Linear stability of longitudinal convective rolls in a non-Darcy porous layer filled with nanofluid due to viscous dissipation effect: A realistic approach

Abstract

The onset of longitudinal convective rolls of nanofluid flow inside a horizontal porous material using Brinkman theory due to the viscous dissipation effect has been addressed numerically. An infinitely long horizontal porous region has been considered which is confined between two rigid boundaries. The boundaries of the channel are considered adiabatic (lower) and isothermal (upper). Brownian motion and thermophoresis properties are taken into consideration for nanofluid. In the linear stability analysis, oblique roll disturbances with arbitrary orientation are taken into account, where the preferred mode of instability i.e., longitudinal rolls (when P=0 or ϑ=π/2) are shown. Finally, the resulting eigenvalue problem is solved in MATLAB using the bvp4c technique. The impact of improving the modified diffusivity ratio (NA<10), Lewis number (Le<,=,>1), concentration Rayleigh number (Rn) and modified particle density increment (NB≈10−2−10−5) is to accelerate the instability boundaries, while the switching parameter (ξ) has a dual character on it. Further, the pattern of the streamlines are slightly compressed in the channel’s center for large values of ξ, whereas no markable changes are noticed for higher values of NA. The isotherms lines are closer near the adiabatic boundary when ξ takes small values.