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.

On Numerical Prediction of the Stability of Hypersonic Boundary-Layer Flow Over a Row of Microcavities

2003 ◽  
Author(s):  
Vassilios Theofilis ◽  
Michel O. Deville ◽  
Peter W. Duck ◽  
Alexander Fedorov
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Flow Instability ◽  
Viscous Sublayer ◽  
Hypersonic Boundary Layer ◽  
Two Dimensional ◽  
Flow Stabilization ◽  
Two Dimensional Flow ◽  
Dimensional Boundary ◽  
Layer Flow

This paper is concerned with the structure of steady two–dimensional flow inside the viscous sublayer in hypersonic boundary–layer flow over a flat surface in which microscopic cavities (‘microcavities’) are embedded. Such a so–called Ultra Absorptive Coating (UAC) has been predicted theoretically [1] and demonstrated experimentally [2] to stabilize passively hypersonic boundary–layer flow. In an effort to further quantify the physical mechanism leading to flow stabilization, this paper focuses on the nature of the basic flows developing in the configuration in question. Direct numerical simulations are performed, addressing firstly steady flow inside a singe microcavity, driven by a constant shear, and secondly a model of a UAC surface in which the two–dimensional boundary layer over a flat plate and a minimum nontrivial of two microcavities embedded in the wall are solved in a coupled manner. The influence of flow– and geometric parameters on the obtained solutions is illustrated. Based on the results obtained, the limitations of currently used theoretical methodologies for the description of flow instability are identified and suggestions for the improved prediction of the instability characteristics of UAC surfaces are discussed.

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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