Ferromagnetic Chaos in thermal convection of fluid through fractal–fractional differentiations

Thermal convection suppresses the thermal stability and instability during the interaction between the magnetic fields because thermal convection is the most significant driver of time-dependent patterns of motion within magnetized and non-magnetized chaotic. In this manuscript, a mathematical model...

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Bibliographic Details
Published in:Journal of thermal analysis and calorimetry 2022-08, Vol.147 (15), p.8461-8473
Main Authors: Abro, Kashif Ali, Atangana, Abdon, Gómez-Aguilar, J. F.
Format: Article
Language:English
Subjects:
Analytical Chemistry
Boussinesq approximation
Chemistry
Chemistry and Materials Science
Darcys law
Differential equations
Dynamic stability
Ferromagnetism
Fluid flow
Fractals
Free convection
Inorganic Chemistry
Laws, regulations and rules
Lorentz force
Magnetic fields
Magnetohydrodynamics
Mathematical analysis
Mathematical models
Measurement Science and Instrumentation
Nonlinear differential equations
Numerical analysis
Operators (mathematics)
Ordinary differential equations
Physical Chemistry
Polymer Sciences
Stability analysis
Stability criteria
Thermal stability
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Summary:Thermal convection suppresses the thermal stability and instability during the interaction between the magnetic fields because thermal convection is the most significant driver of time-dependent patterns of motion within magnetized and non-magnetized chaotic. In this manuscript, a mathematical modeling is proposed subject to the magnetohydrodynamic conductive fluid lying on an infinite horizontal layer subject to heat from below with gravity. The mathematical model is based on nonlinear ordinary differential equations and such model has been investigated by means of the Boussinesq approximation and Darcy's law. The newly defined techniques of fractal–fractional differential operators, namely Atangana–Baleanu and Caputo–Fabrizio fractal–fractional differentiations, have been imposed on the governing equations. The mathematical analysis based on the equilibrium points and stability criteria is investigated to examine the dynamic responses of a magnetized and non-magnetized conductive fluid model. The numerical simulations have been performed by Adams methods, which is so-called the explicit scheme of the Adams–Bashforth method. Our results suggest that the comparative evolution of trajectories between magnetized and non-magnetized chaotic behaviors has strong effects due to Lorentz force that showed the resistivity in chaotic phenomenon.
ISSN:1388-6150
1588-2926
DOI:10.1007/s10973-021-11179-2