Natural convective non-Newtonian nanofluid flow in a wavy-shaped enclosure with a heated elliptic obstacle

A numerical investigation has been carried out in a wavy-shaped enclosure with an elliptical inner cylinder to find out the effect of an inclined magnetic field and a non-Newtonian nanofluid on fluid flow and heat transfer. Here, the dynamic viscosity and thermal conductivity of the nanofluid are also taken into account. These properties change with the temperature and nanoparticle volume fraction. The vertical walls of the enclosure are modeled through complex wavy geometries and are kept at a constant cold temperature. The inner elliptical cylinder is deemed to be heated and the horizontal walls are considered adiabatic. Temperature difference between the wavy walls and the hot cylinder leads to natural convective circulation flow inside the enclosure. The dimensionless set of the governing equations and associated boundary conditions are numerically simulated using the COMSOL Multiphysics software, which is based on finite element methods. Numerical analysis has been scrutinized for varying Rayleigh number (Ra), Hartmann number (Ha), magnetic field inclination angle (γ), rotation angle of the inner cylinder (ω), power-law index (n), and nanoparticle volume fraction (ϕ). The findings demonstrate that the solid volumetric concentration of nanoparticles diminishes the fluid movement at greater values of φ. The heat transfer rate decreases for larger nanoparticle volume fractions. The flow strength increases with an increasing Rayleigh number resulting in a best possible heat transfer. A higher Hartmann number diminishes the fluid flow but converse behavior is exhibited for magnetic field inclination angle (γ). The average Nusselt number (Nu) values are maximum for γ = 90°. The power-law index plays a significant role on the heat transfer rate, and results show that the shear-thinning liquid augments the average Nusselt number.