Paper Title
Dual Solutions on Carreau Fluid Flow Over a Shrinking Sheet with Hybrid Nanoparticles

Abstract
The problem of Carreau fluid flow along a shrinking sheet with hybrid nanoparticles is investigated. The alumina (Al2O3) and copper (Cu) nanoparticles are suspended in water to form Al2O3-Cu/water hybrid nanofluid. The similarity equations are gained from the governing equations using similarity transformations, and their solutions are obtained by the bvp4c solver in Matlab software. Results elucidate that dual solutions exist up to a certain range of the suction strength (S>0) and stretching/shrinking parameter, λ. The critical values Sc for the existence of the dual solutions decrease, as the volume fractions for Cu is increased. Meanwhile, the effect of Weissenberg number, Weis to reduce the skin friction and the heat transfer coefficients. The stability of the dual solutions is determined by the temporal stability analysis, and it is discovered that only one of them is stable and physically applicable. Keywords - Dual Solutions, Carreau Fluid, Hybrid Nanofluid, Stability Analysis, Shrinking Sheet