Exact solutions of starting flows for a fractional Burgers' fluid between coaxial cylinders

被引：32

作者：

Khan, M. ^{[1
]}

Ali, S. Hyder ^{[1
]}

Qi, Haitao ^{[2
]}

机构：

[1] Quaid I Azam Univ, Dept Math, Islamabad 44000, Pakistan

[2] Shandong Univ Weihai, Dept Appl Math, Weihai 264209, Peoples R China

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2009年 / 10卷 / 03期

关键词：

Exact solutions; Burgers' fluid; Fractional calculus; Concentric cylinders; OLDROYD-B FLUID; VISCOELASTIC FLUID; MAXWELL MODEL; VELOCITY;

D O I：

10.1016/j.nonrwa.2008.02.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the unsteady flows of a viscoelastic fluid between two infinitely long concentric circular cylinders. The fractional calculus approach in the constitutive relationship model of a Burgers' fluid is introduced. With the help of integral transforms (the Laplace transform and the Weber transform), exact solutions are constructed for the following two problems: (i) when the outer cylinder makes a simple harmonic oscillation; and (ii) when the outer cylinder suddenly begins rotating while the inner cylinder remains stationary. Some previous and classical results can be recovered from the presented results, such as starting solutions for second grade, Maxwell, Oldroyd-B, and Burgers' fluids. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：1775 / 1783

页数：9

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