28 May 2014 A model of freezing foods with liquid nitrogen using special functions
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Abstract
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.
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Martín Rodríguez Vega, Martín Rodríguez Vega, } "A model of freezing foods with liquid nitrogen using special functions", Proc. SPIE 9108, Sensing for Agriculture and Food Quality and Safety VI, 91080L (28 May 2014); doi: 10.1117/12.2049758; https://doi.org/10.1117/12.2049758
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