foodmetaFOOD METAENGINEERINGFOOD METAENGINEERING2949-6497All-Russian Dairy Research Institute10.37442/fme.2025.1.73foodmeta-73Research ArticleОригинальное теоретическое исследованиеOriginal Theoretical ResearchМоделирование процесса теплообмена с окружающей средой сгущенного молока с сахаромHeat Transfer Modeling in Sweetened Condensed Milkhttps://orcid.org/0000-0002-8427-0387БольшаковаЕкатерина ИвановнаBolshakovaEkaterina I.e_bolshakova@vnimi.orghttps://orcid.org/0009-0002-0077-7891МотылевСергей ВладимировичMotylevSergey V.s_motylev@vnimi.orghttps://orcid.org/0000-0003-1241-0026СемипятныйВладислав КонстантиновичSemipyatnyVladislav C.v_semipyatniy@vnimi.orghttps://orcid.org/0000-0002-3227-8133КручининАлександр ГеннадьевичKruchininAleksandr G.a_kruchinin@vnimi.orghttps://orcid.org/0000-0002-5875-9875ТуровскаяСветлана НиколаевнаTurovskayaSvetlana N.s_turovskaya@vnimi.orghttps://orcid.org/0000-0002-9399-0984ИлларионоваЕлена ЕвгеньевнаIllarionovaElena E.e_illarionova@vnimi.orgВсероссийский научно-исследовательский институт молочной промышленностиРоссияAll-Russian Dairy Research InstituteRussian Federation202504042025315672Copyright © Большакова Е.И., Мотылев С.В., Семипятный В.К., Кручинин А.Г., Туровская С.Н., Илларионова Е.Е., 20252025Большакова Е.И., Мотылев С.В., Семипятный В.К., Кручинин А.Г., Туровская С.Н., Илларионова Е.Е.Bolshakova E.I., Motylev S.V., Semipyatny V.C., Kruchinin A.G., Turovskaya S.N., Illarionova E.E.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.fme-journal.org/jour/article/view/73Введение

Введение: Сгущенное цельное молоко с сахаром (СЦМС) — востребованный продукт среди потребителей и переработчиков. Исследование температурных профилей необходимо для оптимизации его логистики в условиях экстремальных температур, чтобы предотвратить пороки качества и минимизировать затраты на специализированный транспорт при поставках в регионы с жарким климатом и районы Крайнего Севера, с учетом абсолютного температурного диапазона в  РФ, составляющего ~90°C. Ранее данный вопрос в аспекте транспортирования не был исследован, максимально допустимая температура хранения для продукта составляла 25°C, минимальная не регламентировалась.

Цель

Цель: Исследование температурных профилей СЦМС в транспортной упаковке при различных условиях окружающей среды.

Материалы и методы

Материалы и методы: Осуществлено моделирование процессов нагревания и охлаждения СЦМС в транспортной упаковке, представленной в виде одномерной многослойной системы. Для описания задачи теплопередачи в температурных диапазонах от 5°C до 35°C и от 5°C до минус 35°C составлена система дифференциальных уравнений, определены начальные и граничные условия.

Результаты

Результаты: Согласно построенной модели, продолжительность прогрева СЦМС от 5°C до 35°C составит 36,7 ч, а охлаждения от 5°C до минус 35°C – 41,1 ч. По результатам исследования разработано программное обеспечение для расчета продолжительности изменения температуры СЦМС в зависимости от начальных и конечных температур окружающей среды.

Выводы

Выводы: Разработан новый подход к теоретическому прогнозированию продолжительности изменения температуры СЦМС в транспортной упаковке при хранении и транспортировании. Данный подход может быть использован в специальных программных обеспечениях для бизнеса при планировании логистических маршрутов, затрат на транспортирование с учетом срока перевозки и условий окружающей среды. Предложенное решение может быть адаптировано и под другие пищевые продукты. 

Introduction

Introduction: Sweetened condensed whole milk (SCM) is a highly demanded product among consumers and processing plants. The study of temperature profiles is essential for optimizing its logistics under extreme temperature conditions to prevent quality defects and minimize costs associated with specialized transport when delivering to regions with hot climates and the Far North, considering the absolute temperature range in Russia, which is approximately 90°C. Previously, this aspect of transportation had not been studied. The maximum allowable storage temperature for the product was set at 25°C, while the minimum temperature was not regulated.

Purpose

Purpose: To investigate the temperature profiles of SCM in transport packaging under various ambient conditions.

Materials and Methods

Materials and Methods: A simulation of the heating and cooling processes of SCM in transport packaging, modeled as a one-dimensional multilayer system, was conducted. To describe heat transfer within the temperature ranges of 5°C to 35°C and 5°C to -35°C, a system of differential equations was formulated, with specified initial and boundary conditions.

Results

Results: According to the proposed model, the duration of heating SCM from 5°C to 35°C is 36.7 hours, while cooling from 5°C to -35°C takes 41.1 hours. Based on the study results, software was developed to calculate the duration of SCM temperature changes depending on the initial and final ambient temperatures.

Conclusion

Conclusion: A new approach has been developed for theoretically predicting the duration of temperature changes in SCM within transport packaging during storage and transportation. This approach can be utilized in specialized business software solutions for logistics route planning, transportation cost estimation, and consideration of ambient conditions during shipping. Additionally, the proposed solution can be adapted for other food products.

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The authors declare that there are no conflicts of interest present.