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Evaluation of closed-form solutions based on the HPM and HAM approaches for the steady flow of third grade fluids in a porous half space

Evaluation of closed-form solutions based on the HPM and HAM approaches for the steady flow of third grade fluids in a porous half space
Evaluation of closed-form solutions based on the HPM and HAM approaches for the steady flow of third grade fluids in a porous half space
In this paper, a closed-form solution for the steady flow of a third grade fluid in a porous half-space is presented. The governing non-linear ordinary differential equation is solved in closed form by means of the homotopy perturbation method (HPM), and it is shown that just two terms in the series expansion is sufficient to obtain a highly accurate solution which is valid for the whole domain. The results obtained are compared with numerical results obtained using a fourth-order Runge–Kutta method and the homotopy analysis method (HAM). Close agreement of the two sets of results is observed thus demonstrating the accuracy of the HPM approach for the particular problem considered.
homotopy perturbation method, hpm, steady flow, homotopy analysis method, ham, velocity distribution
0272-4960
326-339
Kimiaeifar, A.
2296dad1-aa53-4141-86cd-5d77527a8d13
Thomsen, O.T.
f3e60b22-a09f-4d58-90da-d58e37d68047
Lund, E.
c663d217-9333-4b98-b59c-06c93cf4ba81
Kimiaeifar, A.
2296dad1-aa53-4141-86cd-5d77527a8d13
Thomsen, O.T.
f3e60b22-a09f-4d58-90da-d58e37d68047
Lund, E.
c663d217-9333-4b98-b59c-06c93cf4ba81

Kimiaeifar, A., Thomsen, O.T. and Lund, E. (2011) Evaluation of closed-form solutions based on the HPM and HAM approaches for the steady flow of third grade fluids in a porous half space. IMA Journal of Applied Mathematics, 76 (2), 326-339. (doi:10.1093/imamat/hxq042).

Record type: Article

Abstract

In this paper, a closed-form solution for the steady flow of a third grade fluid in a porous half-space is presented. The governing non-linear ordinary differential equation is solved in closed form by means of the homotopy perturbation method (HPM), and it is shown that just two terms in the series expansion is sufficient to obtain a highly accurate solution which is valid for the whole domain. The results obtained are compared with numerical results obtained using a fourth-order Runge–Kutta method and the homotopy analysis method (HAM). Close agreement of the two sets of results is observed thus demonstrating the accuracy of the HPM approach for the particular problem considered.

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More information

Published date: April 2011
Keywords: homotopy perturbation method, hpm, steady flow, homotopy analysis method, ham, velocity distribution
Organisations: Engineering Mats & Surface Engineerg Gp

Identifiers

Local EPrints ID: 339104
URI: http://eprints.soton.ac.uk/id/eprint/339104
ISSN: 0272-4960
PURE UUID: 622b1dea-8d2a-4f82-af36-82d384cf6e34

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Date deposited: 23 May 2012 11:03
Last modified: 16 Jul 2019 22:03

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