Dual numerical solutions of Casson SA–hybrid nanofluid toward a stagnation point flow over stretching/shrinking cylinder

A computational study of Casson sodium alginate–hybrid nanofluid of stagnation point flow through a shrinking/stretching cylinder with radius effect was carried out. Since the hybrid nanofluid is considered more contemporary type of nanofluid, it is currently being employed to enhance the efficiency of heat transmission rates. The aim of this study is to scrutinize the effect of particular parameters, such as the shrinking parameter, the Reynold number, the Casson fluid parameter, the solid copper volume fraction, and the Prandtl number, on the temperature and velocity profiles. Furthermore, the research looked into the variation of skin friction coefficient as well as the Nusselt number according to the Casson fluid parameters, and the copper solid volume fraction against shrinking parameter was investigated as part of this study. By including the appropriate similarity variables in the alteration, the nonlinear partial differential equation has been transformed into a set of ordinary differential equations (ODEs). In the end, the MATLAB bvp4c solver program is used to rectify ODEs. The findings revealed the existence of two solutions for shrinking surface with varying copper volume fractions and Casson fluid parameter values. Furthermore, the temperature profile rate was reduced in both solutions as the strength of the Reynold number, Casson fluid parameter, and copper volume fraction increased. Finally, non-unique solutions were obtained in the range of λ≥λci\lambda \ge {\lambda }_{{\rm{ci}}}.