NON-OSCILLATORY ELECTROTHERMAL INSTABILITY IN ROTATING RIVLINâERICKSEN NANOFLUID WITH A POROUS MEDIUM: FREEâFREE, RIGIDâRIGID, AND RIGIDâFREE BOUNDARY CONDITIONS

In the present work, the onset of electrothermal instability with a porous medium for a rotating Rivlin-Ericksen nanofluid is studied. It is subjected to various boundary conditions, including free-free, rigid-rigid, and rigid-free conditions. The nanofluid model takes into account thermophoresis and Brownian motion phenomena. Employing linear stability analysis, the governing equations of the problem are formulated and solved using appropriate boundary conditions, and the eigenvalue problem is solved using Galerkin and normal mode analysis method, the dispersion relationship that explains the impact of various parameters like rotation (Taylor number <i>T<sub>a</sub></i>), AC electric field <i>R<sub>ea</sub></i>, Lewis number <i>L<sub>e</sub></i>, nanoparticle Rayleigh number <i>R<sub>n</sub></i>, modified diffusivity ratio <i>N<sub>A</sub></i>, and medium porosity ∈ are analyzed analytically and graphically for stationary convection. The AC electric field, porosity, and nanoparticle Rayleigh number have destabilizing effects on the onset of stationary convection, while Taylor number, Lewis number, and modified diffusivity ratio have stabilizing effects on the onset of stationary convection. We have established good agreement between the results of the present paper and earlier published results. This research holds significant importance for numerous metallurgical processes, polymer solutions, convective chimneys, and implications for various chemical engineering applications involving nanofluids and porous materials subjected to external forces and boundary conditions.