Sucrose crystallization depends on various thermal phenomena, which makes them an important scientific issue for the sugar industry. However, the rationale and theory of sucrose crystallization still remain understudied. Among the least described problems is the effect of time and temperature on the condensation rate of sucrose molecules on crystallization nuclei in a supersaturated sugar solution. This article introduces a physical and mathematical heat transfer model for this process, as well as its numerical analysis. The research featured a supersaturated sugar solution during sucrose crystallization and focused on the condensation of sucrose molecules on crystallization nuclei. The study involved the method of physical and mathematical modeling of molecular mass transfer, which was subjected to a numerical analysis. While crystallizing in a vacuum boiling pan, a metastable solution went through an exothermal reaction. In a supersaturated solution, this reaction triggered a transient crystallization of solid phase molecules and a thermal release from the crystallization nuclei into the liquid phase. This exogenous heat reached 39.24 kJ/kg and affected the mass transfer kinetics. As a result, the temperature rose sharply from 80 to 86 °C. The research revealed the effect of temperature and time on the condensation of solids dissolved during crystalline sugar production. The model involved the endogenous heat factor. The numerical experiment proved that the model reflected the actual process of sucrose crystallization. The obtained correlations can solve a number of problems that the modern sugar industry faces.

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A number of sectors in the food industry practice cooling substances of biological origin. This contributes to the maintenance of their biological properties, as well as prevents microflora growth in the product. One of the ways to intensify production processes and maintain the quality of raw materials and finished products is their accelerated cooling with the help of low-energy cooling equipment. The use of physical bodies cooled to low temperatures is a promising way to accelerate liquid cooling. We used balls with frozen eutectic solution. In our research, the problem of cooling a liquid system is formulated and solved within the framework of classical linear boundary value problem for the equation of a stationary convective heat transfer. In the area of the actual values of the process parameters on the study object, the solution obtained is used as the basis for numerical experiment on the modelling of the cooling liquid flow with the cooling agent system, namely balls filled with eutectic solution. By calculation, the efficiency of the proposed method for cooling liquid was justified based on such factors as temperature, the number of balls in a two-phase liquid system, and the duration of low-temperature treatment. The presented results of the numerical experiment complied with real heat transfer processes during liquid cooling.

Особенность состояния системы жидкость–твердое тело в метастабильном растворе вещества состоит в том, что она (система) претерпевает два фазовых превращения в вакуум-аппарате (ВА) – кристаллообразование и растворение, требующие экспериментального изучения и описания в силу их важности при совершенствовании технологии производства кристаллического сахара. Однако и теоретическое обоснование фазовых превращений в метастабильном растворе разработано недостаточно. В статье предпринята попытка количественно поставить и решить проблему учета возникающего при проведении обработки метастабильного сахарсодержащего раствора повышения температуры в результате конденсации молекул на центре концентрации при пересыщении в ВА. В качестве основы численного моделирования поставленной задачи использовали программные продукты информационной среды Mathcad. С использованием модели диффузионного массопереноса сахарозы в пересыщенном растворе к затравке был разработан алгоритм расчета зависимости массы сахарозы от времени проведения процесса кристаллизации. На примере сахарозы дана оценка влияния физического фактора – выделяющейся при кристаллообразовании теплоты на расчет теплового баланса и производительности ВА. The peculiarity of the state of the liquid-solid system in a metastable solution of a substance is that it (the system) undergoes two phase transformations in a vacuum apparatus (VA) – crystal formation and dissolution, requiring experimental study and description due to their importance in improving the technology of production of crystalline sugar. However the theoretical justification of phase transformations in a metastable solution has not been sufficiently developed. The article attempts to quantify and solve the problem of taking into account the temperature increase that occurs during the processing of a metastable sugar-containing solution as a result of condensation of molecules at the concentration center during supersaturation in VA. Software products of the Mathcad information environment were used as the basis for numerical modeling of the task. Using a model of diffusive mass transfer of sucrose in a supersaturated solution to the seed, an algorithm was developed for calculating the dependence of the sucrose mass on the time of the crystallization process. On the example of sucrose, an assessment of the influence of a physical factor – the heat released during crystallization on the calculation of the thermal balance and the productivity of the VA is given.