Convection in a Ferromagnetic Fluid Layer Influenced by Changeable Gravity and Viscosity

Sumit Pant and Ebrahem A. Algehyne
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Sumit Pant: Department of Mathematics and Statistics, Banasthali Vidyapith, Banasthali 304022, India
Ebrahem A. Algehyne: Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia

Mathematics, 2022, vol. 10, issue 10, 1-21

Abstract: The motive of this work is to numerically evaluate the effect of changeable gravitational fields and varying viscosity on the beginning of convection in ferromagnetic fluid layer. The fluid layer is constrained by two free boundaries and varying gravitational fields that vary with distance across the layer. The authors hypothesized two categories of gravitational field variation, which can be subdivided into six distinct cases: (i) f ( z ) = z , (ii) f ( z ) = e z , (iii) f ( z ) = l o g ( 1 + z ) , (iv) f ( z ) = − z , (v) f ( z ) = − z 2 , and (vi) f ( z ) = z 2 − 2 z . The normal mode method was applied, and the single term Galerkin approach was used to solve the ensuing eigenvalue problem. The results imply that, in the first three cases, the gravity variation parameter speeds up the commencement of convection, while, in the last three cases, the viscosity variation parameter and gravity variation parameter slow down the onset of convection. It was also observed that, in the absence of the viscosity variation parameter, the non-buoyancy magnetization parameter destabilizes the impact on the beginning of convection but, in the presence of the viscosity variation parameter, it destabilizes or stabilizes impact on the beginning of convection. In the case of oscillatory convection, the results illustrate that oscillatory modes are not permitted, suggesting the validity of the theory of exchange of stabilities. Additionally, it was also discovered that the system is more stable for case (vi) and more unstable for case (ii).

Keywords: ferromagnetic fluid; changeable gravitational field; variable viscosity; single term Galerkin approach (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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