Influence of variable viscosity and double di®usion on the convective stability of a nanofluid flow in an inclined porous channel

The influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel is investigated. The Darcy-Brinkman model is used to characterize the fluid flow dynamics in porous materials. The analytical solutions are obtained for the unidirectional and completely developed flow. Based on a normal mode analysis, the generalized eigenvalue problem under a perturbed state is solved. The eigenvalue problem is then solved by the spectral method. Finally, the critical Rayleigh number with the corresponding wavenumber is evaluated at the assigned values of the other flow-governing parameters. The results show that increasing the Darcy number, the Lewis number, the Dufour parameter, or the Soret parameter increases the stability of the system, whereas increasing the inclination angle of the channel destabilizes the flow. Besides, the flow is the most unstable when the channel is vertically oriented.