Journal of the Serbian Society for Computational Mechanics / Vol. 13 / No. 2, 2019 / pp 19-35 (10.24874/jsscm.2019.13.02.03) ELECTROHYDRODYNAMIC THERMAL INSTABILITY IN A WALTERS’ (MODEL B') ROTATING NANOFLUID SATURATING A POROUS MEDIUM Gian C. Rana 1* , Poonam K. Gautam 2 , Hemlata Saxena 2 1 Department of Mathematics, NSCBM Govt. College, Hamirpur-177 005, Himachal Pradesh, India e-mail: drgcrana15@gmail.com 2 Department of Mathematics, Career Point University, Kota, Rajasthan, India e-mail: poornima17gautam@gmail.com *corresponding author Abstract The onset of thermal instability in a dielectric rotating nanofluid layer saturating a porous medium with vertical AC electric field is investigated by employing Darcy model for porous medium. The rheology of the nanofluid is described by Walters’ (model B’) for calculating the shear stresses from the velocity gradients. The employed model incorporates the combined effects of movement of the molecules of the fluid striking the nanoparticles, thermophoresis and electrophoresis due to the embedded particles. The boundaries are considered to be stress free. It is assumed that nanoparticle flux is zero on the boundaries. The eigen-value problem is solved analytically using the first approximation of Galerkin method. The Darcy Rayleigh number for onset of non- oscillatory (stationary) modes is obtained. The effects of the modified Taylor number, the AC electric Rayleigh number, the Lewis number, the modified diffusivity ratio, nanoparticles Rayleigh number and medium porosity have been discussed. The kinematic viscoelasticity accounting for rheology of the nanofluid has no effect on the stationary convection for Walters’ (model B’) nanofluids and behaves like an ordinary Newtonian nanofluid. Oscillatory convection has been ruled out under the considered boundary conditions. Keywords: nanofluid, AC electric field, Rayleigh number, Walters’ (model B'), electrohydrodynamic, Brownian motion, Galerkin method 1. Introduction Electrohydrodynamics (EHD) finds diverse applications in enhancement of thermal transfer, EHD pumps, micromechanic systems, micro-cooling systems, building of thermal insulation, biomechanics etc. Electrohydrodynamic thermal instability in a porous medium is a phenomenon related to various fields. It has various applications in different areas such as EHD enhanced thermal transfer, EHD pumps, EHD in microgravity, micromechanic systems, drug delivery, micro-cooling system, nanotechnology, oil reservoir modeling, petroleum industry, building of thermal insulation, biomechanics, engineering etc. Chandrasekhar (1961) has given a