tatpipТехника и технология пищевых производствFood Processing: Techniques and Technology2074-94142313-1748Кемеровский государственный университет10.21603/2074-9414-2024-1-2491KCTXZNtatpip-181Research ArticleСтатьиМатематическая модель процесса СВЧ и конвективной выпечки хлеба из сбивного тестаMicrowave-Convective Processing of Whipped Bread: Mathematical Modelinghttps://orcid.org/0000-0002-3836-9407ХвостовА. А.KhvostovA. A.

Воронеж

Anatoly А. Khvostov

Voronezh

https://orcid.org/0000-0002-7201-8387МагомедовГ. О.MagomedovG. O.

Воронеж

Gazibeg O. Magomedov

Voronezh

https://orcid.org/0000-0002-2834-3000РяжскихВ. И.RyazhskihV. I.

Воронеж

Victor I. Ryazhskih

Voronezh

https://orcid.org/0000-0002-2194-767XЖуравлевА. А.ZhuravlevA. A.

Воронеж

Aleksey А. Zhuravlev

Voronezh

https://orcid.org/0000-0003-2494-4973МагомедовМ. Г.MagomedovM. G.

Воронеж

Magomed G. Magomedov

Voronezh

mmg@inbox.ruhttps://orcid.org/0000-0001-5959-6652ПлотниковаИ. В.PlotnikovaI. V.

Воронеж

Inessa V. Plotnikova

Voronezh

https://orcid.org/0000-0002-9880-9726ТаратухинА. С.TaratukhinA. S.

Воронеж

Aleksei S. Taratukhin

Voronezh

Воронежский государственный технический университет; Воронежский государственный университет инженерных технологийРоссияVoronezh State Technical University; Voronezh State University of Engineering TechnologiesRussian FederationВоронежский государственный университет инженерных технологийРоссияVoronezh State University of Engineering TechnologiesRussian FederationВоронежский государственный технический университет; Военный учебно-научный центр Военно-воздушных сил «Военно-воздушная академия имени профессора Н.Е. Жуковского и Ю.А. Гагарина» Министерства обороны Российской ФедерацииРоссияVoronezh State Technical University; Military Educational and Scientific Centre of the Air Force N.E. Zhukovsky and Yu.A. Gagarin Air Force Academy of the Ministry of Defence of the Russian FederationRussian FederationВоенный учебно-научный центр Военно-воздушных сил «Военно-воздушная академия имени профессора Н.Е. Жуковского и Ю.А. Гагарина» Министерства обороны Российской ФедерацииРоссияMilitary Educational and Scientific Centre of the Air Force N.E. Zhukovsky and Yu.A. Gagarin Air Force Academy of the Ministry of Defence of the Russian FederationRussian Federation20242108202654193103Copyright © Хвостов А.А., Магомедов Г.О., Ряжских В.И., Журавлев А.А., Магомедов М.Г., Плотникова И.В., Таратухин А.С., 20262026Хвостов А.А., Магомедов Г.О., Ряжских В.И., Журавлев А.А., Магомедов М.Г., Плотникова И.В., Таратухин А.С.Khvostov A.A., Magomedov G.O., Ryazhskih V.I., Zhuravlev A.A., Magomedov M.G., Plotnikova I.V., Taratukhin A.S.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.fptt.ru/jour/article/view/181

При выпечке сбивных бездрожжевых хлебобулочных изделий актуальным является внедрение эффективных источников подвода энергии к тестовым заготовкам для снижения энергозатрат и продолжительности выпечки, а также для повышения качества изделий. Целью работы являлась формализация математической модели процесса СВЧ и конвективной выпечки хлеба из сбивного теста на основе основных уравнений тепломассообмена и ее верификация.

Для проверки точности расчетов по разработанной математической модели провели натурный эксперимент. Он заключался в оценке нагрева сбивных тестовых заготовок влажностью 56 ± 1 % при СВЧ и конвективной выпечке до достижения температуры в центре мякиша хлеба 98 ± 1 °С.

Математическая модель выпечки формализована в виде уравнений сохранения энергии и массы. Это позволяет рассматривать процесс выпечки хлеба как нестационарный процесс теплои массопереноса влаги в изотропной несжимаемой сплошной среде в диффузионном приближении с учетом подвижной границы фазового перехода. Верификация математической модели показала, что оценка средней относительной погрешности составила для СВЧ-выпечки 14,5 % по температуре и 18,2 % по влагосодержанию, для конвективной выпечки 12,6 % по температуре и 9,7 % по влагосодержанию. Проведенные исследования позволили сделать вывод о адекватности математической модели реальным процессам тепломассообмена, а также приемлемой для оптимизации процесса погрешности расчета полей температуры и влагосодержания.

Разработанная физико-математическая модель процесса выпечки позволяет оценить динамику температурных и влагоконцентрационных полей в тестовой заготовке в зависимости от технологических параметров. Математическая модель и результаты вычислительных экспериментов могут быть использованы для идентификации статических и динамических характеристик процесса выпечки как объекта автоматического управления, выявления предпочтительных каналов управления и выбора управляющих воздействий, а также для синтеза системы автоматического управления процессом выпечки по заданным показателям качества.

Whipped yeast-free bakery products require effective energy supply to dough in order to optimize energy consumption, baking time, and quality. This article introduces a verified mathematical model of microwave and convective baking for whipped bread based on heat and mass exchange equations.

A full-scale experiment to verify the calculations involved dough samples with a humidity of 56 ± 1%. The samples underwent microwave and convective processing until the temperature in the crumb center reached 98 ± 1°С.

The mathematical model was formalized as energy and mass conservation equations, which made it possible to consider baking as a non-stationary process of heat and mass transfer of moisture in an isotropic incompressible continuous medium in the diffusion approximation. The equation took into account the unstable phase transition boundary. The practical verification showed the mean error for microwave baking as 14.5% in temperature and 18.2% in moisture content. For convective baking, the results included 12.6% in temperature and 9.7% in moisture content. The mathematical model proved adequate to the real processes of heat and mass transfer. The error in calculating the temperature and moisture content fields was sufficient tooptimize the process.

The physical and mathematical model of the baking process made it possible to evaluate the effect of technological variables on the temperature and moisture concentration fields in the dough samples. The mathematical model and the computational experiment can be used to identify static and dynamic characteristics of baking as an object of automatic control, i.e., to identify optimal control channels and actions, as well as to adjust the automatic control system to specific quality indicators.

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