ISSN 2074-9414 (Print),
ISSN 2313-1748 (Online)

Cooling Caramel in Ethyl Alcohol: Constructing a Mathematical Model

Abstract
Introduction. The process of air-cooling caramel remains one of the most complicated issues of contemporary food industry, since it is time-consuming and requires multi-level cooling units. Therefore, the development of an innovative method of cooling caramel in “cold” potable ethanol is an urgent task the modern food science has to solve. The method op-timizes and intensifies the technological process, as it reduces production areas by eliminating some technological stages and complex units of metal-intensive and energyintensive equipment. It gives caramel antiseptic properties and a perfectly smooth, shiny, and dry surface.
Study objects and methods. The research objective was to develop a fundamentally new and promising caramel technology. The experimental studies on the production and cooling were performed in a mixing and forming multi-unit with a high-performance cooling chamber. The chamber had functions of automatic measurements and control of the main parameters of the cooling process. The research used “cold” potable ethanol.
Results and discussion. The paper introduces a mathematical model of the process of cooling caramel in ethanol. It includes heat transfer processes in alcohol, in the caramel mass, and on their border. The model was based on equations of transient heat conduction in a sphere. The process of heat exchange with the environment, i.e. alcohol, was characterized by the coefficient of heat transfer from the sphere. The model parameters included dynamic viscosity, density, thermal conductivity coefficient, and specific heat capacity. Based on the experimental data, the parameters were ap-proximated as a function of temperature by a cubic polynomial.
Conclusion. The developed mathematical model made it possible to estimate the radial temperature distribution of caramel in the form of a sphere during its convective cooling in ethanol. The model also predicted the change in the average volume temperature of the caramel and energy costs depending on the cooling period, the flow speed of the ethanol, the thermophysical properties of the caramel and the cooling agent. The proposed mathematical model can be used to calculate the required consumption of ethanol for cooling and backwater of the caramel production line.
Keywords
Cooling, sweets, ethanol, heat exchange, mathematical modeling
REFERENCES
  1. Dejneka IG, Ripol-Saragosi TL, Bushkova GB. Automated production line of caramel with interbedded fillings. Scientific Works of NUFT. 2015;21(1):7–14. (In Russ.).
  2. Minifie B. Chocolate, cocoa and confectionery: science and technology. St. Petersburg: Professija; 2008. 816 p. (In Russ.).
  3. Nosenko SM, Chuvakhin SV. Oborudovanie konditerskogo proizvodstva XXI veka [Equipment for confectionery production of the XXI century]. Moscow: DeLi plyus; 2017. 332 p. (In Russ.).
  4. Hartel RW, von Elbe JH, Hofberger R. Confectionery science and technology. Cham: Springer; 2018. 536 p. DOI: https://doi.org/10.1007/978-3-319-61742-8.
  5. Dragilev AI, Marshalkin GA. Osnovy konditerskogo proizvodstva [Confectionery basics]. St. Petersburg: Lan; 2017. 532 p. (In Russ.).
  6. Jeffery MS. The technology of caramel and fudge. European Federation of Food Science and Technology; 2001. 110–113 p.
  7. Chung M-S, Ruan RR, Chen PL, Wang X. Physical and chemical properties of caramel systems. LWT – Food Science and Technology. 1999;32(3):162–166. DOI: https://doi.org/10.1006/fstl.1998.0521.
  8. Kasapis S, Sworn G. Separation of the variables of time and temperature in the mechanical properties of high sugar/ polysaccharide mixtures. Biopolymers. 2000;53(1):40–45. DOI: https://doi.org/10.1002/(SICI)1097-0282(200001)53:1<40::AIDBIP4>3.0.CO;2-N.
  9. Magomedov GO, Oleynikova AYa, Plotnikova IV, Brekhov AF. Tekhnologiya karameli [Caramel technology]. St. Petersburg: GIORD; 2008. 216 p. (In Russ.).
  10. Appolonskiy SM. Differentsialʹnye uravneniya matematicheskoy fizike v ehlektrotekhnike [Differential equations of mathematical physics in electrical engineering]. St. Petersburg: Piter; 2012. 352 p. (In Russ.).
  11. Rathore MM, Kapuno RR. Engineering heat transfer. Jones and Bartlett; 2011. 1178 p.
  12. Kartashov EhM, Kudinov VA. Analiticheskie metody teorii teploprovodnosti i ee prilozheniy [Analytical methods of the theory of heat conduction and its applications]. Moscow: LENAND; 2018. 1080 p. (In Russ.).
  13. Simakov NN. Calculation of the drag and heat transfer from a sphere in the gas flow in a cylindrical channel. Technical Physics. 2016;61(9):1312–1318. DOI: https://doi.org/10.1134/S1063784216090231.
  14. Ostrikov AN, Vasilenko VN, Frolova LN, Terekhina AV. Protsessy i apparaty. Raschet i proektirovanie apparatov dlya teplovykh i teplomassoobmennykh protsessov [Processes and equipment. Calculation and design of equipment for thermal and heatand-mass transfer processes]. St. Petersburg: Lan; 2018. 440 p. (In Russ.).
  15. Stabnikov VN, Royter IM, Protsyuk TB. Ehtilovyy spirt [Ethanol]. Moscow: Pishchevaya promysh-lennost; 1976. 272 p. (In Russ.).
  16. Safarov DT, Shakhverdiev AN. Investigation of the thermophysical properties of ethyl alcohol + water solutions. High Temperature. 2001;39(3):395–400. DOI: https://doi.org/10.1023/A:1017506524963.
  17. Miyazawa T, Kondo S, Suzuki T, Sato H. Specific heat capacity at constant pressure of ethanol by flow calorimetry. Journal of Chemical and Engineering Data. 2012;57(6):1700–1707. DOI: https://doi.org/10.1021/je2013473.
  18. Ahmadi P, Karim Nobakht BN, Chapoy A. Density, speed of sound, and other derived properties of ethanol at pressures up to 65 MPa. Journal of Chemical and Engineering Data. 2018;63(7):2486–2499. DOI: https://doi.org/10.1021/acs.jced.7b01018.
  19. Schroeder JA, Penoncello SG, Schroeder JS. A fundamental equation of state for ethanol. Journal of Physical and Chemical Reference Data. 2014;43(4). DOI: https://doi.org/10.1063/1.4895394.
  20. Dillon HE, Penoncello SG. A fundamental equation for calculation of the thermodynamic properties of ethanol. International Journal of Thermophysics. 2004;25(2):321–335. DOI: https://doi.org/10.1023/B:IJOT.0000028470.49774.14.
  21. Nedoshivin SV. The nonlinear regression analysis in statistical machine experiment. Izvestiya Tula State University. Technical sciences. 2014;(10–1):68–81. (In Russ.).
  22. Kaloshin YuA, Berezovskiy YuM, Vernyaeva LV. Fiziko-mekhanicheskie svoystva syrʹya i gotovoy produktsii [Physical and mechanical properties of raw materials and finished products]. Moscow: DeLi print; 2011. 175 p. (In Russ.).
  23. Dragilev AI, Rub MD. Sbornik zadach po raschetu tekhnologicheskogo oborudovaniya konditerskogo proizvodstva [Tasks for calculating the parameters of technological equipment for confectionery production]. Moscow: DeLi print; 2005. 243 p. (In Russ.).
  24. Chubik IA, Maslov AM. Spravochnik po teplofizicheskim kharakteristikam pishchevykh produktov i polufabrikatov [Handbook of thermophysical characteristics of food and semi-finished products]. Moscow: Pishchevaya promyshlennost; 1970. 184 p. (In Russ.).
  25. Antokolʹskaya MYa, Bronshteyn II, Martynov MI, Smirnov AF, Shklovskaya AE. Spravochnik po syrʹyu, polufabrikatam i gotovym izdeliyam konditerskogo proizvodstva [Reference book on raw materials, semi-finished products, and finished products of confectionery production]. Moscow: Pishchevaya promyshlennost; 1964. 231 p. (In Russ.).
  26. Makarov EG. Inzhenernye raschety v Mathcad 15 [Engineering Calculations in Mathcad 15]. St. Petersburg: Piter; 2011. 400 p. (In Russ.).
  27. Linge S, Langtangen HP. Solving nonlinear algebraic equations. In: Linge S, Langtangen HP, editors. Programming for computations – MATLAB/Octave. Cham: Springer; 2016. pp. 177–201. DOI: https://doi.org/10.1007/978-3-319-32452-4_6.
How to quote?
Khvostov AA, Magomedov GO, Ryazhskih VI, Plotnikova IV, Zhuravlev AA, Magomedov MG. Cooling Caramel in Ethyl Alcohol: Constructing a Mathematical Model. Food Processing: Techniques and Technology. 2020;50(3):425–438. (In Russ.). DOI: https://doi.org/10.21603/2074-9414-2020-3-425-438.
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