# Heat transfer in oblique stagnation-point flow of an incompressible viscous fluid towards a stretching surface

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## Abstract

Steady two-dimensional oblique stagnation-point flow of an incompressible viscous fluid over a flat deformable sheet is investigated when the sheet is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. It is shown that the flow has a boundary layer structure for values of *a*/*c* (> 1), where *ax*+2*by* and *cx* are the *x*-component of the free stream velocity and the stretching velocity of the plate respectively, *x* being the distance from the stagnation-point. On the other hand when *a*/*c* < 1, the flow has an inverted boundary layer structure. It is also observed that the velocity at a point increases with increase in the free stream shear. For a fixed value of *a*/*c*, the streamlines becomes more and more oblique towards the left of the stagnation-point with increase in *b*/*c* where *b* > 0. On the other hand the streamlines become increasingly oblique to the right of the stagnation-point with increase in |*b*/*c*| when *b* < 0. For a fixed value of the Prandtl number *Pr*, temperature at a point decreases with increase in *a*/*c*. Further for a given value of *a*/*c*, the surface heat flux increases with increase in *Pr*.

## Keywords

Free Stream Surface Heat Flux Incompressible Viscous Fluid Surface Shear Stress Boundary Layer Structure## List of symbols

*a*Constant proportional to free stream straining velocity

*b*Constant proportional to free stream shear velocity far away from the sheet

*c*Proportionality constant of the velocity of the stretching sheet

*f*Function proportional to the velocity component normal to the sheet

*g*Function whose derivative is the part of the velocity component parallel to the sheet due to shear

*F*Dimensionless velocity component normal to the sheet

*W*Dimensionless form of g

*p*Fluid pressure

*Pr*Prandtl number

*T*Fluid temperature

*T*_{w}Constant sheet temperature

*T*_{∞}Constant free stream temperature

*u*Dimensional velocity component along the sheet

- \(v\)
Dimensional velocity component normal to the sheet

*U*Dimensionless velocity component along the sheet

*V*Dimensionless velocity component normal to the sheet

*x*Distance along the sheet

*y*Distance normal to the sheet

## Greek symbols

- ψ
_{0} Stream function of the inviscid flow

- τ
_{ij} Stress tensor

*e*_{ij}Rate-of-strain tensor

- η
Dimensionless distance normal to the sheet

- ξ
Dimensionless distance along the sheet

- θ
Dimensionless fluid temperature

- ν
Kinematic viscosity coefficient

- ρ
Fluid density

- μ
Dynamic coefficient of viscosity

- τ
_{0} Dimensionless surface shear stress

- λ
Thermal diffusivity of the fluid

## Notes

### Acknowledgements

We thank the referee for his comments which enabled an improved presentation of the paper. We also thank Dr. I. Pop for his kind help in the preparation of the paper. The work of one of the Authors (T.R.M) is supported under SAP (DRS PHASE I) under UGC, New Delhi, India (Sanction letter no. F.510/8/DRS/2004(SAP-I)).

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