Stability analysis for multiple solutions of boundary layer flow towards a shrinking sheet: Analytical solution by using least square method

Mustafa, Irfan; Abbas, Zaheer; Arif, Ayesha; Javed, Tariq; Ghaffari, Abuzar

doi:10.1016/j.physa.2019.123028

Cited by 31 publications

(11 citation statements)

References 33 publications

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“…Thus, it was concluded that the first solution and the second solution are stable and unstable, respectively. The same conclusion was made by Weidman et al 33 Besides that, the stability analysis was also done by Harris et al, 34 Mahapatra and Nandy, 35 Roşca and Pop 36 and Mustafa et al 37 Meanwhile, in the study of micropolar fluid flow, the analysis was carried out by Roşca and Pop, 25 Sharma et al, 38 Lok et al 39 and Khashi'ie et al 40 In the recent study by Lund et al 3 triple solutions were obtained. Stability analysis was then performed, and only the first solution was found to be stable.…”

Section: Introductionmentioning

confidence: 57%

Magnetohydrodynamics boundary layer flow of micropolar fluid over an exponentially shrinking sheet with thermal radiation: Triple solutions and stability analysis

Yahaya

Arifin

Isa

et al. 2021

Math Methods in App Sciences

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The flow of electrically conducting micropolar fluid past an exponentially permeable shrinking sheet in the presence of a magnetic field and thermal radiation is studied. Similarity transformations are applied to the governing partial differential equations to form ordinary differential equations. The solution for the resultant equations, subject to boundary conditions, is then computed numerically using the bvp4c solver in MATLAB. The effects of several parameters on the local skin friction coefficient, couple stress, Nusselt number, velocity, microrotation and temperature of the fluid are analysed. Because the numerical computations for this problem result in triple solutions, stability analysis is carried out to ascertain the stability and significance of these solutions. The first solution is revealed to be stable, hence more physically meaningful than the other solutions. Meanwhile, it is found that the increase in magnetic and thermal radiation parameters reduces the fluid temperature.

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Section: Introductionmentioning

confidence: 57%

Magnetohydrodynamics boundary layer flow of micropolar fluid over an exponentially shrinking sheet with thermal radiation: Triple solutions and stability analysis

Yahaya

Arifin

Isa

et al. 2021

Math Methods in App Sciences

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“…According to Lund et al [29,30], Hamid et al [31], and Mustafa et al [32], the stability analysis of the dual solutions is verified by perturbing the steady solution by using following functions…”

Section: Stability Analysismentioning

confidence: 99%

Convective Effect on Magnetohydrodynamic (MHD) Stagnation Point Flow of Casson Fluid over a Vertical Exponentially Stretching/Shrinking Surface: Triple Solutions

et al. 2020

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In the current study, the characteristics of heat transfer of a steady, two-dimensional, stagnation point, and magnetohydrodynamic (MHD) flow of shear thickening Casson fluid on an exponentially vertical shrinking/stretching surface are examined in attendance of convective boundary conditions. The impact of the suction parameter is also considered. The system of governing partial differential equations (PDEs) and boundary conditions is converted into ordinary differential equations (ODEs) with the suitable exponential similarity variables of transformations and then solved using the shooting method with the fourth order Runge–Kutta method. Similarity transformation is an important class of phenomena in which scale symmetry allows one to reduce the number of independent variables of the problem. It should be noted that solutions of the ODEs show the symmetrical behavior of the PDES for the profiles of velocity and temperature. Similarity solutions are obtained for the case of stretching/shrinking and suction parameters. It is revealed that there exist two ranges of the solutions in the specific ranges of the physical parameters, three solutions depend on the opposing flow case where stagnation point (A) should be equal to 0.1, two solutions exist when λ1 = 0 where λ1 is a mixed convection parameter and A > 0.1, and a single solution exists when λ1 > 0. Moreover, the effects of numerous applied parameters on velocity, temperature distributions, skin friction, and local Nusselt number are examined and given through tables and graphs for both shrinking and stretching surfaces.

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“…This kind of analysis is important in order to avoid any misleading interpretation of flow. Some important investigations concerning the stability analysis on the solutions of boundary layer flow problem were made by Merkin [35], Weidman et al [36], Harris et al [37] and more recently by Anuar et al [38], Mustafa et al [39] and Aladdin et al [40,41], among others. It has been observed that the second solution has always been unstable and therefore unobtainable in practice, while the other solution is stable.…”

Section: Introductionmentioning

confidence: 99%

Influence of MHD Hybrid Ferrofluid Flow on Exponentially Stretching/Shrinking Surface with Heat Source/Sink under Stagnation Point Region

2021

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The numerical investigations of hybrid ferrofluid flow with magnetohydrodynamic (MHD) and heat source/sink effects are examined in this research. The sheet is assumed to stretch or shrink exponentially near the stagnation region. Two dissimilar magnetic nanoparticles, namely cobalt ferrite, CoFe2O4 and magnetite, Fe3O4, are considered with water as a based fluid. Utilizing the suitable similarity transformation, the governing equations are reduced to an ordinary differential equation (ODE). The converted ODEs are numerically solved with the aid of bvp4c solver from Matlab. The influences of varied parameters on velocity profile, skin friction coefficient, temperature profile and local Nusselt number are demonstrated graphically. The analysis evident the occurrence of non-unique solution for a shrinking sheet and it is confirmed from the analysis of stability that only the first solution is the stable solution. It is also found that for a stronger heat source, heat absorption is likely to happen at the sheet. Further, hybrid ferrofluid intensifies the heat transfer rate compared to ferrofluid. Moreover, the boundary layer separation is bound to happen faster with an increment of magnetic parameter, while it delays when CoFe2O4 nanoparticle volume fraction increases.

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Stability analysis for multiple solutions of boundary layer flow towards a shrinking sheet: Analytical solution by using least square method

Cited by 31 publications

References 33 publications

Magnetohydrodynamics boundary layer flow of micropolar fluid over an exponentially shrinking sheet with thermal radiation: Triple solutions and stability analysis

Magnetohydrodynamics boundary layer flow of micropolar fluid over an exponentially shrinking sheet with thermal radiation: Triple solutions and stability analysis

Convective Effect on Magnetohydrodynamic (MHD) Stagnation Point Flow of Casson Fluid over a Vertical Exponentially Stretching/Shrinking Surface: Triple Solutions

Influence of MHD Hybrid Ferrofluid Flow on Exponentially Stretching/Shrinking Surface with Heat Source/Sink under Stagnation Point Region

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