Boundary effects on electrothermal convection in a dielectric fluid layer

Abstract

The instability characteristics of a dielectric fluid layer heated from below under the influence of a uniform vertical alternating current (AC) electric field is analyzed for different types of electric potential (constant electric potential/ electric current), velocity (rigid/free) and temperature boundary conditions (constant temperature/heat flux or a mixed condition at the upper boundary). The resulting eigenvalue problem is solved numerically using the shooting method for various boundary conditions and the solution is also found in a simple closed form when the perturbation heat flux is zero at the boundaries. The possibility of a more precise control of electrothermal convection (ETC) through various boundary conditions is emphasized. The effect of increasing AC electric Rayleigh number is to hasten while that of Biot number is to delay the onset of ETC. The system is more stable for rigid-rigid boundaries when compared to rigid-free and least stable for free-free boundaries. The change of electric potential boundary condition at the upper boundary from constant electric potential to constant electric current is found to instill more stability on the system. ∗Corresponding Author. Email: ravishmamatha@gmail.com 4 M. Ravisha, K.R. Raghunatha, A.L. Mamatha and I.S. Shivakumara Besides, increase in the AC electric Rayleigh number and the Biot number is to reduce the size of convection cells.