On multiple solutions of cubic catalysis chemically reactive flow of hybrid nanofluids

• Flow and heat transfer of a Graphene Oxide (GO)–Fe 3 O 4 /H 2 O hybrid nanofluids over a shrinking disk are studied. • Effects of magnetic field , non-linear thermal radiation, concentrated species with first order velocity and thermal slip boundary conditions are considered. • Dual solutions exist for a specific range of shrinking strengths by using the bvp4c solver technique. • The mass transfer rate enhanced with an increment in homogenous and Schmidt numbers, whereas the opposite behavior is witnessed for heterogeneous reactions. In past decays, hybrid nanofluids have attracted much interest due to their considerable potential in enhancing heat transportation, conductivity, stability and physical strength. The study of graphene oxide ( G O ) + F e 3 O 4 / H 2 O hybrid nanofluids over shrinking disk remains unexplored territory. The aim of our study to investigate the dual nature solutions of magnetized hybrid nanofluids over permeable shrinking disk, while taking the impacts of various parameters carried out numerically. The roles of thermal radiation, magnetic field, velocity and thermal slip conditions are considered to examine the velocity, thermal and concentration equations. The set of classical similarity variables is considered to obtain the set of non-linear ODEs, which are then solved via bvp4c technique in MATLAB. Dual solutions are obtained for the friction drag, heat transport rate, velocity, thermal distribution and concentration species profiles based on dominating physical parameters. The outcome represents the existence of dual solutions (multiple solutions) in the shrinking sector χ c ≤ χ ≤ 0 , where χ c is the bifurcation point. It is noted that no solution is achievable beyond these bifurcation points. Furthermore, the friction drag coefficient augments for a stable solution due to an increment in mass suction effect and the friction drag coefficient is enhanced rapidly for the slip parameter as compared to no-slip parameter. In addition, the concentration profile is also enhanced by the variation in homogeneous reaction parameter, whereas it is declined for heterogeneous reaction parameter. Finally, the temporal stability analysis of solutions is tested by the sign of the smallest eigenvalue, revealing that first solution is stable and second solution is in general, unstable.