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

• 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
• ISSN: 1388-6150; 1588-2926
• DOI: 10.1007/s10973-021-11179-2

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.