Numerical Study of Non-Newtonian Maxwell Fluid in the Region of Oblique Stagnation Point Flow over a Stretching Sheet

2015 ◽  
Vol 32 (2) ◽  
pp. 175-184 ◽  
Author(s):  
T. Javed ◽  
A. Ghaffari
Keyword(s):  
Boundary Layer ◽  
Stagnation Point ◽  
Shooting Method ◽  
Stretching Sheet ◽  
Numerical Study ◽  
Maxwell Fluid ◽  
Governing Equations ◽  
Boundary Layer Equations ◽  
Parameter Ratio ◽  
Two Dimensional Flow

AbstractIn this article, a numerical study is carried out for the steady two-dimensional flow of an incompressible Maxwell fluid in the region of oblique stagnation point over a stretching sheet. The governing equations are transformed to dimensionless boundary layer equations. After some manipulation a system of ordinary differential equations is obtained, which is solved by using parallel shooting method. A comparison with the previous studies is made to show the accuracy of our results. The effects of involving parameters are discussed in detail and the streamlines are drawn to predict the flow pattern of the fluid. It is observed that increasing velocities ratio parameter (ratio of straining to stretching velocity) helps to decrease the boundary layer thickness. Furthermore, the velocity of fluid increases by increasing the obliqueness parameter.

Elastico-viscous boundary-layer flows I. Two-dimensional flow near a stagnation point

1964 ◽  
Vol 60 (3) ◽  
pp. 667-674 ◽  
Author(s):  
D. W. Beard ◽  
K. Walters
Keyword(s):  
Boundary Layer ◽  
Stagnation Point ◽  
Solid Boundary ◽  
Two Dimensional ◽  
Boundary Layer Flows ◽  
Viscous Boundary Layer ◽  
Boundary Layer Equations ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Viscous Boundary

AbstractThe Prandtl boundary-layer theory is extended for an idealized elastico-viscous liquid. The boundary-layer equations are solved numerically for the case of two-dimensional flow near a stagnation point. It is shown that the main effect of elasticity is to increase the velocity in the boundary layer and also to increase the stress on the solid boundary.

Symmetry Analysis of Boundary Layer Equations of an Upper Convected Maxwell Fluid with Magnetohydrodynamic Flow

2011 ◽  
Vol 66 (5) ◽  
pp. 321-328
Author(s):  
Gözde Deǧer ◽  
Mehmet Pakdemirli ◽  
Yiǧit Aksoy
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Boundary Conditions ◽  
Stretching Sheet ◽  
Mhd Flow ◽  
Maxwell Fluid ◽  
Similarity Solutions ◽  
Variable Magnetic Field ◽  
Physical Parameters ◽  
Boundary Layer Equations

Steady state boundary layer equations of an upper convected Maxwell fluid with magnetohydrodynamic (MHD) flow are considered. The strength of the magnetic field is assumed to be variable with respect to the location. Using Lie group theory, group classification of the equations with respect to the variable magnetic field is performed. General boundary conditions including stretching sheet and injection are taken. Restrictions imposed by the boundary conditions on the symmetries are discussed. Special functional forms of boundary conditions for which similarity solutions may exist are derived. Using the symmetries, similarity solutions are presented for the case of constant strength magnetic field. Stretching sheet solutions with or without injection are presented. Effects of physical parameters on the solutions are depicted.

Boundary layer flow of an Oldroyd-B fluid in the region of a stagnation point over a stretching sheet

2010 ◽  
Vol 88 (9) ◽  
pp. 635-640 ◽  
Author(s):  
M. Sajid ◽  
Z. Abbas ◽  
T. Javed ◽  
N. Ali
Keyword(s):  
Boundary Layer ◽  
Stagnation Point ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
Dimensional Boundary ◽  
Layer Flow ◽  
Parameter Values ◽  
The Mathematical Model

In this paper, the mathematical model for the two-dimensional boundary layer flow of an Oldroyd-B fluid is presented. The developed equations are used to discuss the problem of two-dimensional flow in the region of a stagnation point over a stretching sheet. The obtained partial differential equations are reduced to an ordinary differential equation by a suitable transformation. The obtained equation is then solved using a finite difference method. The influence of the pertinent fluid parameters on the velocity is discussed through graphs. The behaviour of f ″(0) is also investigated with changes in parameter values. It is observed that an increase in the relaxation time constant causes a reduction in the boundary layer thickness. To the best of our knowledge, this type of solution for an Oldroyd-B fluid is presented for the first time in the literature.

Stagnation-point flow of Jeffrey fluid with melting heat transfer and Soret and Dufour effects

2014 ◽  
Vol 24 (2) ◽  
pp. 402-418 ◽  
Author(s):  
T. Hayat ◽  
Z. Iqbal ◽  
M. Mustafa ◽  
A. Alsaedi
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Stagnation Point ◽  
Thermal Diffusion ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Jeffrey Fluid ◽  
Content Type ◽  
Melting Heat ◽  
Layer Flow

Purpose – This investigation has been carried out for thermal-diffusion (Dufour) and diffusion-thermo (Soret) effects on the boundary layer flow of Jeffrey fluid in the region of stagnation-point towards a stretching sheet. Heat transfer occurring during the melting process due to a stretching sheet is considered. The paper aims to discuss these issues. Design/methodology/approach – The authors convert governing partial differential equations into ordinary differential equations by using suitable transformations. Analytic solutions of velocity and temperature are found by using homotopy analysis method (HAM). Further graphs are displayed to study the salient features of embedding parameters. Expressions of skin friction coefficient, local Nusselt number and local Sherwood number have also been derived and examined. Findings – It is found that velocity and the boundary layer thickness are increasing functions of viscoelastic parameter (Deborah number). An increase in the melting process enhances the fluid velocity. An opposite effect of melting heat process is noticed on velocity and skin friction. Practical implications – The boundary layer flow in non-Newtonian fluids is very important in many applications including polymer and food processing, transpiration cooling, drag reduction, thermal oil recovery and ice and magma flows. Further, the thermal diffusion effect is employed for isotope separation and in mixtures between gases with very light and medium molecular weight. Originality/value – Very scarce literature is available on thermal-diffusion (Dufour) and diffusion-thermo (Soret) effects on the boundary layer flow of Jeffrey fluid in the region of stagnation-point towards a stretching sheet with melting heat transfer. Series solution is developed using HAM. Further, the authors compare the present results with the existing in literature and found excellent agreement.

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