Dual Solutions and Stability Analysis for Buongiorno Model of Magnetohydrodynamics Nanofluid Flow Past a Heated Shrinking Slippery Surface

Abstract

This study investigates the combined effects of magnetic field, Joule heating, viscous dissipation, thermophoresis, and Brownian motion towards a convectively heated shrinking and slippery surface on a stagnation point flow of nanofluid is theoretically examined. The modified Buongiorno model for nanofluid flow is employed and numerically solved using a shooting technique together with the Runge-Kutta-Fehlberg integration scheme. It is found that dual solutions appear in certain range of shrinking surface parameter. The temporal stability analysis of the dual solutions to small disturbances was performed and the upper solution branch is found to be a stable and physically realistic solution to the problem. Appropriate results showing the influence of magnetic field, Surface slipperiness, Eckert number, Biot number, Brownian motion, and thermophoresis parameters on the nanofluid temperature, velocity, nanoparticles concentration, Nusselt number, skin friction, and Sherwood number are quantitatively discussed, and depicted graphically and in tables.