Hybrid nanofluid flow and heat transfer over a permeable biaxial stretching/shrinking sheet

Purpose The purpose of this paper is to examine the axisymmetric flow and heat transfer of a hybrid nanofluid over a permeable biaxial stretching/shrinking sheet. Design/methodology/approach In this study, 0.1 solid volume fraction of alumina (Al2O3) is fixed, then consequently, various solid volume fractions of copper (Cu) are added into the mixture with water as the base fluid to form Cu-Al2O3/water hybrid nanofluid. The hybrid nanofluid equations are converted to the similarity equations by using the similarity transformation. The bvp4c solver, which is available in the Matlab software is used for solving the similarity equations numerically. The numerical results for selected values of the parameters are presented in tabular and graphical forms, and are discussed in detail. Findings It is found that dual solutions exist up to a certain value of the stretching/shrinking and suction parameters. The critical value lambda(c) < 0 for the existence of the dual solutions decreases as nanoparticle volume fractions for copper increase. The temporal stability analysis is performed to analyze the stability of the dual solutions, and it is revealed that only one of them is stable and physically reliable. Originality/value The present problem is new, original with many important results for practical problems in the modern industry.