Flow over a Streaming Stretching Surface with Slip Boundary Conditions and Suction/injection Effects

This study is concerned with the 2-D steady laminar boundary layer flow over a stretching surface with slip boundary conditions near the wall embedded in a suction/ injection .The plate is maintained free stream velocity in the form. To find the similar solutions we introduce the modified stream functions. Appropriate similar transformations are used to reduce the arising PDE's into ODE's and solved through the use of Mapple-13 [1]. Expressions for stream function and velocity component are obtained. Nomenclatures x Dimensional coordinate along and normal to the plate y Dimensional coordinate along and normal to the plate Surface velocity along the wall ɳ Similarity parameter Stream function Stream function Velocity profile g Velocity profile 2 2 1) (x c x c x U w   w U f g f 

. To find the similar solutions we introduce the modified stream functions.Appropriate similar transformations are used to reduce the arising PDE's into ODE's and solved through the use of Mapple-13 [1] .Expressions for stream function and velocity component are obtained .

Missing slope
The slip co-efficient having dimension of length a Velocity slip parameter Suction/injection The velocity of suction / injection depending on > 0 or < 0 respectively

Governing Equations and Mathematical analysis [2]
Let us consider the steady ,incompressible, viscous, laminar flow over a stretching plate with connective boundary conditions as shown in figure .The equal and opposite forces are acted along the x-axis .So that the surface is stretched by keeping the origin fixed .That is , and are arbitrary constants .No significant gradient of pressure in the x-direction .Surface slip flow condition is used because of rarefied flow .The simplified equation of motion based on above assumptions are known as the boundary layer equations are given as: ………………………… (2) Subject to the boundary conditions on the problem are given by: , …………………………… 1.1 Scaling analysis: where ∧ are constants.
To find a solution of equations ( 1) and ( 2), we introduce the modified stream functions f(ɳ)and g(ɳ),which for the present problem are given by ,
Using relations (5) we find that Equations ( 1) and ( 2) can be transformed into the corresponding ordinary differential equations.
The effects of suction / injection parameter h on stream function profile f(ɳ) which displayed in figure-1.It is observed that the presence of h causes higher induction to the fluid which enhanced the velocity.

Conclusions
The equation for a laminar boundary layer can be solved nondimensionally in the presence of slip flow conditions.
The similarity solution indicate that: (1) Stream function increases as suction / injection parameter increases.

x
Dimensional coordinate along and normal to the plate y Dimensional coordinate along and normal to the plate Surface velocity along the wall ɳ

Figure- 2
Figure-2 shows the variation in the stream function profile of g(ɳ) with an increase in h.From this figure we see that the g(ɳ) increase with the increasing values of suction/injection parameter.

Figure- 3
Figure-3 illustrates the effects of suction/injection parameter h on velocity profile of the flow f′(ɳ).It is observed that the profile decreases with increasing h.

Figure- 4
Figure-4 illustrates that presence of h causes a huge restriction to the fluid velocity profile of the flow g′(ɳ) which induces less flow motion in momentum boundary layer.

Figure- 8
Figure-8 displays that for an velocity slip parameter the velocity profiles of the flow g′(ɳ) increases as a increases.