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# A rational approximation to the boundary layer flow of a non-Newtonian fluid

• Kourosh Parand
• Mina Fotouhifar
• Hossein Yousefi
• Mehdi Delkhosh
Technical Paper

## Abstract

This paper presents a computational technique for the investigation of boundary layer flow over a stretching sheet for a Powell–Eyring non-Newtonian fluid. The quasilinearization method finds a recursive formula for higher-order deformation equations which are then solved using the rational Boubaker collocation method so-called the QLM-RBC method. The solution for velocity is computed by applying the QLM-RBC method. The governing nonlinear partial differential equations are reduced to the nonlinear ordinary differential equations by similarity transformations. The momentum equation with infinite boundary values using the quasilinearization method converts to the sequence of linear ordinary differential equations to obtain the solution. In addition, the equation is solved on a semi-infinite domain without truncating it to a finite domain by choosing rational bases for the collocation method. Illustrative figures are included to demonstrate the physical influence of different parameters on the velocity profile. The method is easy to implement and yields accurate results.

## Keywords

Boundary layer flow Quasilinearization method Rational Boubaker functions Powell–Eyring fluid

## List of symbols

T (kg/m s2)

Shear stress component of extra stress tensor

$$\mu$$ (kg/m s)

Dynamic viscosity of the fluid

uv (m/s)

Non-dimensional velocity components along x- and y-axes

xy (m)

Non-dimensional Cartesian coordinates

$$\zeta$$ (m2/s)

Kinematic viscosity of the fluid

$$\rho$$ (kg/m3)

fluid density

ax (m/s)

Stretching velocity

$$\beta , c$$

Fluid parameters

$$\psi$$

Stream function

p

Pressure m: the number of basis functions

a

Stretching constant

$$f(\eta )$$

Dimensionless stream function

$$\eta$$

Similarity variable

M

Non-dimensional fluid parameter

$$\lambda$$

Local non-dimensional fluid parameter

$$C_{\text{f}}$$

Local skin-friction coefficient

$$Re_{x}$$

Local Reynolds number

$${\text{RB}}_n$$

Basis function

L

Shape parameter

m

The number of basis functions

## Mathematics Subject Classification

76A05 74S25 76D05 76M55 34B40

## Notes

### Conflict of interest

The authors declare that they have no conflict of interest.

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## Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

## Authors and Affiliations

• Kourosh Parand
• 1
• 2
Email author
• Mina Fotouhifar
• 1
• Hossein Yousefi
• 1
• Mehdi Delkhosh
• 3
1. 1.Department of Computer SciencesShahid Beheshti University, G.C.TehranIran
2. 2.Department of Cognitive Modelling, Institute for Cognitive and Brain SciencesShahid Beheshti University, G.C.TehranIran
3. 3.Department of Mathematics and Computer SciencesIslamic Azad University, Bardaskan BranchBardaskanIran