Stability analysis of triple solutions of Casson nanofluid past on a vertical exponentially stretching/shrinking sheet

Abstract

The MHD two dimensional boundary layer flow of Casson nanofluid on an exponential stretching/shrinking sheet is considered with effects of radiation parameter, nanoparticles volume fractions (i.e. Fe ₃O ₄ and Ti ₆Al ₄V) and thermal convective boundary condition. The partial differential equations are transformed into ordinary differential equations by means of similarity transformations. The solutions of the transferred equations are achieved numerically with the help of shooting technique in Maple software. At different ranges of involved physical parameters, triple solutions are found. Therefore, stability analysis is performed by bvp4c in MATLAB to find the stable and physically reliable solution. Impacts of the physical parameter are presented through graphs and tables. Mainly, it is found that an increase in Casson and suction parameters decrease the corresponding velocity profiles while increase in Prandtl number, stretching/shrinking, and suction parameter decrease the temperature profiles. Furthermore, an increase in nanoparticles volumetric fraction, radiation and magnetic parameters as well as Biot number increase the temperature profiles and their thermal boundary layer thicknesses.