The onset of double-diffusive nanofluid convection in a rotating porous medium layer with thermal conductivity and viscosity variation: A revised model

In this paper, the combined effect of thermal conductivity and viscosity variation with nanoparticle fraction on the onset of doublediffusive nanofluid convection in a rotating porous layer is studied based on a new set of boundary conditions for the nanoparticle fraction, which is physically more realistic. The boundary condition considers here that the nanoparticle flux is assumed to be zero on the boundaries. This shows that the nanoparticle fraction value at the boundary alters accordingly. In this way, the present model is more realistic physically than those previous studies. The model used for nanofluid combines the effects of Brownian motion and thermophoresis, while for porous medium the Darcy model is taken into account. Due to the Brownian motion, the nanoparticle volumetric fraction becomes stratified, and hence the thermal conductivity and the viscosity are stratified. The nanofluid is assumed to be dilute and this causes the porous medium to be treated as a weakly heterogeneous medium with variation in the vertical direction of conductivity and viscosity. In turn this permits an analytical solution to be obtained using a Galerkin method that gives the criterion for the onset of convection. Several results are obtained as limiting cases of the present study.