Buoyancy-surface tension driven forces on electro-thermal-convection in a rotating dielectric fluid-saturated porous layer: effect of cubic temperature gradients

Abstract

This paper analyses the onset of buoyancy-surface tension driven forces on rotating electro-thermal-convection in a dielectric fluid-saturated porous layer under the influence of different basic temperature gradients. The lower surface is rigid-isothermal, and the upper surface is stress-free and flat at which the Robin-type of thermal boundary condition is invoked. The principle of exchange of stability is valid and the stability eigenvalue problem is solved numerically using the Galerkin method. The parameters influencing the stability characteristics of the system are the thermal Rayleigh number (\( R_{t} \)), electric Rayleigh number (\( R_{e} \)), Marangoni number (\( Ma \)), Taylor number (\( Ta \)), Darcy number (\( Da \)), Biot number (\( Bi \)) and the viscosity ratio (\( \varLambda \)). The onset of convection is delayed for a nonlinear temperature profile when compared to the linear temperature profile. It is observed that the strength of surface tension force and an AC electric field is to hasten the onset. The system is found to be more stable with increasing \( Bi \), \( Ta \) and \( \varLambda \) as well as decrease in \( Da \). The surface tension and electric forces complement each other and always observed to be \( Ma_{c} < \text{R}_{ec} \).