Eur. Phys. J. Plus (2015) 130: 114
https://doi.org/10.1140/epjp/i2015-15114-5

Regular Article

Shock wave development in couple stress fluid-filled thin elastic tubes

¹ Department of Mathematical Sciences, Redeemer’s University, Ede, Nigeria
² Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
³ Department of Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
⁴ Department of Mathematical Sciences, Delaware State University, Dover, DE, 19901-2277, USA
⁵ Faculty of Science, Department of Mathematics, King Abdulaziz University, 21589, Jeddah, Saudi Arabia

^* e-mail: mostafa.eslami@umz.ac.ir

Received: 17 March 2015
Revised: 5 May 2015
Accepted: 14 May 2015
Published online: 18 June 2015

Abstract

This paper looks at the propagation of nonlinear waves through a fluid-filled elastic tube. Viscosity of fluid is taken into account. Using the reductive perturbation method, a nonlinear evolution equation (NLEE) is obtained and the exact travelling wave solution of the equation is obtained using the tanh method. The result shows that blood hyper-viscosity has a significant effect on the propagation of flow and pressure pulse waves.