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Comparison of heat transfer phenomena for two different cryopreservation methods : slow freezing and vitrification

Skorupa Anna, Piasecka-Belkhayat Alicja

Journal of Applied Mathematics and Computational Mechanics

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2023

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Vol. 22, nr 1

57--69

EN

The purpose of the research is to prepare a mathematical and numerical model for the phenomenon of heat transfer during cryopreservation. In the paper, two popular methods, slow freezing and vitrification, are compared. Furthermore, the basic model of thermal processes is supplemented by the phenomenon of phase transitions. To determine the temperature distribution during cryopreservation processes, one uses the heat transfer equation proposed by Pennes. An integral part of the energy equation is the substitute thermal capacity (STC) performed according to the concept named one domain method (fixed domain method), The numerical model is developed using the finite difference method (FDM) connected with directed interval arithmetic. The final part of the article contains the results of numerical simulations.

2

Analysis of ultrashort laser pulse irradiation with 2d thin metal films using the fuzzy lattice Boltzmann method

Piasecka-Belkhayat Alicja, Korczak Anna

Journal of Theoretical and Applied Mechanics

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2020

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Vol. 58 nr 1

209--219

EN

This paper presents the numerical modelling of heat transfer in two-dimensional metal films. The mathematical model of the problem analyzed consists on fuzzy coupled lattice Boltzmann equations for electrons and phonons supplemented by adequate boundary-initial conditions. In this model, the standard two-dimensional 9-speed lattice (D2Q9) is used. The main concept behind this work was to use the fuzzy lattice Boltzmann method (FLBM) to analyze the thermal process proceeding in a thin metal film. The application of α-cuts allows one to simplify mathematical operations in the fuzzy numbers set. Additionally, the trapezoidal approximation of fuzzy relaxation times and boundary conditions is considered. In the final part of the paper, the results of numerical computations are shown.

3

Application of the interval Lattice Boltzmann method for a numerical modeling of 2D thin metal films irradiated by ultrashort laser pulses

Piasecka-Belkhayat Alicja, Korczak Anna

Journal of Applied Mathematics and Computational Mechanics

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2019

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Vol. 18, nr 4

63--71

EN

In the paper, the two-dimensional numerical modelling of heat transfer in thin metal films irradiated by ultrashort laser pulses using the D2Q9 scheme is considered. In the mathematical description, the relaxation times and the boundary conditions for phonons and electrons are given as interval numbers. The problem has been formulated using the interval coupled lattice Boltzmann equations for electrons and phonons. The solution has been obtained by means of the interval lattice Boltzmann method using the rules of directed interval arithmetic. Examples of numerical computations are presented in the final part of the paper.