Similarity solutions for non-Newtonian power-law fluid flow

doi:10.1007/s10483-014-1854-6

Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (9): 1155-1166.doi: https://doi.org/10.1007/s10483-014-1854-6

Similarity solutions for non-Newtonian power-law fluid flow

D. M. WEI¹, S. AL-ASHHAB²

1. Department of Mathematics, University of New Orleans, LA 70148, U. S. A.;
2. Department of Mathematics, Al Imam Mohammad Ibn Saud Islamic University, Riyadh 11623, Saudi Arabia

收稿日期:2013-03-18 修回日期:2014-02-19 出版日期:2014-09-01 发布日期:2014-09-01
通讯作者: S. AL-ASHHAB, samer_ashhab@yahoo.com E-mail:samer_ashhab@yahoo.com

Similarity solutions for non-Newtonian power-law fluid flow

D. M. WEI¹, S. AL-ASHHAB²

1. Department of Mathematics, University of New Orleans, LA 70148, U. S.A.;
2. Department of Mathematics, Al Imam Mohammad Ibn Saud Islamic University, Riyadh 11623, Saudi Arabia

Received:2013-03-18 Revised:2014-02-19 Online:2014-09-01 Published:2014-09-01

摘要/Abstract

摘要： The problem of the boundary layer flow of power law non-Newtonian fluids with a novel boundary condition is studied. The existence and uniqueness of the solutions are examined, which are found to depend on the curvature of the solutions for different values of the power law index n. It is established with the aid of the Picard-Lindelöf theorem that the nonlinear boundary value problem has a unique solution in the global domain for all values of the power law index n but with certain conditions on the curvature of the solutions. This is done after a suitable transformation of the dependent and independent variables. For 0 < n 1, the solution has a positive curvature, while for n > 1, the solution has a negative or zero curvature on some part of the global domain. Some solutions are presented graphically to illustrate the results and the behaviors of the solutions.

关键词: uniqueness, existence, boundary layer flow, non-linear boundary value problem, power law fluid

Abstract: The problem of the boundary layer flow of power law non-Newtonian fluids with a novel boundary condition is studied. The existence and uniqueness of the solutions are examined, which are found to depend on the curvature of the solutions for different values of the power law index n. It is established with the aid of the Picard-Lindelöf theorem that the nonlinear boundary value problem has a unique solution in the global domain for all values of the power law index n but with certain conditions on the curvature of the solutions. This is done after a suitable transformation of the dependent and independent variables. For 0 < n 1, the solution has a positive curvature, while for n > 1, the solution has a negative or zero curvature on some part of the global domain. Some solutions are presented graphically to illustrate the results and the behaviors of the solutions.

Key words: boundary layer flow, non-linear boundary value problem, uniqueness, power law fluid, existence

中图分类号:

O357.1

D. M. WEI;S. AL-ASHHAB. Similarity solutions for non-Newtonian power-law fluid flow[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(9): 1155-1166.

参考文献

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Similarity solutions for non-Newtonian power-law fluid flow

Similarity solutions for non-Newtonian power-law fluid flow

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