0
Flows in Complex Systems

Analytic Approximations for Cooling Turbine Disks

[+] Author and Article Information
A. El-Nahhas

Mathematics Department, Helwan Faculty of Science,  Helwan University, Helbawy Street, 11795 Cairo, Egyptaasayed35@yahoo.com

J. Fluids Eng 134(8), 081103 (Jul 27, 2012) (7 pages) doi:10.1115/1.4006993 History: Received February 01, 2012; Revised June 20, 2012; Published July 27, 2012; Online July 27, 2012

In this paper, we use the homotopy analysis method as a tool to obtain analytic approximations to the nonlinear problem of the cooling of turbine disks with a non-Newtonian viscoelastic fluid. The application of this method is executed via a polynomial exponential basis. The effects on velocity and temperature profiles with variations of the cross viscosity parameter, the Reynolds number, and the Prandtl number are discussed. A comparison with corresponding results of the perturbation method is illustrated and also, as a result of application of the homotopy analysis method, an analytic evaluation for the Nusselt number compared to the perturbation method is achieved.

FIGURES IN THIS ARTICLE
<>
Copyright © 2012 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 13

Comparison of homotopy solution for the temperature profile qn(η) (solid) with the perturbation solution (dashed) at n = 0,Re = 10,K = 0.01,Pr = 2.5

Grahic Jump Location
Figure 12

Comparison of the homotopy solution for velocity profile f'(η) (solid) with the perturbation solution (dashed) at K = 0,Re = 50

Grahic Jump Location
Figure 11

Comparison of the homotopy solution for velocity profile f'(η) (solid) with the perturbation solution (dashed) at K = 0,Re=10

Grahic Jump Location
Figure 7

Effects on the friction factor profile f′(0) for continuous values of Re and different values of K

Grahic Jump Location
Figure 6

Effects on the velocity profile f'(η) at Re = 50 and different values of K

Grahic Jump Location
Figure 5

Effects on the velocity profile f'(η) at Re = 10 and different values of K

Grahic Jump Location
Figure 4

Effects on the velocity profile f'(η) at Re = 1 and different values of K

Grahic Jump Location
Figure 3

The h-curve of q′n(0) at n = 2,K = 0.01,Re = 1,Pr = 1

Grahic Jump Location
Figure 2

The h-curve of f′(0) at n = 2,K = 0.01,Re = 1,Pr = 1

Grahic Jump Location
Figure 1

Physical model for channel flow

Grahic Jump Location
Figure 10

Comparison of the homotopy solution for velocity profile f'(η) (solid) with the perturbation solution (dashed) at K = 0,Re=1

Grahic Jump Location
Figure 9

Effects on temperature profile qn(η) at Re = 10,Pr = 2.5, K = 0.01 and different values of n

Grahic Jump Location
Figure 8

Effects on temperature profile qn(η) at Re = 2.5,Pr = 2.5,K = 0.01 and different values of n

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In