https://doi.org/10.1140/epjp/s13360-022-03474-0
Regular Article
Multiple solutions in aqueous titanium alloy nanofluid: the eigenvalue approach
Department of Mathematics, National Institute of Technology, 506004, Warangal, Telangana State, India
b chittetiram@gmail.com, chramreddy@nitw.ac.in
Received:
26
September
2022
Accepted:
4
November
2022
Published online:
16
November
2022
The authors aimed to explore multiple solutions and their stability for an exponentially shrinking sheet embedded in an aqueous titanium alloy water-based nanofluid with the magnetic field, Joule heat and thermal buoyancy forces. The Tiwari–Das model is used to formulate the mathematical equations, which are then translated into nonlinear ODEs using the appropriate similarity transformations. The dual solutions are noticed for the resultant boundary value problem using the shooting approach, which utilized the Newton–Raphson and Runge–Kutta techniques and then provided the comparative analysis with existing results. But, the first solutions are found to be more stable and physically valid over time according to the eigenvalue approach. It is also observed that the bifurcation of solutions exists for both assisting and opposing buoyancy flows, as well as the shrinking areas. The major outcomes of this analysis (based on stability analysis) are given: (i) the Ti-alloy nanofluid’s Nusselt number, skin friction and velocity rise when the buoyancy parameter rises, (ii) the delay of boundary layer separation is noticed with the enhancing values of volume fraction of Ti-alloy nanoparticles, thermal buoyancy and inclined magnetic parameters, (iii) the value of smallest eigenvalues is growing with the growing values of the magnetic parameter, and (iv) the enhancing values of Joule heating parameters enhances the temperature but it reduces the velocity. In addition, the flow separation point is identified and this kind of analysis is useful in aerospace technology as per the Prandtl theory. Finally, the streamline patterns are provided in this study to have a better understanding of the fluid flow behavior.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
