Quadratic density and viscosity variations on electro-thermal-convection in a dielectric fluid-saturated porous layer

An investigation is carried out to determine the effect of three types of boundary conditions as well as variation in density and viscosity with temperature on electro-thermal-convection (ETC) in a dielectric fluid-saturated porous layer. A Galerkin-type of weighted residual method (WRM) is used to extract the eigenvalues. The electrohydrodynamic boundary conditions are included namely, (i) lower and upper boundaries rigid (R-R), (ii) lower-rigid and upper-free boundaries (R-F), and (iii) lower and upper boundaries free (F-F). The governing parameters of the problem are the Biot number Bi, the ratio of viscosity Λ, the porous parameter Da^− 1, the temperature dependent viscosity η and thermal expansion co-efficient increases is to delay the onset, while strength electric Rayleigh number R_e increases is to destabilize the system. The electric force R_ec , and buoyancy force R_tc adjunct with each other and always found R_ec < R_tc. For stress free surface condition advances the ETC compared at rigid surfaces. In limiting cases, some results published previously are recovered from our results.