Multiple solutions of unsteady Darcy–Forchheimer porous medium flow of Cu–Al 2 O 3 /water based hybrid nanofluid with joule heating and viscous dissipation effect

Suspended solid particles in a fluid used to transport energy can improve the fluid's thermal conductivity and heat transport characteristics. The primary aim of current investigation is to investigate the magnetized unsteady two-dimensional (2D) flow on a continuously horizontally symmetrical contracting sheet with suction for a hybrid water-based nanofluid and an aligned field of Darcy–Forchheimer porous material, including the joule heating and viscous dissipation effect. In this work, the solid volume fraction is taken into consideration by the model of nanofluid equations developed by Tiwari and Das. Equations of similarity in ordinary form are derived using transformations of similarity, and the associated equations are simplified numerically using the bvp4c method in MATLAB software for a range of nanoparticle volume fraction, inertia coefficient, unsteadiness, porous medium permeability, Eckert number, and wall mass suction in water values. It is discovered that two solutions exist within the given unsteadiness parameter range. In addition, as volume fraction of copper increases, the skin friction coefficient increases in the first solution but decreases in the second. A temporal stability analysis reveals that only one of the two branches is long-term stable, while the other is unstable. The velocity profiles are declined for the larger porosity parameter in the first solution.