Dual solutions of time-dependent magnetohydrodynamic stagnation point boundary layer micropolar nanofluid flow over shrinking/stretching surface

Time-dependent, two-dimensional (2D) magnetohydrodynamic (MHD) micropolar nanomaterial flow over a shrinking/stretching surface near the stagnant point is considered. Mass and heat transfer characteristics are incorporated in the problem. A model of the partial differential expressions is altered into the forms of the ordinary differential equations via similarity transformations. The obtained equations are numerically solved by a shooting scheme in the MAPLE software. Dual solutions are observed at different values of the specified physical parameters. The stability of first and second solutions is examined through the stability analysis process. This analysis interprets that the first solution is stabilized and physically feasible while the second one is un-stable and not feasible. Furthermore, the natures of various physical factors on the drag force, skin-friction factor, and rate of mass and heat transfer are determined and interpreted. The micropolar nanofluid velocity declines with a rise in the suction and magnetic parameters, whereas it increases by increasing the unsteadiness parameter. The temperature of the micropolar nanofluid rises with increase in the Brownian motion, radiation, thermophoresis, unsteady and magnetic parameters, but it decreases against an increment in the thermal slip constraint and Prandtl number. The concentration of nanoparticles reduces against the augmented Schmidt number and Brownian movement values but rises for incremented thermophoresis parameter values.

Automated summary

In this study, time-dependent, two-dimensional magnetohydrodynamic micropolar nanomaterial flow over a shrinking/stretching surface near the stagnant point is investigated with consideration of mass and heat transfer characteristics. The equations are solved numerically using a shooting scheme in MAPLE software, revealing dual solutions with different physical parameters. The stability analysis indicates that the first solution is stable and physically feasible, while the second solution is unstable and infeasible. Additionally, the impact of various physical factors on drag force, skin-friction factor, and mass and heat transfer rates is determined and interpreted.