Vacuum cooling is a rapid cooling method widely used in cooling some food products. Simulating the vacuum cooling process with mathematical models helps to acquire a more intuitive understanding and optimize the whole cooling process. However, there is no review summarizing the mathematical models of vacuum cooling. In this review, heat and mass transfer process during vacuum cooling, types of mathematical models for vacuum cooling, and numerical methods including finite difference method, finite element method and finite volume method used for process simulation are introduced in details. The food products used in numerical simulation study of vacuum cooling generally include liquid food, vegetables and cooked meat. The ranges of application of various numerical methods are also discussed. Moreover, heat and mass transfer coefficients have a great influence on the accuracy of the model, and are generally provided by the literature. The investigations presented in this review invariably demonstrate that mathematical modeling can provide good prediction of key information of vacuum cooling process, and has a great potential to improve vacuum cooling process in the food industry. However, more efforts are still needed to realize the industrial translation of laboratory results.

中文翻译：

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模拟食品真空冷却过程的数学模型的发展–综述

真空冷却是一种广泛用于冷却某些食品的快速冷却方法。使用数学模型模拟真空冷却过程有助于获得更直观的了解并优化整个冷却过程。然而，没有综述真空冷却的数学模型的综述。在这篇综述中，详细介绍了真空冷却过程中的传热和传质过程，真空冷却数学模型的类型以及用于过程模拟的数值方法，包括有限差分法，有限元法和有限体积法。用于真空冷却的数值模拟研究的食品通常包括液体食品，蔬菜和熟肉。还讨论了各种数值方法的应用范围。而且，传热和传质系数对模型的准确性有很大影响，通常由文献提供。本综述中的研究始终表明，数学建模可以为真空冷却过程的关键信息提供良好的预测，并且在改善食品工业中的真空冷却过程方面具有巨大的潜力。但是，仍需要更多的努力来实现实验室结果的工业翻译。