Electrothermal Convection in Dielectric Maxwellian Nanofluid Layer

The influence of rheological behavior on the natural convection in a dielectric nanofluid with vertical AC electric field is investigated. The rheology of the nanofluid is described by Maxwell model for calculating the shear stresses from the velocity gradients. The employed model introduces the combined effects of movement of the molecules of the fluid striking the nanoparticles, thermophoresis and electrophoresis due to embedded nanoparticles. The exact solutions of the eigen model value problem for stress-free bounding surfaces are obtained analytically using one term Galerkin method to find the thermal Rayleigh number for onset of both non-oscillatory (stationary) and oscillatory motions. It is found that the oscillatory modes are possible for both bottom and top-heavy distributions of nanoparticles. It is observed that the value of critical Rayleigh number is decreased by a substantial amount with the increase in electric field intensity, whereas role of viscoelasticity (time relaxation parameter) is to hasten the occurence of oscillatory modes appreciably. The thermal Prandtl number is found to delay the occurence of oscillatory modes. These results are also shown graphically.