Stability Analysis of Binary Casson Nanofluid Convection With Viscosity and Conductivity Variations Using Darcy–Brinkman Model

Abstract

Abstract The onset of binary/double-diffusive convection with conductivity and viscosity variations has been investigated for Casson nanofluids using Darcy–Brinkman model. Nanoparticle conductivity and viscosity are used as linear functions of volume fraction. The normal mode approach, linearized stability theory, and one-term Galerkin method are used to obtain the expressions of Darcy–Rayleigh number for stationary and oscillatory convection. Different base-fluids (water, blood, honey) for different porous phases (glass, limestone, sand) have been examined numerically using the software mathematica (version 12.0). When Darcy parameter, conductivity, and viscosity variation parameters are combined, the layer's stability is significantly enhanced. The top-heavy layer of fluid instability state is shown to be dominated by stationary mode. It is observed that non-Newtonian Casson parameter and solute Lewis number destabilize the system while porosity parameter, Darcy number, and solute Rayleigh number postpone the same. Interestingly, thermal capacity ratio, conductivity, and viscosity parameters have stabilizing effects. A comparison of stability patterns of Newtonian and non-Newtonian nanofluids is carried out numerically by taking different base fluids like water (Newtonian fluid), blood, and honey (non-Newtonian Casson fluids). The system is found to be more stable for non-Newtonian fluids. It is observed that conductivity variation pattern for different porous media is: glass < limestone < sand for all the base fluids. As far as base fluids are concerned, they follow the conductivity pattern as water < honey < blood for different porous phases.