The Onset of Electrothermoconvection in a Viscoelastic Rotating Dielectric Fluid Layer: Navier‐Stokes‐Voigt Model

ABSTRACT Thermally induced fluid motion (thermal convection) is an important phenomenon observed in nature, playing an essential role in the dynamics of the Earth's atmosphere, lakes, oceans, and in the interior of stellar objects. The present study investigates the combined effect of uniform vertical rotation and an electric field on thermal convection in a horizontal layer of viscoelastic dielectric fluid, utilizing the Navier–Stokes–Voigt model for both free and rigid boundary conditions. A linear stability analysis has been conducted to investigate the behavior of a dielectric viscoelastic fluid layer, which is assumed to be heated from either below or above. Thermal Rayleigh number expressions for both stationary and oscillatory convection modes are obtained using exact solutions when both the surfaces are free and series solutions when both the surfaces are rigid. Furthermore, numerical analysis is conducted using the Mathematica software, and the findings are presented through graphical representations. The study reveals that the impact of vertical electric field is to destabilize the system, while rotation exerts a stabilizing influence on both stationary and oscillatory modes of convection. Furthermore, the Kelvin–Voigt viscoelastic parameter is found to delay the initiation of oscillatory instability. It is also observed that when the system is heated from above, there is a marked delay in the onset of instability compared to the case when it is heated from below. The present study of electrothermoconvection in the context of the Navier‐Stokes–Voigt model, in particular, has not been reported yet in the literature.