Hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface

Purpose This paper aims to investigate the steady flow and heat transfer of a Cu-Al 2 O 3 /water hybrid nanofluid over a nonlinear permeable stretching/shrinking surface with radiation effects. The surface velocity condition is assumed to be of the power-law form with an exponent of 1/3. The governing equations of the problem are converted into a system of similarity equations by using a similarity transformation. Design/methodology/approach The problem is solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The results of the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are presented through graphs and tables for several values of the parameters. The effects of these parameters on the flow and heat transfer characteristics are examined and discussed. Findings Results found that dual solutions exist for a certain range of the stretching/shrinking and suction parameters. The increment of the skin friction coefficient and reduction of the local Nusselt number on the shrinking sheet is observed with the increasing of copper (Cu) nanoparticle volume fractions for the upper branch. The skin friction coefficient and the local Nusselt number increase when suction parameter is increased for the upper branch. Meanwhile, the temperature increases in the presence of the radiation parameter for both branches. Originality/value The problem of Cu-Al 2 O 3 /water hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface with radiation effects is the important originality of the present study where the dual solutions for the flow reversals are obtained.