The stability of the nanofluid flow in an inclined porous channel with variable viscosity

The effect of variable viscosity on the stability of nanofluid flow in an inclined porous channel is investigated. The nanofluid model considers the consideration of thermophoresis and Brownian motion. In addition, the Brinkman model has been employed in the momentum equation. The eigenvalue problem for the perturbed state is obtained using normal mode analysis, and the spectral method is used to solve it. The influence of numerous parameters on the critical Rayleigh number and associated wavenumber are graphically displayed. It is noticed that the increasing impact of the Darcy number, Prandtl number, and porosity parameter increases the system's stability, whereas the variable viscosity parameter and the channel's inclination destabilize the flow. Also, the dynamics of the flow field, behavior of temperature, and volume fraction are presented through streamlines, isotherms, and isonanoconcentration at the critical level.