Дробно-дифенційний підхід для опису процесу живлення металів і сплавів, що твердіють в умовах регульованого газового тиску
Date
2021
Authors
Селівьорстова, Тетяна Віталіївна
Селівьорстов, Вадим Юрійович
Мала, Юлія Анатоліївна
Journal Title
Journal ISSN
Volume Title
Publisher
НМетАУ, Дніпро
Abstract
UKR: Для опису процесів фільтрації в складних дендритно-пористих середовищах запропонований ряд дробно-диференційних математичних моделей дифузійного типу. Описано нелінійне рівняння, що містить дробові похідні Рімана-Ліувілля за часом, яке може бути застосовано для коректного опису однофазної фільтрації не ньютонівської рідини в пористому середовищі.
RUS: Для описания процессов фильтрации в сложных дендритно-пористых средах предложен ряд дробно-дифференциальных математических моделей диффузионного типа. Описано нелинейное уравнение, содержащее дробные производные Римана-Лиувилля по времени, которое может быть применено для корректного описания однофазной фильтрации неньютоновской жидкости в пористой среде.
ENG: To describe the processes of filtration in the folding dendritic-porous middle of the proponation, a number of fractional-differential mathematical models of the diffusion type. Described non-linear, how to take the shot of the abducted Riman-Leeuwill for an hour, as it can be stuck for a correct description of the single-phase filtration of not Newtonian age in the porous middle. The two-phase zone, which is established during the transition from melting from hard to hard mill, can often be characterized by abnormal kinetics of resistance. The peculiarities of kinetics in the whole range of winners are related to the issues of widespread nonlocality, in a number of types, memory defects, which adhere to the progressive laws. The mathematical apparatus, which allows to adequately describe such processes, is the theory of integration-differentiation of the fractional order. Victorians in robotic thinking have a phenomenological character, so the possibility of their dependence in a specific, practical dermal condition is blamed on the basis of experimental results, so that the validity of other differences is confirmed. Stagnation of the given approach for describing the dynamics of the process of vitality of the two-phase zones and metals and alloys, which solidifies in the minds of a regulated gas vice. Presented in the fractional-differential robotic model of filtration are classified as abnormal diffusion. A characteristic feature of the ryvnyan, which is derived from different types of differential models of filtration, is not the same. With a whole model, they preserve the structure of the classical lines of filtration in the whole order and pass into them in boundary drops, if the order of the other differentiation is old. Vivchennya yakіsnyh authorities otrimanih іvnyans, and also prompts їh numerical decisions є to finish nontrivial zavdannyi, as vimagayut in the skin okremomu vampad of independent thought.
RUS: Для описания процессов фильтрации в сложных дендритно-пористых средах предложен ряд дробно-дифференциальных математических моделей диффузионного типа. Описано нелинейное уравнение, содержащее дробные производные Римана-Лиувилля по времени, которое может быть применено для корректного описания однофазной фильтрации неньютоновской жидкости в пористой среде.
ENG: To describe the processes of filtration in the folding dendritic-porous middle of the proponation, a number of fractional-differential mathematical models of the diffusion type. Described non-linear, how to take the shot of the abducted Riman-Leeuwill for an hour, as it can be stuck for a correct description of the single-phase filtration of not Newtonian age in the porous middle. The two-phase zone, which is established during the transition from melting from hard to hard mill, can often be characterized by abnormal kinetics of resistance. The peculiarities of kinetics in the whole range of winners are related to the issues of widespread nonlocality, in a number of types, memory defects, which adhere to the progressive laws. The mathematical apparatus, which allows to adequately describe such processes, is the theory of integration-differentiation of the fractional order. Victorians in robotic thinking have a phenomenological character, so the possibility of their dependence in a specific, practical dermal condition is blamed on the basis of experimental results, so that the validity of other differences is confirmed. Stagnation of the given approach for describing the dynamics of the process of vitality of the two-phase zones and metals and alloys, which solidifies in the minds of a regulated gas vice. Presented in the fractional-differential robotic model of filtration are classified as abnormal diffusion. A characteristic feature of the ryvnyan, which is derived from different types of differential models of filtration, is not the same. With a whole model, they preserve the structure of the classical lines of filtration in the whole order and pass into them in boundary drops, if the order of the other differentiation is old. Vivchennya yakіsnyh authorities otrimanih іvnyans, and also prompts їh numerical decisions є to finish nontrivial zavdannyi, as vimagayut in the skin okremomu vampad of independent thought.
Description
Т. В. Селівьорстова: ORCID 0000-0002-2470-6986; В. Ю. Селівьорстов: ORCID 0000-0002-1916-625X
Keywords
фільтрація, математична модель, дробна похідна, дрібно-диференційне рівняння, узагальнений закон Дарсі, КІТС, КЛВ
Citation
Селівьорстова Т. В., Селівьорстов В. Ю., Мала Ю. А. Дробно-дифенційний підхід для опису процесу живлення металів і сплавів, що твердіють в умовах регульованого газового тиску. Системні технології. Дніпро, 2021. Т. 4. № 135. С. 149–155. DOI: 10.34185/1562-9945-4-135-2021-15.