Piasecka-Belkhayat Alicja, Skorupa Anna
Department of Computational Mechanics and Engineering, Silesian University of Technology, Konarskiego 18A, 44-100 Gliwice, Poland.
Materials (Basel). 2023 Mar 9;16(6):2186. doi: 10.3390/ma16062186.
This paper presents the numerical modelling of heat transfer and changes proceeding in the homogeneous sample, caused by the crystallisation phenomenon during cryopreservation by vitrification. Heat transfer was simulated in a microfluidic system in which the working fluid flowed in micro-channels. The analysed process included single-phase flow during warming, and two-phase flow during cooling. In the model under consideration, interval parameters were assumed. The base of the mathematical model is given by the Fourier equation, with a heat source including the degree of ice crystallisation. The formulated problem has been solved using the interval version of the finite difference method, with the rules of the directed interval arithmetic. The fourth order Runge-Kutta algorithm has been applied to determine the degree of crystallisation. In the final part of this paper, examples of numerical computations are presented.
本文介绍了在玻璃化冷冻保存过程中，由结晶现象引起的均匀样品内传热及变化过程的数值模拟。传热模拟是在一种微流体系统中进行的，工作流体在微通道中流动。分析的过程包括升温过程中的单相流和降温过程中的两相流。在所考虑的模型中，假定了区间参数。数学模型的基础是傅里叶方程，并带有一个包含冰晶化程度的热源项。所提出的问题已通过有限差分法的区间版本，并结合定向区间算法的规则得到解决。已应用四阶龙格 - 库塔算法来确定结晶程度。本文的最后一部分给出了数值计算的示例。
