# Water Boundary Layer Flow over an Exponentially Permeable Stretching Sheet with Variable Viscosity and Prandtl Number

• Abhishek Kumar Singh
• N. Govindaraj
• S. Roy
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 308)

## Abstract

The present work focus on water boundary layer flow over an exponential permeable stretching sheet in the presence of suction/injection with variable viscosity and prandtl number. The nonlinear partial differential equations governing flow and thermal fields are presented in non-dimensional form using suitable non-similar transformation. Finally non dimensional partial differential the equations are solved by the implicit finite difference method in combination with the Quasi-linearization technique. The numerical results for skin-friction and local Nusselt number are shown graphically to display effects of physical parameters.

## Keywords

Exponential permeable stretching sheet Water boundary layer Variable Prandtl number Quasilinearization technique Variable viscosity

## Nomenclature

Pr

Prandtl number

f

Dimensionless streamfunction

$$C_{p}$$

Specific heat at constant pressure

T

Temperature

g

Acceleration due to gravity

$$U_{W}$$

Moving plate velocity

$$Nu_{x}$$

Nusselt number

$$Cf_{x}$$

Skin friction coefficient

$$U_{\infty }$$

Free stream velocity

v

Velocity component in the y direction

u

Velocity component in the x direction

$$\nu$$

Kinematic viscosity

$$\rho$$

Density

xy

Cartesian coordinates

$$Re_{L}$$

Local Reynolds number

$$\mu$$

Dynamic viscosity

## Notes

### Acknowledgements

Let me thanks organization team of International Conference on Mathematical Modelling and Scientific Computing who brought the platform to express our idea about mathematical modelling and simulation in applied mathematics. The current work is completely based on modelling of fluid dynamics problem and solution has been obtained by using finite difference method and given in terms of velocity profile (F), temperature profile $$(\theta )$$, skin friction coefficient $$(C_{fx} \left( Re_L\xi exp({\xi })\right) ^{1/2})$$ and heat transfer coefficients $$(Nu_x (Re_L\xi exp({\xi }))^{-1/2})$$.

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