Onset of natural convection under an electric fieldt

Abstract

The convective instability problem in a.c. and d.c. electric fields is studied theoretically. Linearized perturbation equations are solved by the Galerkin method where the critical a.c. or d.c. electric Rayleigh number, the critical Rayleigh number and the critical Marangoni number are expressed as eigenvalues. Nondimensional parameters, Biot number Bi, a.c. electric Rayleigh number Ea, Rayleigh number Ra and Marangoni number Ma, determine the onset of natural convection in the case of the a.c. electric field, while parameters Bi, S, K, Ea, Ra and Ma become the governing factors in the case of the d.c. electric field. It is found that the critical a.c. electric Rayleigh number, the critical Rayleigh number and the critical Marangoni number become smaller as the electric field increases in the case of the a.c. electric field. However, in the case of the d.c. electric field, the critical d.c. electric Rayleigh number, the critical Rayleigh number and the critical Marangoni number increase as the electric field increases when | S| and K are small, while the critical d.c. electric Rayleigh number, the critical Rayleigh number and the critical Marangoni number decrease as the electric field increases when | S| and K are large.