MODELING THERMODYNAMIC PROCESSES USING MATLAB PDE TOOLBOX FOR CREATING DIGITAL TWINS IN THE FOOD INDUSTRY

The article discusses an approach to modeling thermodynamic processes in food industry production systems using MATLAB PDE Toolbox. The main goal of the research is to create digital twins that allow simulating thermal processes and optimizing production operations. The work focuses on the application of heat equations taking into account the Neumann and Dirichlet boundary conditions, which ensures the accuracy and reliability of modeling. The results of computational experiments demonstrating dynamic changes in temperature fields in 2D space are presented. The main attention is paid to the influence of physical parameters such as thermal conductivity, density and specific heat capacity on temperature distribution. The obtained data can be used to improve energy efficiency and quality of production processes in the food industry.
As a result of the research, a model describing temperature fields was developed in the MATLAB PDE Toolbox. The developed model serves as a basis for further research in the field of digital twins and integration with industrial modeling tools such as SIEMENS NX, as well as PML platforms. During this study, various heat transfer coefficients and boundary conditions were tested, which made it possible to determine the optimal model parameters. The final result, presented at the end of the article, demonstrates a smooth and correct distribution of thermodynamic processes, confirming the effectiveness of the proposed approach. In the future, this approach can be used to create more complex virtual production systems that allow not only to analyze thermal processes, but also to develop intelligent heat treatment control systems, improving the adaptability and efficiency of technological processes.

1. Digital twins of food process operations: the next step for food process models? / P. Verboven et al // Current Opinion in Food Science. – 2020. – Vol. 35. – P. 79-87. (In English).

2. Huang Y. Implementation of Digital Twins in the Food Supply Chain / Y. Huang, Dr A. Ghadge, N. M Yates // A Review and Conceptual Framework. International Journal of Production Research. – 2023. – 28 p. https://doi.org/10.1080/00207543.2024.2305804. (In English).

3. Tukembaeva G.CH. Mdelirovanie uravnenii termodinamiki dinamicheskimi sistemami / G.CH. Tukembaeva, B.K. Temirov // Problemy avtomatiki i upravleniya. – 2023. – № 2. – S. 109-115. (In Russian).

4. Sidel'nikova N.A. Differentsial'nye uravneniya v chastnykh proizvodnykh pervogo poryadka: uchebnoe posobie / N.A. Sidel'nikova; Bashkirskii gosudarstvennyi universitet. – Ufa: RITS BaSHGU, 2020. (In Russian).

5. Nerobeev A.D. Metody Resheniya Uravnenii Teploprovodnosti / A.D. Nerobeev, O.D. Dyachkin // Tekhnologii fiziki, avtomatizatsii i informatiki. Aktual'nye issledovaniya v sovremennoi nauke. – 2020. – S. 50-51. (In Russian).

6. Mukhidova G.EH. Primenenie metoda konechnykh ehlementov k odnoi zadache teploperedachi / G.EH. Mukhidova // International Sonference on Learning and Teaching. – 2022. – T. 1, № 7. – S. 388-390. (In Russian).

7. Das S. An Introduction to Finite Element Analysis Using Matlab Tools. – Springer, 2023. (In English).

8. Arendt W. Dirichlet and Neumann boundary conditions: What is in between? / W. Arendt, M. Warma // Nonlinear Evolution Equations and Related Topics: Dedicated to Philippe Bénilan. – 2004. – R. 119-135. (In English).

9. Dehghan M. Parameter determination in a partial differential equation from the overspecified data / M. Dehghan // Mathematical and computer modelling. – 2005. – T. 41, № 2-3. – R. 196-213. (In English).

10. Cess R.D. The interaction of thermal radiation with conduction and convection heat transfer / R.D. Cess // Advances in heat transfer. – Elsevier, 1964. – T. 1. – R. 1-50. (In English).

11. Digital twin in a manufacturing integrated system: Siemens TIA and PLM case study / D.A. Guerra-Zubiaga et al // ASME International Mechanical Engineering Congress and Exposition. – American Society of Mechanical Engineers, 2019. – T. 59384. – R. V02BT02A008. (In English).