Boundary-layer flow on a continuously moving surface through a quiet ambient fluid is a significant topic in engineering because it has several applications in engineering processes. A number of engineering problems have been encountered where the flow is generated by continuous surface movement, which has numerous applications in industries such as rubber sheet manufacture, glass fiber production, paper production, petroleum extraction, polymer processing, filament extrusion continuously from a die and strengthening of copper wires.

The boundary layer flow of viscous incompressible fluid on moving surface with constant velocity was first examined by

The similarity analysis of MHD boundary layer flow of non-Newtonian Prandtl-Eyring fluid was investigated by

In view of aforementioned literature survey, it is concluded that Prandtl-Eyring fluid flow on stretching sheet is discussed using deductive group theoretic method first time. In the paper, the problem of Blasius boundary layer for Prandtl-Eyring fluid the governing partial differential equations past a stretching sheet is discussed. The governing equations of the flow problem are non-linear partial differential equations. The similarity of these equations is obtained using one parameter deductive group theoretic method, the most powerful similarity method. The resulting higher order non-linear ODE are then solved using MATLAB bvp4c solver and presented graphically. We also carried out the analysis of different parameters

The two-dimensional laminar boundary layer flows pasts a stretching sheet is considered. The governing equation of continuity and momentum equation of Blasius boundary layer flow of Prandtl-Eyring fluid past a stretching sheet are:

With boundary conditions

Using stream function

The dimensionless basic partial differential equations for forced convection flow of nonNewtonian fluid with stream function

Subject to boundary conditions:

With stress-strain relation

Where, B and C are fluid parameters.

In this paper, the deductive one parameter group theoretic method is used. Under this group transformation, two independent variables will be reduced by one, and boundary value type partial differential

Introduced a one-parameter group transformation of the form

Where '

Therefore

The invariance of

Therefore

and

Therefore,

The invariance of boundary condition gives:

Combining the results

Our aim to represent the problem in the form of ordinary differential equation. Now we have proceeded in our analysis to obtain a complete set of absolute invariants. If

is the absolute invariant for dependent variables

Where,

and

Using definition of

The absolute invariant of independent variable owing the

Applying the variable separable method we get,

Similarly, the absolute invariants for dependent variables owing (

Independent and dependent absolute invariants are used to convert

Where,

Subject to the boundary conditions

Finally, we have third order ordinary non-linear differential

Numerical calculations are performed to analyze the behavior of the Blasius boundary layer model for Prandtl-Eyring fluid flow on stretching sheet. Differential

The following two cases depict the graphical representations of the numerical results for different governing parameters influencing the proposed model's flow behavior.

1.

2.

The present study shows the flow behavior of the Blasius boundary layer model for PrandtlEyring fluid flow on stretching sheet. The key findings of the current analysis are summarized as

• The parameter

• The parameter

In the present work, we consider

This helps in regulating the rate of fluid velocity in manufacturing processes and hence industrial applications to produce product of the appropriate quality.

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