Unsteady MHD Couette flow of a generalized Oldroyd-B fluid with fractional derivative

被引：75

作者：

Liu, Yaqing ^{[1
,2
]}

Zheng, Liancun ^{[1
]}

Zhang, Xinxin ^{[2
]}

机构：

[1] Univ Sci & Technol Beijing, Dept Math & Mech, Beijing 100083, Peoples R China

[2] Univ Sci & Technol Beijing, Sch Mech Engn, Beijing 100083, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2011年 / 61卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Oldroyd-B fluid; Couette flow; Laplace transform; Fox H-function; Analytical solution; CONSTANTLY ACCELERATING PLATE; VISCOELASTIC FLUID;

D O I：

10.1016/j.camwa.2010.11.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents an analytical study for the magnetohydrodynamic (MHD) flow of a generalized Oldroyd-B fluid. The fractional calculus approach is used to establish the constitutive relationship model of a viscoelastic fluid. Exact analytic solutions for the velocity field and shear stress in terms of Fox H-function are obtained by means of the Laplace transform. The influence of the relaxation and retardation times, the orders of the time fractional derivative and the magnetic body force on the velocity and shear stress are analyzed. It is shown that the ordinary Oldroyd-B fluid, generalized second grade fluid and Maxwell fluid are the limiting cases of the presented results. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：443 / 450

页数：8

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