Multiple solutions and their stability for a Ti-alloy nanofluid saturated Darcy porous medium: Flow separation and reversal

Abstract

In this article, the authors provided the stability analysis for Darcy porous medium saturated by a Ti-alloy nanofluid in the presence of tilted magnetic field, Joule heating, heat generation, and velocity slip effects. The Tiwari-Das model is implemented and the relevant similarity transformations are identified for mathematical modeling of the proposed fluid flow problem. The set of resultant ODEs has been solved using the shooting method in conjunction with the RK-4th order scheme. The existence of dual solutions is observed along with their critical values for the present setup at and after the bifurcation point but for a limited range of certain fixed parameters. Through the eigenvalue approach, it is shown that the first solutions are stable, but not the second solutions. The streamlines are depicted to understand the flow patterns in addition to the identification of flow separation point and flow reversal. The important findings are as follows: (a) the delay of boundary layer separation is pointed out with the enhancing values of volume fraction of Ti-alloy nanoparticles and the inclined magnetic parameter in the presence of suction, (b) the Ti-alloy nanofluids velocity rises but the temperature decays with rising values of the Ti-alloy nanoparticle volume fraction, and (c) the value of smallest eigenvalues is growing with the growing values of magnetic parameter. Finally, this type of research may be extremely beneficial in the fields of aerodynamics (i.e. production of engine components, aircraft turbines, and high-performance automatic parts) and medicine.