Comparison of efficiency between two different numerical modeling methods to predict tomato paste temperature during pasteurization process

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Dalvi Isfahan M.

Title

Comparison of efficiency between two different numerical modeling methods to predict tomato paste temperature during pasteurization process

Author(s)

Dalvi Isfahan M. | Issue Writer Certificate

Keywords

Finite element

pasteurization

finite difference

tomato paste

Abstract

Introduction: Tomato (Solanum lycopersicum) is the second most consumed vegetable next to potato, with an estimated world production of over 180 million tonnes per year. Iran has always been among the top tomato producing countries in the world due to the diverse topography and climactic conditions prevailing in different parts of Iran. tomato paste is the most important tomato product that is produced by removal of water content from tomato juice by evaporation and or thermal processing (Singh and Headman, 2014). Water removal from the juice would not only extend the shelf life of product but could also control its microbial growth and guarantee its safety. Conventional thermal processing (pasteurization and sterilization) is still widely used in the Iranian food industry though several emerging food preservation technologies have been developed (e. g., ohmic heating, microwave heating, and non-thermal processing techniques such as pulsed electric fields and highpressure processing). However, the challenges of accurately determining both optimal operating conditions and developing a control system for industrial pasteurization process to prevent either under-or over-processing are significant (Chen and Ramaswamy, 2007). Mathematical modeling and simulation are one of the most used methods to gain a better understanding of processes. Modeling can cost-effectively provide insights into complex processes, shorten the design cycle, and optimize the process as a function of various variables in shorter time. Different mathematical methods for solving heat conduction problems have been proposed, but numerical methods are more useful, especially when problems cannot be handled by exact analysis because of nonlinearities, complex geometries, and complicated boundary conditions (Incropera and De Witt, 1990). Among the numerical methods developed so far, finite difference and Finite element techniques have been widely used to analyze heat transfer phenomena in cylindrical cans of food. Many have attempted to develop mathematical models based on numerical methods for predicting temperatures in tomato products during thermal processing (Bichier et al., 1995), (Nicolai et al., 1998), (Tattiyakul et al., 2002) and (Plazl et al., 2006). Nonetheless, to the knowledge of authors data about thermal processing of tomato paste in Iran is scarce. In this study, the efficiency of two different modeling approaches (finite difference vs. Finite element) for predicting temperature of tomato paste during pasteurization process were compared. The model would contribute to energy consumption reduction during operations while producing high-quality products in a short time. Material and method: Experiments were run with batches of 400 g of tomato paste (pH of 4. 1 and 28° Brix) in cylindrical cans (211×400 inches). Hot water was used as the heating medium. The chemical analysis of tomato paste sample (Brix, pH salt, moisture, fat and protein) was performed in the first step and the thermal properties of the tomato paste product including thermal conductivity, specific heat and density were determined based on the sample chemical composition and structures model. Temperature changes at various positions in the container were checked with a data logger (Testo, Germany) coupled with computer and thermocouples type-K (at 2 min intervals). The cylindrical can was immersed in a vertical position in the water bath and the temperature recording was started. After finishing the heating time, the can was cooled in another water bath (20º C). The data were used to validate the developed model. In the next step, 2D heat transfer model was developed in a cylindrical can by using the numerical solution of the Fourier second law with two different methods; (1) finite difference (explicit scheme) and (2) Finite element methods. Computer simulation was done using MATLAB R2009a software (Math works, Inc., Natick, MA, USA) and COMSOL Multiphysic, Ver. 4. 0. To evaluate the best model, two criteria, coefficient of determination (R 2 ) and root mean squared error (RMSE) were used. Result and discussion: The results showed that, by placing the sample in the bath, the surface temperature rises rapidly, while the temperature in the center is much lower. In addition, as expected, increasing hot water temperature enhanced the heating rate considerably due to the larger temperature gradient between the center and surface of the can at the higher temperatures. The models were verified by comparing results with two analytical solutions and validated against experimental data. The statistical analysis results showed that the Finite element model (developed by COMSOL software) can more accurately predict temperature compared to the finite difference. The variation in the results could be due to the consideration of a layer of air-steam mixture on the top of the can (head space) in the Finite element method which increases the accuracy of the model in temperature prediction. After validation, the developed model was used to determine the cold spot location of the tomato paste can. In addition, results showed that the cold point was a stationary point and located at the radial center at a height of 60% of the can height from the bottom (Tattiyakul et al., 2002). Two simulations were conducted at two different head space volume (6 and 12% of total can height) to determine the importance of head space volume on cold point location. Results showed that there was no significant difference in the location and temperature of the cold spot in two simulations (Khakbaz Heshmati et al., 2014). Conclusion: In this study, the pasteurization process of tomato paste (Brix=28) was investigated by two different numerical methods (finite difference and Finite element). The results were compared with experimental data and it was found that the predicted temperature by Finite element model is more accurate than finite difference method. Moreover, we demonstrated that the slowest cooling point was located at a height of 60% of can height from the bottom which was in disagreement with others reporting geometric centre of cylinder being the coldest point of a solid product. The developed model can predict temperature in tomato paste with different degree of concentration (brix) or different thermal processing conditions. The model, with slight modifications, may be used to design and control industrial pasteurization for various solid products. In addition, the results of this study is expected to be a significant contribution for further optimization studies.

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APA: Copy

Dalvi Isfahan, M.. (2021). Comparison of efficiency between two different numerical modeling methods to predict tomato paste temperature during pasteurization process. JOURNAL OF FOOD RESEARCH (UNIVERSITY OF TABRIZ), 31(1 ), 83-94. SID. https://sid.ir/paper/960534/en

Vancouver: Copy

Dalvi Isfahan M.. Comparison of efficiency between two different numerical modeling methods to predict tomato paste temperature during pasteurization process. JOURNAL OF FOOD RESEARCH (UNIVERSITY OF TABRIZ)[Internet]. 2021;31(1 ):83-94. Available from: https://sid.ir/paper/960534/en

IEEE: Copy

M. Dalvi Isfahan, “Comparison of efficiency between two different numerical modeling methods to predict tomato paste temperature during pasteurization process,” JOURNAL OF FOOD RESEARCH (UNIVERSITY OF TABRIZ), vol. 31, no. 1 , pp. 83–94, 2021, [Online]. Available: https://sid.ir/paper/960534/en

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Scientific Information Database

ISSN: 2588-4824

Journal Paper

Comparison of efficiency between two different numerical modeling methods to predict tomato paste temperature during pasteurization process