Analytical and numerical study for oscillatory flow of viscoelastic fluid in a tube with isosceles right triangular cross section

A theoretical investigation is carried out to analyze the oscillatory flow of second-grade fluid under the periodic pressure gradient in a long tube of isosceles right triangular cross section in the present study. The analytical expressions for the velocity profile and phase difference are obtained. The numerical solutions are calculated by using the finite difference method with Crank-Nicolson (C-N) scheme. In comparison with the Newtonian fluid (lambda = 0), the effects of retardation time, Deborah number and Womersley number on the velocity profile and phase difference are discussed numerically and graphically. For smaller Womersley number, the behavior of second-grade fluid is dominated by viscosity. For larger Womersley number alpha = 20, the flow becomes more difficult to be generated under periodic pressure gradient with increasing retardation time. Furthermore, the analytical expressions of the mean velocity amplitude and phase difference are given explicitly for discussing.