Dual solutions of magnetohydrodynamic boundary layer flow and a linear temporal stability analysis

Sarkar, Golam Mortuja; Sahoo, Bikash

doi:10.1177/0954408920934220

Cited by 8 publications

(5 citation statements)

References 25 publications

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“…However, the effects of other flow parameters in the velocity and temperature profiles show similar results comparing to the related articles given some of them in references (see Ref. 7–9 , 13 , 25 ). The common feature is that the momentum and thermal boundary layer thicknesses in USB it lower than LSB.…”

Section: Resultssupporting

confidence: 80%

“…The present authors discussed about two different numerical schemes to find the smallest eigenvalue in their latest article (see Ref. 25 ) in detail. To do this, we convert equation (20) into a system of first order ODEs as follow: subject to the BCs where ϕ0=z1, ϕ0′=z2, ϕ0″=z3, trueϕ¯0=z4, trueϕ¯0′=z5 and trueϕ¯0″=z6.…”

Section: Numerical Methods and Discussionmentioning

confidence: 99%

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

Sarkar

Sahoo

2020

Proceedings of the Institution of Mechanical Engineers, Part E:

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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.

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Section: Resultssupporting

confidence: 80%

Section: Numerical Methods and Discussionmentioning

confidence: 99%

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

Sarkar

Sahoo

2020

Proceedings of the Institution of Mechanical Engineers, Part E:

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“…Cebeci and Keller, 1971). Recently, Sarkar and Sahoo (2020a) discussed the shooting technique in detail that was used to determine the smallest eigenvalue numerically in their latest publication.…”

Section: Stability Analysismentioning

confidence: 99%

“…The pioneering work was first proposed by Merkin (1986). Later, Merkin’s technique was implemented by (Weidman et al , 2006; Weidman and Ma, 2016; Kamal et al , 2018; Sarkar and Sahoo, 2020a) and many others in their works.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Hiemenz flow of Reiner-Rivlin fluid over a stretching/shrinking sheet

Sarkar

Sahoo

2021

WJE

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Purpose This paper aims to theoretically and numerically investigate the steady two-dimensional (2D) Hiemenz flow with heat transfer of Reiner-Rivlin fluid over a linearly stretching/shrinking sheet. Design/methodology/approach The Navier–Stokes equations are transformed into self-similar equations using appropriate similarity transformations and then solved numerically by using shooting technique. A simple but effective mathematical analysis has been used to prove the existence of a solution for stretching case (λ> 0). Moreover, an attempt has been laid to carry the asymptotic solution behavior for large stretching. The obtained asymptotic solutions are compared with direct numerical solutions, and the comparison is quite remarkable. Findings It is observed that the self-similar equations exhibit dual solutions within the range [λc, −1] of shrinking parameter λ, where λc is the turning point from where the dual solutions bifurcate. Unique solution is found for all stretching case (λ > 0). It is noticed that the effects of cross-viscous parameter L and shrinking parameter λ on velocity and thermal fields show opposite character in the dual solution branches. Thus, a linear temporal stability analysis is performed to determine the basic feasible solution. The stability analysis is based on the sign of the smallest eigenvalue, where positive or negative sign leading to a stable or unstable solution. The stability analysis reveals that the first solution is stable that describes the main flow. Increase in cross-viscous parameter L resulting in a significant increment in skin friction coefficient, local Nusselt number and dual solutions domain. Originality/value This work’s originality is to examine the combined effects of cross-viscous parameter and stretching/shrinking parameter on skin friction coefficient, local Nusselt number, velocity and temperature profiles of Hiemenz flow over a stretching/shrinking sheet. Although many studies on viscous fluid and nanofluid have been investigated in this field, there are still limited discoveries on non-Newtonian fluids. The obtained results can be used as a benchmark for future studies of higher-grade non-Newtonian flows with several physical aspects. All the generated results are claimed to be novel and have not been published elsewhere.

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“…The effect of MHD Casson fluid over an exponentially permeable stretching sheet has been explored by Raju et al 27 Sulochana et al 28 provided the detailed explanation of aligned magnetic field on kerosene-based nanofluid. The multiple slip effects on magnetic-Carreau fluid over a slendering sheet have been elaborated by Raju et al 29 Sarkar and Sahoo 30 noticed a unique solution for the stretching sheet case whereas the dual solutions for a limited range of shrinking (strength) parameter. Further, they accomplished that the thermal and momentum boundary layer thicknesses diminish with the enhancement of magnetic parameter in the first solution branches.…”

Section: Introductionmentioning

confidence: 99%

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

RamReddy

Saran

2022

Proceedings of the Institution of Mechanical Engineers, Part E:

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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.

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Dual solutions of magnetohydrodynamic boundary layer flow and a linear temporal stability analysis

Cited by 8 publications

References 25 publications

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

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

Analysis of Hiemenz flow of Reiner-Rivlin fluid over a stretching/shrinking sheet

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

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