SERIES SOLUTIONS FOR UNSTEADY STAGNATION POINT FLOWS OF A NON-NEWTONIAN FLUID OVER A SHRINKING SHEET

2013 ◽  
Vol 4 (4) ◽  
pp. 303-318
Author(s):  
Sohail Nadeem ◽  
Anwar Hussain ◽  
Noreen Sher Akbar
Keyword(s):  
Stagnation Point ◽  
Newtonian Fluid ◽  
Shrinking Sheet ◽  
Series Solutions

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

2020 ◽  
pp. 095440892097113
Author(s):  
Golam Mortuja Sarkar ◽  
Bikash Sahoo
Keyword(s):  
Stability Analysis ◽  
Stagnation Point ◽  
Newtonian Fluid ◽  
Stokes Equations ◽  
Temporal Stability ◽  
Dual Solutions ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Solution Branch ◽  
Upper Solution

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.

scholarly journals Heat Transfer Analysis on the Hiemenz Flow of a Non-Newtonian Fluid: A Homotopy Method Solution

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yasir Khan ◽  
Zdeněk Šmarda
Keyword(s):  
Heat Transfer ◽  
Linear Operator ◽  
Stagnation Point ◽  
Newtonian Fluid ◽  
Fluid Flows ◽  
Heat Transfer Analysis ◽  
Shrinking Sheet ◽  
Nonlinear Ordinary Differential Equations ◽  
Two Dimensional ◽  
Homotopy Perturbation

The mathematical model for the incompressible two-dimensional/axisymmetric non-Newtonian fluid flows and heat transfer analysis in the region of stagnation point over a stretching/shrinking sheet and axisymmetric shrinking sheet is presented. The governing equations are transformed into dimensionless nonlinear ordinary differential equations by similarity transformation. Analytical technique, namely, the homotopy perturbation method (HPM) with general form of linear operator is used to solve dimensionless nonlinear ordinary differential equations. The series solution is obtained without using the diagonal Padé approximants to handle the boundary condition at infinity which can be considered as a clear advantage of homotopy perturbation technique over the decomposition method. The effects of the pertinent parameters on the velocity and temperature field are discussed through graphs. To the best of authors’ knowledge, HPM solution with general form of linear operator for two-dimensional/axisymmetric non-Newtonian fluid flows and heat transfer analysis in the region of stagnation point is presented for the first time in the literature.

scholarly journals MHD stagnation point flow of micro nanofluid towards a shrinking sheet with convective and zero mass flux conditions

2017 ◽  
Vol 65 (2) ◽  
pp. 155-162 ◽  
Author(s):  
A. Rauf ◽  
S. A. Shehzad ◽  
T. Hayat ◽  
M. A. Meraj ◽  
A. Alsaedi
Keyword(s):  
Stagnation Point ◽  
Mass Flux ◽  
Numerical Technique ◽  
Convective Boundary Condition ◽  
Momentum Equation ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Convective Boundary ◽  
Electrically Conducting ◽  
Zero Mass

AbstractIn this article the stagnation point flow of electrically conducting micro nanofluid towards a shrinking sheet, considering a chemical reaction of first order is investigated. Involvement of magnetic field occurs in the momentum equation, whereas the energy and concentrations equations incorporated the influence of thermophoresis and Brownian motion. Convective boundary condition on temperature and zero mass flux condition on concentration are implemented. Partial differential equations are converted into the ordinary ones using suitable variables. The numerical technique is utilized to discuss the results for velocity, microrotation, temperature, and concentration fields.

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