MHD Laminar Boundary Layer Flow of Radiative Fe-Casson Nanofluid: Stability Analysis of Dual Solutions

2021 ◽  
Author(s):  
H.B. Lanjwani ◽  
M.S. Chandio ◽  
M.I. Anwar ◽  
S.A. Shehzad ◽  
M. Izadi
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flow ◽  
Dual Solutions ◽  
Casson Nanofluid ◽  
Nanofluid Stability ◽  
Layer Flow

scholarly journals Stability Analysis of the Laminar Boundary Layer Flow

1970 ◽  
Vol 29 ◽  
pp. 23-34
Author(s):  
Nazma Parveen ◽  
Md MK Chowdhury
Keyword(s):  
Differential Equation ◽  
Boundary Layer ◽  
Stability Analysis ◽  
Finite Difference ◽  
Difference Scheme ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flow ◽  
Finite Difference Scheme ◽  
Linear Set ◽  
Layer Flow

In this paper, stability analysis of incompressible laminar boundary layer flow is presented. For this approach, the partial differential equation is converted to ordinary differential equation by suitable approximation. The implicit finite difference scheme is used to find the point of separations of the boundary layer equations. The finite difference equations for the given flow at each longitudinal position form a linear set with a tridiagonal coefficient matrix. To ensure the correct results, the methods are checked with standard flows like flow past circular cylinder, Howarth’s linear decelerating flows. These methods are demonstrated to compute accurately the separation points of several flows for which comparisons are made with previously published results. Then various series are tested with computer codes. At last, the stability diagram for plane poiseuille flow is shown. Key words: Stability; finite difference scheme; point of separation GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 29 (2009) 23-34  DOI: http://dx.doi.org/10.3329/ganit.v29i0.8512

The effect of vertical throughflow on the boundary layer flow of a nanofluid past a stretching/shrinking sheet

2017 ◽  
Vol 27 (9) ◽  
pp. 1910-1927 ◽  
Author(s):  
Ioan Pop ◽  
Kohilavani Naganthran ◽  
Roslinda Nazar ◽  
Anuar Ishak
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Dual Solutions ◽  
Shrinking Sheet ◽  
Content Type ◽  
Boundary Layer Equations ◽  
Vertical Throughflow ◽  
Layer Flow

Purpose The purpose of this paper is to study the effects of vertical throughflow on the boundary layer flow and heat transfer of a nanofluid driven by a permeable stretching/shrinking surface. Design/methodology/approach Similarity transformation is used to convert the system of boundary layer equations into a system of ordinary differential equations. The system of governing similarity equations is then reduced to a system of first-order differential equations and solved numerically using the bvp4c function in Matlab software. The generated numerical results are presented graphically and discussed based on some governing parameters. Findings It is found that dual solutions exist in both cases of stretching and shrinking sheet situations. Stability analysis is performed to determine which solution is stable and valid physically. Originality/value Dual solutions are found for positive and negative values of the moving parameter. A stability analysis has also been performed to show that the first (upper branch) solutions are stable and physically realizable, while the second (lower branch) solutions are not stable and, therefore, not physically possible.

Additional results for the problem of MHD boundary-layer flow past a stretching/shrinking surface

2016 ◽  
Vol 26 (7) ◽  
pp. 2283-2294 ◽  
Author(s):  
Ioan Pop ◽  
Natalia C. Roşca ◽  
Alin V. Roşca
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Boundary Layer Flow ◽  
Similarity Solutions ◽  
Lower Solution ◽  
Dual Solutions ◽  
Suction Parameter ◽  
Content Type ◽  
Layer Flow ◽  
The Stability

Purpose The purpose of this paper is to reinvestigate the problem of multiple similarity solutions of the two-dimensional magnetohydrodynamic boundary-layer flow of an incompressible, viscous and electrically conducting fluid past a stretching/shrinking permeable surface studied by Aly et al. (2007). Design/methodology/approach The transformed ordinary (similarity) differential equation was solved numerically using the function bvp4c from MATLAB. The relative tolerance was set to 10^(−10). Findings Dual solutions were found and a stability analysis was performed to show which solutions are stable and which are not stable. On the other hand, Aly et al. (2007) have shown that for each value of the power index and magnetic parameter in the range and for any specific values of the stretching/shrinking parameter and suction parameter the problem has only a solution. Originality/value The paper describes how multiple (dual) solutions for the flow reversals were obtained. The stability analysis has shown that the lower solution branches are unstable, while the upper solution branches are stable.

scholarly journals DUAL SOLUTIONS OF BOUNDARY LAYER FLOW WITH HEAT AND MASS TRANSFERS OVER AN EXPONENTIALLY SHRINKING CYLINDER: STABILITY ANALYSIS

2020 ◽  
Vol 50 (4) ◽  
pp. 247-253
Author(s):  
Debasish Dey ◽  
Rupjyoti Borah
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Numerical Results ◽  
Dual Solutions ◽  
Suction Parameter ◽  
Similarity Transformations ◽  
Layer Flow ◽  
Mass Transfers

Boundary layer flow with heat and mass transfers over a stretching/shrinking cylinder has been investigated. The governing partial differential equations are converted into a set of ordinary differential equations using suitable similarity transformations and have been solved numerically using MATLAB built in bvp4c solver technique. The numerical results are graphically discussed in the form of velocity, temperature and concentration distributions for various values of flow parameters. Numerical results show that dual solutions are possible in specific range of the suction parameter. A stability analysis is executed to obtain which solution is linearly stable and physically realizable.

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