Flow on oscillating rectangular duct for Maxwell fluid  

作　　者：M.NAZAR F.SHAHID M.SAEED AKRAM Q.SULTAN 

机构地区：[1]Centre for Advanced Studies in Pure and Applied Mathematics,Bahauddin Zakariya University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2012年第6期717-730,共14页应用数学和力学（英文版）

基　　金：Project supported by the Higher Education Commission of Pakistan

摘　　要：This paper presents an analysis for the unsteady flow of an incompress- ible Maxwell fluid in an oscillating rectangular cross section. By using the Fourier and Laplace transforms as mathematical tools, the solutions are presented as a sum of the steady-state and transient solutions. For large time, when the transients disappear, the solution is represented by the steady-state solution. The solutions for the Newtonian fluids appear as limiting cases of the solutions obtained here. In the absence of the fre- quency of oscillations, we obtain the problem for the flow of the Maxwell fluid in a duct of a rectangular cross-section moving parallel to its length. Final!y, the required time to reach the steady-state for sine oscillations of the rectangular duct is obtained by graphical illustrations for different parameters. Moreover, the graphs are sketched for the velocity.This paper presents an analysis for the unsteady flow of an incompress- ible Maxwell fluid in an oscillating rectangular cross section. By using the Fourier and Laplace transforms as mathematical tools, the solutions are presented as a sum of the steady-state and transient solutions. For large time, when the transients disappear, the solution is represented by the steady-state solution. The solutions for the Newtonian fluids appear as limiting cases of the solutions obtained here. In the absence of the fre- quency of oscillations, we obtain the problem for the flow of the Maxwell fluid in a duct of a rectangular cross-section moving parallel to its length. Final!y, the required time to reach the steady-state for sine oscillations of the rectangular duct is obtained by graphical illustrations for different parameters. Moreover, the graphs are sketched for the velocity.

关 键 词：Maxwell fluid oscillating rectangular duct velocity field 

分 类 号：O357.2[理学—流体力学]