Casson Nanofluid Instability with Viscosity and Conductivity Variation Using Brinkman Model

Abstract

The present work investigates the onset of convective instability of a non-Newtonian Casson nanofluid layer saturating a porous medium. Conductivity and viscosity are taken to be linear functions of nanoparticle volume fraction and Darcy-Brinkman model is used to modify the momentum equation. It is assumed that all the physical variables undergo a small disturbance on the basic solution and the normal mode technique is used to convert partial differential equations into ODE’s to get the expression of thermal Rayleigh number. Darcy parameter, non-Newtonian fluid property and conductivity variation parameter are coupled together leading to a significant increase in the stability of the layer. Numerical computations are carried out for various base fluids (water, oil, blood, glycol) under different porous phases (glass wool, limestone, sand) for metallic and non-metallic nanoparticles (copper, Iron, alumina, silicon oxide) using the software Wolfram Mathematica (version 12.0). The novelty of the work lies in the fact that the conductivity variation pattern for porous media is established as glass wool < limestone < sand and for base fluids as water < blood < glycol < oil. Maximum conductivity variation is observed for copper-oil nanofluid with sand as porous medium and glass saturated with alumina-water nanofluid shows the minimum variation. Oscillatory mode is found to dominate the instability state for bottom-heavy fluid layer. Darcy parameter stabilizes the fluid layer while porosity effects are destabilizing. Metals are found to be more stable as compare to non-metals.