Eq. (1). In order to destroy the spores of

*, 12 decimal log reductions are needed [2, 15, 34, 35, 36]. The F*C. botulinum

_{0}value is the standard used worldwide to quantify the F-value at a reference temperature. The reference temperature used for commercial sterilization is 121.1°C on the Celsius scale, or 250°F on the Fahrenheit scale. The F

_{0}value is the minutes that are necessary to evaluate the lethal effect of heat at the reference temperature of 121.1°C = 250°F [2, 15, 16, 21].

Other important values to determine are the D value and the z value, which are determined in the laboratory, using different methods. The D-value and z-value are derived from the thermal death or destruction curves and the thermal resistance curve, respectively [2]. The D-value is defined as the time required to destroy 90% of the initial microbial load, or go through a logarithmic cycle. The smaller the D value the faster the destruction rate [15]. The z-value is defined as the variation in degrees Celsius or degrees Fahrenheit required to reduce 90% of the D-value, or for the D-value to go through a logarithmic cycle [2, 15, 16].

One of the methods to determine the z-value and the decimal reduction time or D-value is the thermoresistometer [37, 38, 39]. The D-value and z-value can also be determined to the nutrients by means of a thermoresistometer [40, 41, 42]. The D value or decimal reduction time, is related to the number decimal log reductions through Eq. (2). Furthermore, the D-value and the z-value are characteristic of each spore or vegetative cell of the microorganism, or nutrient [43, 44, 45].

where

Cans and/or packaging have an important role in heat transfer efficiency and, therefore, they should be properly selected, considering their physical, mechanical, thermal and even electrical and optical characteristics. According to Berk [31], the most commonly used material is tinplate, especially because of its low cost. Aluminum is also widely used in the manufacture of cans for alcoholic and non-alcoholic beverages, and although it is more ductile and lighter than tinplate, it has a higher cost [18]. Glass is also used for the packaging of beverages and canned food, being characterized by its impermeability, rigidity, thermal resistance and transparency, obtaining attractive containers; however, they are very fragile and have a high weight [29]. Considering its thermal properties at 20°C, it has a thermal conductivity (k) of 0.75 W m^{−1} K^{−1}, a specific heat (C_{p}) of 800 J kg^{−1} K and a thermal diffusivity (α) of 0.35 x 106 m^{2} s^{−1}, with a great difference compared to aluminum, whose k, C_{p} and α values are 230 W m^{−1} K^{−1}, 900 J kg^{−1} K and 95 x 106 m^{2} s^{−1}, respectively. It is important to mention that these values depend on other characteristics, such as thickness, which, the higher the thickness, the better the thermal resistance, with a lower heat transfer rate [2, 16]. To avoid environmental impact, thinner materials are used, as in the case of tinplate, but like other metallic materials, they still maintain optimum qualities [34].

## 3. Heat penetration studies of canned foods

Heat penetration testing or studies is done by placing containers with temperature sensors in the coldest zone of the autoclave or retort. From the heat penetration tests it is interesting to determine the heat penetration factors f and j [51, 52].

The EVATMi-ZA v 1.0 software includes the determination of the heat penetration parameters f and j [1, 2] (heating, f_{h} and j_{h} [53, 54, 55] or cooling, f_{c} and j_{c}). The heat penetration parameters for heating include the determination of the delay factor j_{_CUT}, based on the CUT value “come-up time” [56]. The come-up time is the time it takes for the autoclave or retort to reach process temperature. The 0.58 CUT is the new origin when using the Charles Olin Ball model or Ball’s Formula Method [57, 58, 59, 60]. Figure 3 shows the behavior of steam within a canned food. The trend of temperature versus retort temperature or autoclave temperature is linear on semi logarithmic paper [61, 62, 63, 64].

From Figure 3 we deduce:

Therefore, f_{h} as a function of CUT, j and j_{_CUT} is:

The EVATMi-ZA v 1.0 software includes the determination of the broken curve penetration parameters (f_{h}, f_{h2}, x_{bh}, x_{bh_CUT}, j_{h}, j_{h_CUT}). There are many canned foods that exhibit a broken curve [55, 65, 66, 67, 68, 69, 70].

## 4. Heat treatment evaluation general method

Willard Dell Bigelow in 1920 presented a method for calculating the F-value of packaged foods, which was essentially graphical, it was determined by weighing (using scissors and analytical balance), counting squares (using graph paper) or planimetry (using planimeter) [71, 72, 73, 74]. Initially, they constructed a graph in Cartesian coordinates, the curve of rise and fall of the temperature (heat penetration) at the slowest heating point (critical point) of the product during sterilization [75, 76, 77, 78, 79, 80]. The thermal resistance of the bacteria was represented by the thermal destruction time curve (TDT-curve) obtained by plotting the time required to destroy a high percentage of spores from a population versus the degree temperature [81, 82, 83]. From the TDT-curve, the values of “thermal death or destruction time” (TDT) were calculated for each time of the heat penetration curve. This is known as the Original General Method (OGM).

To use the Original General Method, the Improved General Method and the Combined General Method it is necessary to calculate 1/TDT (min^{−1}), L (lethal rate) and LF (min) respectively. For which the following expressions will be used respectively [5, 15]:

Figure 4 shows how to solve using General Methods using the counting of squares technique in a practical way. Also, it can be solved using numerical techniques such as Simpson’s rule, the rectangular rule, or the trapezoidal rule. The EVATMi-ZA v 1.0 software can solve the General methods using numerical techniques (rectangular, trapezoidal and/or Simpson) [15].

## 5. Calculation and prediction of heat treatment by Ball’s method

Charles Olin Ball developed and published his Formula Method in 1923 [84, 85, 86, 87, 88, 89, 90]. Olin Ball had already participated in research with Willard Dell Bigelow in 1920 [86]. The success of the Ball’s Formula Method is that it appears in a Bulletin that goes directly to the canning industry [91]. Ball uses a hyperbola to represent the curvilinear part at the beginning of cooling. Ball does not use a hyperbolic function [91, 92, 93]. Ball’s Formula Method is the favorite of the food industry. Ball’s Formula Method is ninety-eight years old, it has crossed the threshold of time, although its handling is not well understood [91, 93]. Ball’s Formula Method uses the heat penetration factors of heating. The Formula Method has two variants, simple curve and broken heating curve [94, 95, 96]. Formula Methods, such as Ball’s Formula Method allow you to predict the F-value of the process, or calculate the process time. There are two cases to solve, or the time, or the F value. The Formula Methods are preferred to simulate or predict the process time, knowing the heat penetration parameters [97, 98]. The EVATMi-ZA v 1.0 software can solve time or F-value cases using Ball’s Formula Method [99, 100].

## 6. Heat treatment modeling and simulation

Although heat treatments are of utmost importance due to their role in food preservation and also because they confer specific characteristics to food [101], the heat used during the process causes the degradation of nutrients, significantly affecting their quality; therefore, it is essential to minimize such damage, but without affecting the desired sterility of the products. For this purpose, it is necessary to develop a heat treatment that involves precise operating conditions in terms of temperature and time, achieving a minimal but efficient process [102], which guarantees optimum food quality [103]. Although currently it is still a challenge, thanks to technological advances, there are mathematical modeling and computer simulation techniques [104] that allow predicting the quality of food during processing and storage, in addition to providing the opportunity to optimize the process [105]. To achieve an ideal design, it is essential to have knowledge of the transport phenomena [106], such as mass, heat (by conduction, convection and radiation) and momentum, involved in the process [107], principles such as, for example, for solid foods, heat and moisture transfer, which are generally modeled by Fourier’s and Fick’s law, respectively [108] and for fluids, the continuity and Navier–Stokes Equations [109]. Likewise, the other physical mechanisms involved in the respective thermal process must be understood in order to achieve better results.

As it is known, preventing the deterioration of the organoleptic and nutritional characteristics of food [110], improves food safety, an important objective in the industry [108] and which is difficult to fulfill, due to the complex and dynamic nature of food [111] and thermal processing, requiring knowledge not only in engineering, but also in chemistry and microbiology [103]; therefore, as mentioned, numerical solutions are required [101] that, unlike traditional analytics, allow a fast and intelligent management of the large database obtained [112], helping to estimate the behavior of the food during thermal processing. It is necessary to mention that the pioneering study on the subject was by Datta & Teixeira [113], who performed a numerical modeling of the natural convection heating process of a liquid food packaged in cylindrical cans, successfully predicting the thermal (TP) and velocity (VP) profiles [114, 115].

By predicting and optimizing the process, modeling also helps to reduce time and costs, due to the reduction of experiments [116], which are very high under normal conditions [117], having as a disadvantage the obtaining of results in long periods [118]. Basically, one could, for example, after determining the effect of pasteurization temperature on the microbial load in different areas of a food, generate a mathematical model to help predict what the microbial spoilage would be if the processing temperature increases, without neglecting its influence on food quality. Likewise, a correct modeling enhanced with simulation, it would be possible to experiment with different changes in the variables, besides acquiring other advantages such as having control, and a broad and concise vision of the process [119].

For the execution of the computational techniques, first of all, the transfer phenomena that govern the thermal process, mainly heat, are represented by partial differential equations (PDE) [120] to be subsequently converted into a discrete model [107], which will be solved with some numerical method, such as finite differences, finite element and finite volume [108] or also called computational fluid dynamics (CFD) which is the most used [121], since it allows effectively designing a process or optimizing an existing one [122], through the development of three-dimensional models of the system and a numerical solution that describes it with high accuracy and realism. Similarly, it should be noted that, thanks to artificial intelligence, there are other modeling and optimization techniques, such as artificial neural networks and genetic algorithms, which are based on human intelligence and evolution, respectively [103].

CFD has been used since the 1950s, and has developed rapidly up to the present [117], since it is characterized by providing, through numerical algorithms, an easy resolution of the multiple physical phenomena involved in the process [120], which, in addition to heat, mass and momentum transfer (or fluid mechanics), also includes phase changes and chemical reactions [123]. Regarding thermal processing of canned foods, in which thermal processing is more difficult, because the temperature change is affected by the complex characteristics of the product [124], but also, the shape [125], type, size and orientation of the package [126]. CFD has been widely employed to solve challenges such as TP and VP monitoring [109], determination of the slowest heating zone (SHZ), slowest cooling zone (SCZ) [118] and even the kinetics of microbial inactivation and nutrient degradation. Specifically, in addition to sterilization [119] and pasteurization [127], it has covered a wide range of thermal treatments such as cooking [101] baking, drying [103] and cooling [128], and there is even information on its use in non-thermal processes such as microwave heating, ohmic heating, among others, which confirms its feasibility, versatility and suitability for food processing.

Since the since the development of CFD, there have been several commercial software, having in the early 1970s, a great boom and continuous improvement until today [127], emphasizing greater ease of use [129]. Of the extensive list of computer codes, some are FIDAP [116], CFX, FLUENT, PHOENICS [10], ANSYS, ANDINA-F, CFD++ [120], FLOW-3D, STAR-CD, CFD-ACE+ [128] and MSC Marc [105], of which most are still operational or have had some changes; for example, FLUENT and CFX are currently owned by ANSYS inc [129, 130], a leading developer of advanced engineering software. ANSYS offers several types of analysis and concerning heat treatments, it includes the three forms of heat transfer, phase change, internal heat source, contact thermal resistance, among other evaluations [131]. It is based on the creation of a geometry, which is divided into a finite number of units to form a computational geometry, then the governing PDEs are discretized, solved with numerical methods [122] and finally, the results are interpreted by the analyst. CFD simulation with ANSYS, has been applied to different packaged products such as in the pasteurization of beer [102] and water [115], in solid–liquid mixtures such as peas in water [132] and carrot-orange soup [133], food models such as waxy corn starch [126] and sucrose solution [134], in potato refrigeration [135], and even in the improvement of equipment processing parameters, such as in those of an industrial meat dryer [136] and a hydrofluidization freezing chamber [137]. There are also studies on the use of other software in solving the equations of energy, mass and moment, to determine the thermal behavior. A research deals with the effect of using 3.5% cornstarch packaging with an immobile can and rotating continuously at 146 rpm, using FIDAP 7.6 as software [138]. Furthermore, the same authors carried out a similar experiment, but evaluating the effect of intermittent axial agitation (0–146 rpm), and two retort temperatures (111 and 131°C) [139]. In another study, LabVIEW 8.5 was used to compare freezing results of guava pulp packed in stacked boxes, buckets, and unstacked drums, 34, 20, and 200 L, respectively [140].

## 7. Optimization of heat treatment

Until now, process optimization is essential to determine the best parameters that help to obtain the ideal results, in less time and with a significant reduction in costs. Considering the food industry, this task is much more difficult since there are multiple variables that intervene in the quality of the product [141] or process. Likewise, if it focuses mainly on the thermal processing of packaged foods and its importance in food safety, its optimization and especially its control are a challenge [142], due to the excessive use of high temperatures and for prolonged periods of time, and for Therefore, the improvement of the treatment conditions is essential to maintain the maximum characteristics of the food [143] and, consequently, a better acceptance by the consumer.

Regarding modeling and simulation, optimization, being related, for its application requires computational modeling and prediction techniques and that, due to advances in hardware, software and engineering related to processing thermal, it is becoming easier and faster to find the best solution [144]. In addition, one must have knowledge of heat transfer, quality change and microbial reduction, the three axes on which heat treatment is based.

Some techniques are the parametrization of the control vector, the principle of the continuous minimum, the super-simple optimization, the dynamic optimization, the neural network [145], the genetic algorithms, the simulated annealing of multiple initiation, among others. It should be noted that local optimization techniques have been used for thermal processing, which are the oldest and are hardly used, and global optimization techniques that are becoming increasingly popular [146]. This is due to the fact that, with the traditional ones, only the influence of a factor (independent variable) on a response (dependent variable) could be evaluated, therefore, as a general result of the processing was not obtained, the effect that the other variables had. This is problematic considering the complexity of the food, its dynamics [147] and also the characteristics of the container [145], including all the changes caused during heat treatment. For this, in contrast, global techniques [143], such as TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution), focus on multiobjective optimization. In an investigation, it was applied in pressure pasteurization of green soybean tofu, managing to optimize the process with a thermal denaturation of 85°C and 10 min, and a high pressure homogenization of 80 MPa, for 4 cycles, achieving an increase in hardness, capacity of retention of water, proteins, fat and yield, in 155.7, 34.48, 30.31, 29.11 and 21.42%, respectively [148].

## 8. Conclusions

In this chapter we explore general and technical aspects of the heat treatment of canned foods, which become the basis or foundation. Heat penetration studies are the requirement for evaluation of heat treatment either by the General Method or by the Ball’s Formula Method. Finally, in the final part, we review the modeling and simulation of the heat treatment, in order to achieve the optimization of the heat treatment. Thanks to the computational advances, it has been possible to improve the optimization techniques and even more the global ones, which are ideal to face the complexity of the thermal processing of packaged foods; however, there are still certain limitations such as the relative delay in executing the experimental design, due to the number of dependent and independent variables, with their respective levels (values) and replicas (repetitions).

## References

- 1.
Ling B, Tang J, Kong F, Mitcham EJ, Wang S. Kinetics of food quality changes during thermal processing: A review. Food and Bioprocess Technology. 2014; 8(2), 343–358. DOI:10.1007/s11947-014-1398-3 - 2.
Tucker GS, Featherstone S, Miranda-Zamora WR. Fundamentos del procesamiento térmico de alimentos. Madrid: AMV; 2020. 516 p - 3.
van Boekel M, Fogliano V, Pellegrini N, Stanton C, Scholz G, Lalljie S, Somoza V, Knorr D, Jasti PR, Eisenbrand G. A review on the beneficial aspects of food processing. Molecular Nutrition & Food Research. 2010; 54(9), 1215–1247. DOI:10.1002/mnfr.200900608 - 4.
Stier RF. Technical and quality management of canning. Swainson’s Handbook of Technical and Quality Management for the Food Manufacturing Sector. 2019; 505–527. DOI:10.1016/b978-1-78242-275-4.00020-4 - 5.
Pillai SD, Shayanfar S. Aseptic packaging of foods and its combination with electron beam processing. Electron Beam Pasteurization and Complementary Food Processing Technologies. 2015; 83–93. DOI:10.1533/9781782421085.2.83 - 6.
Hayakawa K, Ball CO. Charts for calculating average temperature of thermally conductive food in a cylindrical can during heat processing. Canadian Institute of Food Technology Journal. 1969; 2(1), 12–19. DOI:10.1016/s0008-3860(69)74336-7 - 7.
Sablani S., Shayya WH. Computerization of Stumbo’s method of thermal process calculations using neural networks. Journal of Food Engineering. 2001; 47(3), 233–240. DOI:10.1016/s0260-8774(00)00121-7 - 8.
Serment-Moreno V, Welti-Chanes J. Sterilization of foods. Encyclopedia of Food and Health. 2016; 175–180. DOI:10.1016/b978-0-12-384947-2.00663-2 - 9.
Afaghi M, Ramaswamy, HS, Prasher SO. Thermal process calculations using artificial neural network models. Food Research International. 2001; 34(1), 55–65. DOI:10.1016/s0963-9969(00)00132-0 - 10.
Mittal GS, Zhang J. Prediction of food thermal process evaluation parameters using neural networks. International Journal of Food Microbiology. 2002; 79(3), 153–159. DOI:10.1016/s0168-1605(02)00109-5 - 11.
Noronha J, Hendrickx M, Van Loey A, Tobback P. New semi-empirical approach to handle time-variable boundary conditions during sterilisation of non-conductive heating foods. Journal of Food Engineering. 1995; 24(2), 249–268. DOI:10.1016/0260-8774(94)p2646-m - 12.
Hayakawa K, Giannoni-Succar EB, Huang F, Zhou L. Use of the empirical temperature response function for modified Duhamel’s theorem application. Journal of Food Engineering. 1997; 34(3), 331–353. DOI:10.1016/s0260-8774(97)00084-8 - 13.
Rattan NS. Heating behavior and quality changes in canned potatoes subjected to agitation processing [thesis]. Montreal, Canada: McGill University; 2012 - 14.
Stoforos NG. Thermal process design. Food Control. 1995; 6(2), 81–94. DOI:10.1016/0956-7135(95)98911-j - 15.
Miranda-Zamora WR, Teixeira AA. Principios matemáticos del proceso térmico de alimentos. Madrid: AMV; 2012. 560 p - 16.
Heldman DR, Hartel RW. Principles of food processing. Gaithersburg, Maryland: Aspen Publishers, Inc; 1997. 288 - 17.
Friso D. A new mathematical model for food thermal process prediction. Modelling and Simulation in Engineering. 2013; 1–8. DOI:10.1155/2013/569473 - 18.
Simpson R, Almonacid S, Teixeira A. Bigelow’s General method revisited: Development of a New Calculation Technique. Journal of Food Science. 2003; 68(4), 1324–1333. DOI:10.1111/j.1365-2621.2003.tb09646.x - 19.
Körmendy L, Zsarnóczay G, Mihályi V. A new, modified acid phosphatase assay for determining the extent of heat treatment in canned hams. Food Chemistry. 1992; 44(5), 367–375. DOI:10.1016/0308-8146(92)90270-c - 20.
Simpson R, Figueroa I, Teixeira A. Optimum on-line correction of process deviations in batch retorts through simulation. Food Control. 2006; 17(8), 665–675. DOI:10.1016/j.foodcont.2005.06.004 - 21.
Miranda Zamora WR, Sanchez Chero MJ, Sanchez Chero JA. Software for the determination of the time and the F value in the thermal processing of packaged foods using the Modified Ball Method. In: Ahram T., Karwowski W., Vergnano A., Leali F., Taiar R. (eds) Intelligent Human Systems Integration 2020. IHSI 2020. Advances in Intelligent Systems and Computing. 2020; vol 1131. Springer, Cham. DOI:10.1007/978-3-030-39512-4_78 - 22.
Zamora WRM, Villarreyes SSC, Povis NLL, More LAV, Chero MJS, Panca CMA, Morales MVS. A new mathematical solution for packaged food thermal processing. In: Mrugalska B., Trzcielinski S., Karwowski W., Di Nicolantonio M., Rossi E. (eds) Advances in Manufacturing, Production Management and Process Control. AHFE 2020. Advances in Intelligent Systems and Computing. 2020; vol 1216. Springer, Cham. DOI:10.1007/978-3-030-51981-0_49 - 23.
Zamora WRM, Chero MJS, Timaná-Alvarez M, Seminario-Morales V, Niño-Carmona C, Leyva N, More LAV, Ticona-Carrizales L, Ygnacio A. Program in Visual Basic Language: A Simplified Procedure for Thermal Treatment Evaluation of Packaged Foods. In: Russo D., Ahram T., Karwowski W., Di Bucchianico G., Taiar R. (eds) Intelligent Human Systems Integration 2021. IHSI 2021. Advances in Intelligent Systems and Computing. 2021; vol 1322. Springer, Cham. DOI:10.1007/978-3-030-68017-6_71 - 24.
Özişik MN, Orlande HRB, Colaço MJ, Cotta RM. Finite difference methods in heat transfer. 2nd Edition. Boca Raton, FL: CRC Press; 2017. 600 - 25.
Welt BA, Teixeira AA, Chau KV, Balaban MO, Hintenlang DE. Explicit finite difference methods for heat transfer simulation and thermal process design. Journal of Food Science. 1997; 62(2), 230–236. DOI:10.1111/j.1365-2621.1997.tb03974.x - 26.
Gosz MR. Finite Element Method. Boca Raton, FL: CRC Press; 2006. 400 - 27.
Banga JR, Alonso AA, Gallardo JM, Perez-Martin RI. Mathematical modelling and simulation of the thermal processing of anisotropic and non-homogeneous conduction-heated canned foods: Application to canned tuna. Journal of Food Engineering. 1993; 18(4), 369–387. DOI:10.1016/0260-8774(93)90053-m - 28.
Tucker GS. Development and use of numerical techniques for improved thermal process calculations and control. Food Control. 1991; 2(1), 15–19. DOI:10.1016/0956-7135(91)90113-b - 29.
Teixeira AA, Dixon JR, Zabradnik JW, Zinsmeister GE. Computer optimization of nutrient retention in the thermal processing of conduction heated foods. Food Techology. 1969; 23, 137–142 - 30.
Sekhon AS, Singh A, Michael M. Short communication: Decimal log reductions of Salmonella Senftenberg 775 W and other Salmonella serovars in nonfat milk and powder. Journal of Dairy Science. 2020; 103, 8, 6894–6899. DOI:10.3168/jds.2019-17844 - 31.
Berk Z. Thermal processing. Food Process Engineering and Technology. 2018; 399–420. DOI:10.1016/b978-0-12-812018-7.00017-8 - 32.
Sant’Ana AS, Rosenthal A, Massaguer PR. Heat resistance and the effects of continuous pasteurization on the inactivation of Byssochlamys fulva ascospores in clarified apple juice. Journal of Applied Microbiology. 2009; 107(1), 197–209. DOI:10.1111/j.1365-2672.2009.04195.x - 33.
Rachon G. Survival of pathogens in low moisture foods [thesis]. Whiteknights, United Kingdom: University of Reading; 2017 - 34.
Tucker G, Featherstone S. Essentials of thermal processing. Second edition. Chichester, UK: Wiley-Blackwell; 2021. 352 - 35.
Diao MM, André S, Membré J-M. Meta-analysis of D-values of proteolytic Clostridium botulinum and its surrogate strainClostridium sporogenes PA 3679. International Journal of Food Microbiology. 2014; 174, 23–30. DOI:10.1016/j.ijfoodmicro.2013.12.029 - 36.
Rosnes JT, Fernandez PS, Periago PM, Shara T. Microorganisms of relevance in thermally processed foods. In: Valdramidis, V., Van Impe, J.F.M. (Eds.), Progress on Quantitative Approaches of Thermal Food Processing. Nova Science Publishers, New York; 2012. p. 1–37 - 37.
Condón S, Arrizubieta MJ, Sala FJ. Microbial heat resistance determinations by the multipoint system with the thermoresistometer TR-SC Improvement of this methodology. Journal of Microbiological Methods. 1993; 18(4), 357–366. DOI:10.1016/0167-7012(93)90017-c - 38.
André S, Leguerinel I, Palop A, Desriac N, Planchon S, Mafart P. Convergence of Bigelow and Arrhenius models over a wide range of heating temperatures. International Journal of Food Microbiology. 2019; 291, 173–180. DOI:10.1016/j.ijfoodmicro.2018.11.019 - 39.
Garre A, González-Tejedor GA, Aznar A, Fernández PS, Egea JA. Mathematical modelling of the stress resistance induced in Listeria monocytogenes during dynamic, mild heat treatments. Food Microbiology. 2019; 84, 103238. DOI:10.1016/j.fm.2019.06.002 - 40.
Al Fata N, Georgé S, André S, Renard CMGC. Determination of reaction orders for ascorbic acid degradation during sterilization using a new experimental device: The thermoresistometer Mastia ®. LWT - Food Science and Technology. 2017; 85, 487–492. DOI:10.1016/j.lwt.2016.08.043 - 41.
Blasco R, Esteve MJ, Frígola A, Rodrigo M. Ascorbic acid degradation kinetics in mushrooms in a high-temperature short-time process controlled by a thermoresistometer. LWT - Food Science and Technology. 2004; 37(2), 171–175. DOI:10.1016/j.lwt.2003.08.003 - 42.
Al Fata N, Georgé S, Dlalah N, Renard CMGC. Influence of partial pressure of oxygen on ascorbic acid degradation at canning temperature. Innovative Food Science & Emerging Technologies. 2018; 49, 215–221. DOI:10.1016/j.ifset.2017.11.007 - 43.
Gabriel AA, Ubana MA. Decimal reduction times of Salmonella Typhimurium in guinataang kuhol: An indigenous Filipino dish. LWT - Food Science and Technology. 2007; 40(6), 1108–1111. DOI:10.1016/j.lwt.2006.06.003 - 44.
Membré J-M, Diao M, Thorin C, Cordier G, Zuber F, André S. Risk assessment of proteolytic Clostridium botulinum in canned foie gras. International Journal of Food Microbiology. 2015; 210, 62–72. DOI:10.1016/j.ijfoodmicro.2015.06.002 - 45.
Wei X, Lau SK, Chaves BD, Danao M-GC, Agarwal S, Subbiah J. Effect of water activity on the thermal inactivation kinetics of Salmonella in milk powders. Journal of Dairy Science. 2020; 103, 8, 6904–6917. DOI:10.3168/jds.2020-18298 - 46.
Mulla R, Dunnill CW. Single material thermocouples from graphite traces: Fabricating extremely simple and low cost thermal sensors. Carbon Trends. 2021; 4, 100077. DOI:10.1016/j.cartre.2021.100077 - 47.
Fryer PJ, Simmons MJH, Cox PW, Mehauden K, Hansriwijit S, Challou F, Bakalis S. Temperature Integrators as tools to validate thermal processes in food manufacturing. Procedia Food Science. 2011; 1, 1272–1277. DOI:10.1016/j.profoo.2011.09.188 - 48.
Tarzan-Lorente M, Ceravalls J, Bosch J, Cama JMG, Pardo A. Electronic system for controlling the food cooking process. Procedia Chemistry. 2009; 1(1), 489–492. DOI:10.1016/j.proche.2009.07.122 - 49.
Gil AG, Ochoa González OA, Cardona Sepúlveda LF, Alvarado Torres PN. Venting stage experimental study of food sterilization process in a vertical retort using temperature distribution tests and energy balances. Case Studies in Thermal Engineering. 2020; 100736. DOI:10.1016/j.csite.2020.100736 - 50.
Sullivan JJ. Wireless data loggers to study heat penetration in retorted foods. In-Pack Processed Foods. 2008; 116–130. DOI:10.1533/9781845694692.2.116 - 51.
Stumbo CR. Thermobacteriology in food processing. Second edition. New York: Academic Press; 1973. 329 - 52.
Etzel MR, Willmore P, Ingham BH. Heat penetration and thermocouple location in home canning. Food Science & Nutrition. 2014; 3(1), 25–31. DOI:10.1002/fsn3.185 - 53.
Ranganathan K, Rangaswamy S, Subramanian V, Shanmugam N. Modelling of drying kinetics and heat penetration studies on carrot. International Journal of Engineering and Technical Research. 2015; 3(5), 371–376 - 54.
Awuah GB, Khurana A, Weddig LM, Balestrini CG. A comparative study of heat penetration data using remote sensors and needle or rod-in-tube thermocouples. Journal of Food Process Engineering. 2007; 30(4), 458–471. DOI:10.1111/j.1745-4530.2007.00106.x - 55.
Smout C, Ávila I, Van Loey AML, Hendrickx, MEG, Silva C. Influence of rotational speed on the statistical variability of heat penetration parameters and on the non-uniformity of lethality in retort processing. Journal of Food Engineering. 2000; 45(2), 93–102. DOI:10.1016/s0260-8774(00)00045-5 - 56.
Simpson R, Almonacid S, Nuñez H, Urtubia A, Teixeira AA. Is there a need for the come-up time correction factor in Ball’s Formula Method? A critical analysis. Food Engineering Reviews. 2012; 4(2), 107–113. DOI:10.1007/s12393-012-9049-9 - 57.
Radrigan R. Computer simulation of thermal processing for food. Heat Transfer Phenomena and Applications. 2012; 183–202.DOI:10.5772/51815 - 58.
Dixon WR, Watts EG, King JA, Fu X, Wicker L. Shelf-stable sustainable shrimp thermally processed with reciprocal agitation. Frontiers in Sustainable Food Systems. 2020; 4, 1–12 DOI:10.3389/fsufs.2020.569790 - 59.
Adepoju MA, Omitoyin BO, Mohan CO, Zynudheen AA. Heat penetration attributes of milkfish (Chanos chanos) thermal processed in flexible pouches: a comparative study between steam application and water immersion. Food Science & Nutrition. 2016; 5(3), 521–524. DOI:10.1002/fsn3.426 - 60.
Berry MR. Prediction of Come-Up time correction factors for batch-type agitating and still retorts and the influence on thermal process calculations. Journal of Food Science. 1983; 48(4), 1293–1299. DOI:10.1111/j.1365-2621.1983.tb09214.x - 61.
Datta AK. On the theoretical basis of the asymptotic semilogarithmic heat penetration curves used in food processing. Journal of Food Engineering. 1990; 12(3), 177–190. DOI:10.1016/0260-8774(90)90009-w - 62.
Körmendy I, Körmendy L. Considerations for calculating heat inactivation processes when semilogarithmic thermal inactivation models are non-linear. Journal of Food Engineering. 1997; 34(1), 33–40. DOI:10.1016/s0260-8774(97)00071-x - 63.
Körmendy I, Körmendy L, Ferenczy A. Thermal inactivation kinetics of mixed microbial populations. A hypothesis paper. Journal of Food Engineering. 1998; 38(4), 439–453. DOI:10.1016/s0260-8774(98)00119-8 - 64.
Downing DL. Heat penetration determinations and thermal process calculations. A Complete Course in Canning and Related Processes. 1996; 39–102. DOI:10.1533/9781845696207.39 - 65.
Reynaga W. Estudio del tratamiento térmico de enlatado de pechuga de pollo ( Gallus gallus ) en trozos y desmenuzado [thesis]. La Molina, Lima: Universidad Nacional Agraria La Molina; 2014 - 66.
Yang WH, Rao MA. Numerical study of parameters affecting broken heating curve. Journal of Food Engineering. 1998; 37(1), 43–61. doi:10.1016/s0260-8774(98)00070-3 - 67.
Berry MR, Bush RC. Establishing thermal processes for products with broken-heating curves from data taken at other retort and initial temperatures. Journal of Food Science. 1987; 52(4), 958–961. DOI:10.1111/j.1365-2621.1987.tb14252.x - 68.
Denys S, Noronha J, Stoforos NG, Hendrickx M, Tobback P. Evaluation of process deviations, consisting of drops in rotational speed, during thermal processing of foods in rotary water cascading retorts. Journal of Food Engineering. 1996; 30(3–4), 327–338. DOI:10.1016/s0260-8774(96)00057-x - 69.
Wiese KL, Wiese, KF. A comparison of numerical techniques to calculate broken line heating factors of a thermal process. Journal of Food Processing and Preservation. 1992; 16(5), 301–312. DOI:10.1111/j.1745-4549.1992.tb00211.x - 70.
Llave YA, Hagiwara T, Sakiyama T. Artificial neural network model for prediction of cold spot temperature in retort sterilization of starch-based foods. Journal of Food Engineering. 2012; 109(3), 553–560. DOI:10.1016/j.jfoodeng.2011.10.024 - 71.
Fellows PJ. Heat sterilisation. Food Processing Technology. 2017; 581–622. DOI:10.1016/b978-0-08-100522-4.00012-2 - 72.
Kramer A, Twigg BA. Principles and instrumentation for the physical measurement of food quality with special reference to fruit and vegetable products. Advances in Food Research. 1960; 9, 153–220. DOI:10.1016/s0065-2628(08)60276-1 - 73.
Stumbo CR. The General Method. Thermobacteriology in Food Processing. 1973; 143–151. DOI:10.1016/b978-0-12-675352-3.50019-x - 74.
Biran A. Geometric properties of areas and volumes. Geometry for Naval Architects. 2019; 121–194. DOI:10.1016/b978-0-08-100328-2.00012-2 - 75.
Rinaldi M, Chiavaro E, Massini R. Real-time estimation of slowest heating point temperature and residual cooking time by coupling multipoint temperature measurement and mathematical modelling: Application to meat cooking automation. Food Control. 2012; 23(2), 412–418. DOI:10.1016/j.foodcont.2011.08.009 - 76.
Huang XJ, Hanzawa T, Sakai N. The characteristics of the slowest heating point in a canned food in oil. Nippon Shokuhin Kogyo Gakkaishi. 1992; 39(1), 1–7. DOI:10.3136/nskkk1962.39.1 - 77.
Hanzawa T, Wang QH, Suzuki M, Sakai N. Numerical analysis of slowest heating or cooling point in a canned food in oil. Journal of Chemical Engineering of Japan. 1998; 31(3), 451–455.DOI:10.1252/jcej.31.451 - 78.
Wang Q-Z, Hanzawa T, Sakai N. Estimating heating time for sterilizing process in a canned liquid foods with particles. Nippon Shokuhin Kagaku Kogaku Kaishi. 1998; 45(11), 676–682. DOI:10.3136/nskkk.45.676 - 79.
Assan MYA, Watanabe H, Mihori T. Temperature distribution at the surface of cans in an industrial scale static retort during saturated steam sterilization. Food Science and Technology Research. 2000; 6(3), 196–200. DOI:10.3136/fstr.6.196 - 80.
Yasui T, Esselen WB, Fukazawa T, Hashimoto Y. Processing studies on canned corned beef and canned luncheon meat. Agricultural and Biological Chemistry. 1961; 25(8), 632–636. DOI:10.1271/bbb1961.25.632 - 81.
Hayakawa K. Selective review of research results related to thermal process lethality estimation. Japan Journal of Food Engineering. 2001; 2(2), 47–52. DOI:10.11301/jsfe2000.2.47 - 82.
Yamamoto Y, Ono N, Higashi K, Yoshii H. Studies on growth inhibition of food spoilage microorganisms for low salt foods. Part VIII. Effects of adipic acid on growth and thermal resistance of spores of anaerobic sporeforming bacteria. Nippon Shokuhin Kogyo Gakkaishi. 1989; 36(7), 551–556. DOI:10.3136/nskkk1962.36.7_551 - 83.
Nakae T, Nakanishi T. Application of steady state conduction system to microbiology Part V. Journal of the Agricultural Chemical Society of Japan. 1967; 41(9), 465–469. DOI:10.1271/nogeikagaku1924.41.9_465 - 84.
Gould WA. Understanding our past. Fundamentals of Food Processing and Technology. 1997; 9–20. DOI:10.1533/9781845696092.9 - 85.
Robertson GL. History of food packaging. Reference Module in Food Science. 2019; 1–49. DOI:10.1016/b978-0-08-100596-5.22535-3 - 86.
Hayakawa K, Ball CO. A note on theoretical heating curve of a cylindrical can of thermally conductive food. Canadian Institute of Food Technology Journal. 1968; 1(2), 54–60. DOI:10.1016/s0008-3860(68)74464-0 - 87.
Bermudez A, Martinez A. A state constrained optimal control problem related to the sterilization of canned foods. Automatica. 1994; 30(2), 319–329. DOI:10.1016/0005-1098(94)90033-7 - 88.
Heldman DR. Introduction. Food Preservation Process Design. 2011; 1–18. DOI:10.1016/b978-0-12-372486-1.00001-4 - 89.
Mitchell EL. A review of aseptic processing. Advances in Food Research. 1988; 1–37. DOI:10.1016/s0065-2628(08)60284-0 - 90.
Mohamed IO. Computer simulation of food sterilization using an alternating direction implicit finite difference method. Journal of Food Engineering. 2003; 60(3), 301–306. DOI:10.1016/s0260-8774(03)00051-7 - 91.
Miranda-Zamora WR, Ludeña AL, Tapia DA, Bazán JF. Herramientas computacionales aplicadas a la evaluación de tratamientos térmicos de los alimentos envasados usando el método de Ball. Piura: UNP; 2010. 94 - 92.
Miranda WR. Note: hyperbolic function or equation of the hyperbola? Research, March 2016, 11. DOI:10.13140/RG.2.1.1239.5287 - 93.
Miranda-Zamora WR, Heldman DR. Diseño de procesos térmicos y alta presión de alimentos. Madrid: AMV; 2018. 634 p - 94.
Miranda-Zamora WR, Tucker GS. Procedimientos del tratamiento térmico de alimentos. Madrid: AMV; 2017. 290 p - 95.
Miranda-Zamora WR. Manual de tratamiento térmico y envasado de alimentos. Madrid: AMV; 2017. 622 p - 96.
Miranda-Zamora WR, Stoforos NG. Procesamiento térmico de alimentos teoría, práctica y cálculos. Madrid: AMV; 2016. 330 p - 97.
Miranda-Zamora WR, Vignolo TG, Leyva NL. Ingeniería del tratamiento térmico de alimentos. Piura: UNP; 2012. 268 p - 98.
Hayakawa K. Selective review of research results related to thermal process lethality estimation I. Lethality estimation and heat transfer. Japan Journal of Food Engineering. 2001; 2(1), 1–9. DOI:10.11301/jsfe2000.2.1 - 99.
Ball CO, Olson FCW. Sterilization in food technology theory, practice, and calculations. New York: McGraw-Hill; 1957. 654 p - 100.
Ball CO. Mathematical solution of problems on thermal processing of canned food. Berkeley: University of California Press; 1928. 245 p - 101.
Trystram G. Modelling of food and food processes. Journal of Food Engineering. 2012;110:269-277. DOI: 10.1016/j.jfoodeng.2011.05.001 - 102.
Augusto PED, Pinheiro TF, Cristianini M. Using Computational Fluid-Dynamics (CFD) for the evaluation of beer pasteurization: effect of orientation of cans. Ciência e Tecnologia de Alimentos. 2010;30(4):980-986. DOI: 10.1590/S0101-20612010000400022 - 103.
Singh A, Singh AP, Ramaswamy HS. Computational techniques used in heat transfer studies on canned liquid-particulate mixtures. Trends in Food Science & Technology. 2015;43: 83-103. DOI: 10.1016/j.tifs.2015.02.001 - 104.
Lemus-Mondaca RA, Vega-Gálvez A, Moraga NO. Computational Simulation and Developments Applied to Food Thermal Processing. Food Engineering Reviews. 2011;3:121-135. DOI: 10.1007/s12393-011-9040-x - 105.
Martins RC. Simple finite volumes and finite elements procedures for food quality and safety simulations. Journal of Food Engineering. 2006;73:327-338. DOI: 10.1016/j.jfoodeng.2005.01.033 - 106.
Ho QT, Carmeliet J, Datta AK, Defraeye T, Delele MA, Herremans E, Opara L, Ramon H, Tijskens E, van der Sman R, Liedekerke PV, Verboven P, Nicolaï, BM. Multiscale modeling in food engineering. Journal of Food Engineering. 2013;114:289-291. DOI: 10.1016/j.jfoodeng.2012.08.019 - 107.
Erdogdu F, Sarghini F, Marra F. Mathematical Modeling for Virtualization in Food Processing. Food Engineering Reviews. 2017;9:295-313. DOI: 10.1007/s12393-017-9161-y - 108.
Wang L, Sun DW. Recent developments in numerical modelling of heating and cooling processes in the food industry—a review. Trends in Food Science & Technology. 2003; 14:408-423. DOI: 10.1016/S0924-2244(03)00151-1 - 109.
Augusto PED, Cristianini M. Numerical Simulation of Packed Liquid Food Thermal Process Using Computational Fluid Dynamics (CFD). International Journal of Food Engineering. 2011;7(4):16. DOI: 10.2202/1556-3758.2418´ - 110.
Norton T, Sun DW. Computational fluid dynamics (CFD) -an effective and efficient design and analysis tool for the food industry: A review. Trends in Food Science & Technology. 2006;17:600-620. DOI: 10.1016/j.tifs.2006.05.004 - 111.
Datta AK. Status of Physics-Based : Models in the Design of Food Products, Processes, and Equipment. Comprehensive Reviews in Food Science and Food Safety. 2008;7:121-129. DOI: 10.1111/j.1541-4337.2007.00030.x - 112.
Verboven P, Defraeye T, Datta AK, Nocolai B. Digital twins of food process operations: the next step for food process models? Current Opinion in Food Science. 2020;35:79-87. DOI: 10.1016/j.cofs.2020.03.002 - 113.
Datta AK, Teixeira AA. Numerically predicted transient temperature and velocity profiles during natural convection heating of canned liquid foods. Journal of Food Science. 1988;53:191-195. DOI: 10.1111/j.1365-2621.1988.tb10206.x - 114.
Boz Z, Erdogdu Z. Evaluation of two-dimensional approach for computational modelling of heat and momentum transfer in liquid containing horizontal cans and experimental validation. Foods and Bioproducts Processing. 2013;91:37-45. DOI: 10.1016/j.fbp.2012.08.005 - 115.
Lee MG, Yoon WB. Developing an effective method to determine the deviation of F value upon the location of a still can during convection heating using CFD and subzones. Journal of Food Process Engineering. 2014;37:493-505. DOI: 10.1111/jfpe.12107 - 116.
Farazbakht F, Zamindar N, Hojjatoleslamy M, Toghraie D. Numerical simulation of transient heat transfer for tomato paste in semi rigid aluminum container. Journal of Food Measurement and Characterization. 2017;11:479-487. DOI 10.1007/s11694-016-9415-z - 117.
Malekjani N, Jafari SM. Simulation of food drying processes by Computational Fluid Dynamics (CFD); recent advances and approaches. Trends in Food Science & Technology. 2018;78:206-223. DOI: 10.1016/j.tifs.2018.06.006 - 118.
Serami MS, Ramezan Y, Khashehchi M. CFD simulation and experimental validation of in-container thermal processing in Fesenjan stew. Food Science & Nutrition. 2020;9:1079-1087. DOI: 10.1002/fsn3.2083 - 119.
Fadiji T, Coetzee CJ, Berry TM, Ambaw A, Opara UL. The efficacy of finite element analysis (FEA) as a design tool for food packaging: A review. Biosystems Engineering. 2018;174:20-40. DOI: 10.1016/j.biosystemseng.2018.06.015 - 120.
Norton T, Tiwari B, Sun DW. Computational Fluid Dynamics in the Design and Analysis of Thermal Processes: A Review of Recent Advances. Critical Reviews in Food Science and Nutrition. 2013;53(3):251-275. DOI: 10.1080/10408398.2010.518256 - 121.
Park HWP, Yoon WB. Computational Fluid Dynamics (CFD) Modelling and Application for Sterilization of Foods: A Review. Processes. 2018;6:62. DOI: 10.3390/pr6060062 - 122.
Boz Z, Erdogdu F, Tutar M. Effects of mesh refinement, time step size and numerical scheme on the computational modeling of temperature evolution during natural-convection heating. Journal of Food Engineering. 2014;123:8-16. DOI: 10.1016/j.jfoodeng.2013.09.008 - 123.
Zhao CJ, Han JW, Yang XT, Qian JP, Fan BL. A review of computational fluid dynamics for forced-air cooling process. Applied Energy. 2016;168:314-331. DOI: 10.1016/j.apenergy.2016.01.101 - 124.
Erdogdu F, Karatas O, Sarghini F. A short update on heat transfer modelling for computational food processing in conventional and innovative processing. Current Opinion in Food Science. 2018;23:113-119. DOI: 10.1016/j.cofs.2018.10.003 - 125.
Shafiekhani S, Zamindar N, Hojatoleslami M, Toghraie D. Numerical simulation of transient temperature profiles for canned apple puree in semi-rigid aluminum based packaging during pasteurization. Journal of Food Science and Technology. 2016;53:2770-2778 - 126.
Rinaldi M, Malavasi M, Cordioli M, Barbanti D. Investigation of influence of container geometry and starch concentration on thermal treated in-package food models by means of Computational Fluid Dynamics (CFD). Food and Bioproducts Processing. 2018;108:1-11. DOI: 10.1016/j.fbp.2017.12.003 - 127.
Kuriakose R, Anandharamakrishnan C. Computational fluid dynamics (CFD) applications in spray drying of food products. Trends in Food Science & Technology. 2010;21:383-398. DOI: 10.1016/j.tifs.2010.04.009 - 128.
Xia B, Sun DW. Applications of computational fluid dynamics (CFD) in the food industry: a review. Computers and Electronic in Agriculture. 2002;34(1–3):5-24. DOI: 10.1016/S0168-1699(01)00177-6 - 129.
Nicolaï BM, Verboven P, Scheerlinck N. Modelling and simulation of thermal processes. In: Richardson P, editor. Thermal technologies in food processing. 1st ed. Cambridge: Woodhead Publishing; 2001. p. 91-112. DOI: 10.1533/9781855736610.2.91 - 130.
Lyczkowski WR. The Rise of the First Commercial CFD Codes: PHOENICS, FLUENT, FIDAP, CFX, FLOW-3D, and STAR-CD. In: Memoir P, editor. The History of Multiphase Science and Computational Fluid Dynamics. 1st ed. Cham: Springer;2018. P. 185-187. DOI: 10.1007/978-3-319-66502-3_14 - 131.
Li B, Kang Z, Ma H. Research on the Meat Food Vacuum Cooling Model based on ANSYS Simulation. Revista Ibérica de Sistemas e Tecnologias de Informação. 2016;E6: 184-196 - 132.
Kızıltas S, Erdogdu F, Palazoglu TK. Simulation of heat transfer for solid–liquid food mixtures in cans and model validation under pasteurization conditions. Journal of Food Engineering. 2010;97:449-456. DOI:10.1016/j.jfoodeng.2009.10.042 - 133.
Ghani AGA, Farid MM, Chen XD, Richards P. Thermal sterilization of canned food in a 3-D pouch using computational ¯uid dynamics. Journal of Food Engineering. 2001;48(2):147-156. DOI: 10.1016/S0260-8774(00)00150-3 - 134.
Siriwattanayotin S, Yoovidhya T, Meepadung T, Ruenglertpanyakul W: Simulation of sterilization of canned liquid food using sucrose degradation as an indicator. Journal of Food Engineering. 2006;73(4):307-312. DOI: 10.1016/j.jfoodeng.2004.08.008 - 135.
Chourasia MK, Goswaki TK. CFD simulation of effects of operating parameters and product on heat transfer and moisture loss in the stack of bagged potatoes. Journal of Food Engineering. 2007;80:947-960. DOI: 10.1016/j.jfoodeng.2006.07.015 - 136.
Mirade PS. Prediction of the air velocity field in modern meat dryers using unsteady computational fluid dynamics (CFD) models. Journal of Food Engineering. 2003;60:41-48. DOI: 10.1016/S0260-8774(03)00009-8 - 137.
Stebel M, Smolka J, Palacz M, Adamczyk W, Piechnik E. Numerical investigation of the fluid flow distribution for the hydrofluidisation food freezing method. International Journal of Thermal Sciences. 2020;151:106284. DOI: 10.1016/j.ijthermalsci.2020.106284 - 138.
Tattiyakul J, Rao MA, Datta AK. Simulation of heat transfer to a canned corn starch dispersion subjected to axial rotation. Chemical Engineering and Processing. 2001;40(4):391-399. DOI: 10.1016/S0255-2701(01)00116-7 - 139.
Tattiyakul J, Rao MA, Datta AK. Heat transfer to a canned corn starch dispersion under intermittent agitation. Journal of Food Engineering. 2002;54(4):321-329. DOI: 10.1016/S0260-8774(01)00218-7 - 140.
Okita WM, Reno MJ, Peres AP, Resende JV. Heat transfer computational fluid dynamics in the air blast freezing of guava pulp in large containers. Brazilian Journal of Chemical Engineering. 2013;30(4):811-824. DOI: 10.1590/S0104-66322013000400013 - 141.
Malekjani N, Jafari SM. Food process modeling and optimization by response surface methodology (RSM). In: Sevda S, Singh A, editors. Mathematical and Statistical Applications in Food Engineering. 1st ed. Florida: CRC Press; 2020. p. 181-203. DOI: 10.1201/9780429436963-13 - 142.
Simpson R, Ramirez C, Jiménez D, Almonacid S, Nuñez H, Angulo A: Simultaneous multi-product sterilization: Revisited, explored, and optimized. 2019;241:149-158. DOI: 10.1016/j.jfoodeng.2018.08.007 - 143.
Alonso AA, Pitarch JL, Antelo LT, Vilas C. Event-based dynamic optimization for food thermal processing: High-quality food production under raw material variability. Food and Bioproducts Processing. 2021;127:162-173. DOI: 10.1016/j.fbp.2021.02.013 - 144.
Abakarov A, Nuñez M. Thermal food processing optimization: Algorithms and software. Journal of Food Engineering. 2013;115(4):428-442. DOI: 10.1016/j.jfoodeng.2012.02.013 - 145.
Holdsworth SD, Simpson R. Thermal processing of packaged foods. 3rd edition. Cham: Springer; 2016. 516 p. DOI: 10.1007/978-3-319-24904-9 - 146.
Miri T, Tsoukala A, Bakalis S, Pistikopoulos EN, Rustem B, Fryer PJ. Global optimization of process conditions in batch thermal sterilization of food. Journal of Food Engineering. 2008;87(4):485-494. DOI: 10.1016/j.jfoodeng.2007.12.032 - 147.
Banga JR, Balsa-Canto E, Alonso AA. Quality and Safety Models and Optimization as Part of Computer-Integrated Manufacturing. Comprehensive Reviews in Food Science and Food Safety. 2008;7:168-174. DOI: 10.1111/j.1541-4337.2007.00023.x - 148.
Li J, Wang K, Gao Y, Ma C, Sun D, Hussain MA, Qayum A, Jiang Z, Hou J. Effect of thermal treatment and pressure on the characteristics of green soybean tofu and the optimization conditions of tofu processing by TOPSIS analysis. LWT – Food Science and Technology. 2021;136(1):110314. DOI: 10.1016/j.lwt.2020.110314