Dual solutions of a magnetohydrodynamic stagnation point flow of a non-Newtonian fluid over a shrinking sheet and a linear temporal stability analysis

Abstract

The present study accentuates the magnetohydrodynamic and suction/injection effects on the two-dimensional stagnation point flow and heat transfer of a non-Newtonian fluid over a shrinking sheet. The set of Navier-Stokes equations are converted into a system of highly non-linear ordinary differential equations by employing suitable similarity variables. The obtained self-similar equations are then solved numerically with the aid of shooting technique. The similarity equations exhibit dual solutions over a certain range of the shrinking strength. It is observed that the solution domain increases as the suction/injection parameter, the non-Newtonian parameter and the magnetic parameter increase. Moreover, it is further noticed that these two solution branches show opposite behavior on the velocity and temperature profiles for the combined effects of the several flow parameters. Emphasis has been given to determine the most feasible and physically stable solution branch. Thus a linear temporal stability analysis has been carried out and the stability of the these two branches are tested by the sign of the smallest eigenvalue. The smallest eigenvalues are found numerically which suggest that the upper solution branch is stable and the flow dynamics can be describe by the behavior of the upper solution branch.

Flow and heat transfer analysis of a special third grade fluid over a stretchable surface in a parallel free stream

“…Note that the stability of the steady state dual solutions is determined by the sign of the smallest eigenvalue γ 1 (see Merkin 25 and Mortuja Sarkar and Sahoo 30 for details). The above system has an unknown parameter γ , the eigenvalue.…”

“…In this problem, we relax F ′ 0 ( ∞ ) → 0 and determine the smallest eigenvalue γ 1 by shooting technique with an additional BC F ′ ′ 0 ( 0 ) = 1 (without loss of generality). The reader may follow Weidman et al 26 and Mortuja Sarkar and Sahoo 30 for further details.…”

“…The pioneering work on the stability analysis was reported by Merkin 25 and several researchers adopted Merkin’s method to carry the stability analysis (see Refs. 26–31 ). Naganthran et al 13 investigated an unsteady flow of a special third grade fluid over a stretching/shrinking sheet and found dual solutions for both the stretching and shrinking of the sheet.…”

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

“…This transverse (vertical) magnetic field has numerous fundamental applications such as a nuclear reactor, blood flow, electrical furnace, turbo-machinery, etc. The impact of a transverse magnetic field on electrically conducting liquid over a flat surface has been studied by Rossow 26 The works of Vajravelu and Rollins, 27 Sharma et al, 28 Sarkar and Sahoo 29 gained attention among others toward the existence and feasibility of dual solutions. Since then, many researchers have started working on this model by considering nanofluids.…”