Numerical and stability analysis of Cu-Al2O3 water based hybrid nanofluid through a permeable shrinking sheet: Multiple solutions

The aim of the current study is to investigate the numerical and theoretical analysis of hybrid nanofluid (NF)-suspended Cu and Al2O3 nanoparticles in water. The basic flow equations contain the influence of thermal radiation, magnetic field, temperature-dependent viscosity, cross-diffusion, and heat source. The basic flow equations described by Navier-Stokes have been altered to self-similar equations via transformations of variables. The transformed system is then solved numerically via the BVP4C approach. For stability exploration, the stability analysis is performed via mathematically and graphically. The impact of emerging factors on flow characteristics is elaborated through graphs. The present numerical results are correlated to the published work, and excellent agreement has been established. It is investigated that the velocity curves show decreasing phenomena due to the augmented values of variable viscosity and magnetic field. Opposite behaviour is reported for the permeability factor, Grashop, and modified Grashop numbers. The fluid energy and concentration are increasing functions of the Dafour number, Eckert number, and Soret number.