Meccanica

, Volume 48, Issue 4, pp 875–886

# Approximate solution of non-Newtonian viscoelastic fluid flow on a turbine disc for cooling purposes by using Adomian decomposition method

• G. Domairry
• Z. Ziabakhsh
• H. Doumiri Ganji
• Modil Habibi
Article

## Abstract

In this work, a powerful semi-analytical method, called Adomian decomposition method (ADM) is introduced to obtain the exact solution of heat transfer equation of a non-Newtonian fluid flow in an axisymmetric channel with a porous wall which is useful for turbine cooling applications. This method is employed to obtain the expressions for velocity and temperature fields. Then, the influence of the two dimensionless numbers: the Prandtl number (Pr) and the Reynolds number (Re) for the dynamic forces have been considered. Comparisons are made between the numerical method (NM) solution, Homotopy perturbation method (HPM), Variation iteration method (VIM) and the results of Adomian decomposition method (ADM). The results reveal that this method is very effective and simple and can be applied for other nonlinear problems.

## Keywords

Adomian decomposition method (ADM) Numerical method (NM) Viscoelastic fluid Non-Newtonian fluid Heat transfer

## Nomenclature

VIM

Variational iteration method

NM

Numerical method

HPM

Homotopy perturbation method

P

Pressure

q

Rate of heat transfer

$$\operatorname{Re}$$

Reynolds number

u

Dimensionless velocity

$$\operatorname{Pr}$$

Prandtl number

k

Thermal conductivity

T

Temperature

C

Specific heat

L

Linear parameter

N

Nonlinear parameter

## Greek symbols

ρ

Fluid density

υ

Kinematic viscosity

τ

Stress matrix

Φ

Dissipation function

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## Authors and Affiliations

• G. Domairry
• 1
• Z. Ziabakhsh
• 1
• H. Doumiri Ganji
• 2
• Modil Habibi
• 1
1. 1.Department of Mechanical EngineeringBabol University of TechnologyBabolIran
2. 2.Young Researchers club, Science and Research BranchIslamic Azad UniversityTehranIran