The effect of thermal and velocity boundary conditions on electrothermal convection in a dielectric fluidsaturated
layer of Brinkman porous medium with temperature dependent viscosity (TDV) has been studied. The lower
rigid/free boundary is either fixed temperature or fixed heat flux with respect to temperature perturbations, while at
the upper rigid/free boundary the Robin type of thermal boundary condition is invoked. The eigenvalue problem is
solved numerically using the Galerkin-type of weighted residual method. The instability threshold depends
significantly on boundary conditions and dimensionless physical parameters namely, the Biot number, temperature
dependent viscosity and permeability parameters. The critical gravity thermal or electric thermal Rayleigh number
making the onset of electrothermal convection is found to be higher for fixed temperature conditions and also for both
boundaries rigid while it is lower for fixed heat flux conditions and also for both boundaries free. Some known results
are recovered as special cases from the present study.