Dual solutions and their stability analysis for inclined magnetohydrodynamics and Joule effects in Ti-alloy nanofluid: Flow separation

Abstract

This article emphasizes the roles of Joule heating and inclined magnetic field on the Ti-alloy nanofluid towards an exponentially permeable shrinking/stretching surface for the first time. Adopting the Tiwari and Das model, this nanofluid incorporates water as the base fluid and Ti-alloy as the nanoparticles in the mathematical formulation. Non-dimensional form of resultant flow governing equations is solved numerically for dual solutions using the Shooting method along with the Runge-Kutta fourth order technique and also the stability of the system is verified through the eigenvalue approach. The streamlines and eigenvalue patterns are provided to show the stability of obtained solutions and the significance of the problem undertaken. In these solutions, the first solution is found to be realistic and stable whereas the second solution is not stable for each combination of inclined magnetic, Joule heating, stretching/shrinking, Ti-alloy volume fraction, and suction parameters within the limited ranges. The existence of a flow separation point is identified between the shrinking and stretching regions. Finally, the delay of boundary layer separation is pointed out with the enhancing values of volume fraction of Ti-alloy nanoparticles and magnetic parameter in the presence of suction. This kind of analysis plays a very important role in the fields of aerodynamics, medical, and space sciences.