Analytical Analysis of Convection in Rotatory Walters B´ Viscoelastic Fluid in Presence of Magnetic Field

Pardeep Kumar¹

1. Dept. of Mathematics, ICDEOL, Himachal Pradesh University, Shimla, India.

Section:Research Paper, Product Type: Journal-Paper
Vol.13 , Issue.1 , pp.25-30, Feb-2025

Online published on Feb 28, 2025

Copyright © Pardeep Kumar . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
An attempt has been made to investigate the effects of uniform vertical magnetic field and uniform rotation on thermal convection in Walters B` viscoelastic fluid. Following the linearized stability theory, Boussinesq approximation and normal mode analysis, the dispersion relation is obtained. In the scenario of stationary convection, Walters B` viscoelastic fluid behaves like a Newtonian Fluid. Further, it is found that rotation has a stabilizing effect whereas the magnetic field has both stabilizing and destabilizing effects. In addition to this, it has been discovered that the system is reliable for g??/???(1-2?_r F) (27?^4)/4 and under the conditions g??/??>(1-2?_r F) (27?^4)/4 and 0??_r?1/2F the system goes into an unstable state. Overstability has also been looked at from the perspective of a scenario in which sufficient circumstances are met to rule out the possibility of the phenomenon occurring. It has been discovered that the rotation, magnetic field and viscoelasticity introduce oscillatory modes in the system which were non-existent in their absence.

Key-Words / Index Term :
Thermal Convection; Walters B` Viscoelastic Fluid; Uniform Vertical Magnetic Field; Uniform Rotation; Linear Stability Theory; Normal Mode Analysis method

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