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

2020 ◽  
Vol 540 ◽  
pp. 123028 ◽  
Author(s):  
Irfan Mustafa ◽  
Zaheer Abbas ◽  
Ayesha Arif ◽  
Tariq Javed ◽  
Abuzar Ghaffari
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Analytical Solution ◽  
Boundary Layer Flow ◽  
Multiple Solutions ◽  
Least Square Method ◽  
Least Square ◽  
Shrinking Sheet ◽  
Layer Flow

scholarly journals Effects of Second-Order Slip and Viscous Dissipation on the Analysis of the Boundary Layer Flow and Heat Transfer Characteristics of a Casson Fluid

2016 ◽  
Vol 21 (1) ◽  
pp. 48 ◽  
Author(s):  
Mohammad M. Rahman ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Stability Analysis ◽  
Boundary Layer Flow ◽  
Casson Fluid ◽  
Shrinking Sheet ◽  
Solution Branch ◽  
Heat Transfer Characteristics ◽  
Flow And Heat Transfer ◽  
Layer Flow

The aim of the present study is to analyze numerically the steady boundary layer flow and heat transfer characteristics of Casson fluid with variable temperature and viscous dissipation past a permeable shrinking sheet with second order slip velocity. Using appropriate similarity transformations, the basic nonlinear partial differential equations have been transformed into ordinary differential equations. These equations have been solved numerically for different values of the governing parameters namely: shrinking parametersuction parameterCasson parameterfirst order slip parametersecond order slip parameter  Prandtl number  and the Eckert number  using the bvp4c function from MATLAB. A stability analysis has also been performed. Numerical results have been obtained for the reduced skin-friction, heat transfer and the velocity and temperature profiles. The results indicate that dual solutions exist for the shrinking surface for certain values of the parameter space. The stability analysis indicates that the lower solution branch is unstable, while the upper solution branch is stable and physically realizable. In addition, it is shown that for a viscous fluida very good agreement exists between the present numerical results and those reported in the open literature. The present results are original and new for the boundary-layer flow and heat transfer past a shrinking sheet in a Casson fluid. Therefore, this study has importance for researchers working in the area of non-Newtonian fluids, in order for them to become familiar with the flow behavior and properties of such fluids.  

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.

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