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A model of freezing foods with liquid nitrogen using special functions

机译：使用特殊功能的液氮冷冻食品模型

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摘要

A food freezing model is analyzed analytically. The model is based on the heat diffusion equation in the case of cylindrical shaped food frozen by liquid nitrogen; and assuming that the thermal conductivity of the cylindrical food is radially modulated. The model is solved using the Laplace transform method, the Bromwich theorem, and the residue theorem. The temperature profile in the cylindrical food is presented as an infinite series of special functions. All the required computations are performed with computer algebra software, specifically Maple. Using the numeric values of the thermal and geometric parameters for the cylindrical food, as well as the thermal parameters of the liquid nitrogen freezing system, the temporal evolution of the temperature in different regions in the interior of the cylindrical food is presented both analytically and graphically. The duration of the liquid nitrogen freezing process to achieve the specified effect on the cylindrical food is computed. The analytical results are expected to be of importance in food engineering and cooking engineering. As a future research line, the formulation and solution of freezing models with thermal memory is proposed.
机译：分析食物冻结模型。该模型基于液氮冷冻的圆柱形食品的热扩散方程。并假设圆柱状食物的热导率受到径向调节。使用Laplace变换方法，Bromwich定理和残差定理对模型进行求解。圆柱形食物的温度曲线以一系列特殊功能表示。所有必需的计算都是使用计算机代数软件（特别是Maple）执行的。利用圆柱形食品的热和几何参数的数值以及液氮冷冻系统的热参数，可以分析和图形方式显示圆柱形食品内部不同区域的温度随时间的变化。计算液氮冷冻过程的持续时间，以达到对圆柱形食品的特定效果。分析结果有望在食品工程和烹饪工程中发挥重要作用。作为未来的研究方向，提出了具有热记忆的冻结模型的提出和解决方案。

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