Numerical Analysis and Applicable Mathematics
Title
On Magneto-Rotatory Viscoelastic Convection
Authors
Pardeep Kumar
Department of Mathematics, ICDEOL, Himachal Pradesh University, Summer-Hill, Shimla-171005 (HP), India.
*Corresponding author E-mail address: pkdureja@gmail.com
Article History
Publication details: Received: 16th June 2022; Revised: 30th August 2022; Accepted: 30th August 2022; Published: 15th September 2022
Cite this article
Kumar P. On Magneto-Rotatory Viscoelastic Convection. Numer. Anal. Appl. Math., 2022, 3(6), 30-38.
Abstract
The aim of the present work was to study the effects of uniform vertical magnetic field and uniform rotation on the double-diffusive convection in Rivlin-Ericksen viscoelastic fluid through permeable media. Following the linearized stability theory, Boussinesq approximation and normal mode analysis, the dispersion relation is obtained. The stationary convection, stability of the system and oscillatory modes are discussed. For the case of stationary convection, it is found that the stable solute gradient and rotation have stabilizing effects on the system. In the presence of rotation, the medium permeability has a destabilizing (or stabilizing) effect and magnetic field has stabilizing (or destabilizing) effect on the system, whereas, in the absence of rotation, medium permeability and magnetic field have destabilizing effect and stabilizing effect on the system, respectively. The kinematic viscoelasticity has no effect for stationary convection. The kinematic viscoelasticity, rotation, stable solute gradient and magnetic field introduce oscillatory modes in the system, which were non-existent in their absence. The sufficient conditions for the non-existence of over stability are also obtained.
Keywords
Convection; Viscoelastic Fluid; Porous Medium; Uniform Magnetic Field; Uniform Rotation