On transport of reactive solute in a pulsatile Casson fluid flow through an annulus

Abstract

This paper examines the effect of heterogeneous chemical reaction on the transport of a solute in a Casson fluid flow through an annular pipe under a periodic pressure gradient. Aris–Barton's method of moments is employed to understand the transport process. A finite difference implicit scheme is utilized to solve the momentum equation as well as the integral moment equation arising from the unsteady convective diffusion equation. Using the Hermite polynomial representation, the mean concentration distribution in the axial direction is acquired from the first four central moments. The transport phenomenon is discussed by three transport coefficients, namely exchange, advection, and dispersion coefficients owing to wall reactions, yield stress, radius ratio, etc. The present study can, therefore, be helpful to understand the transport process in blood flow through arteries.

Keywords:

• Casson fluid
• yield stress
• integral moments
• reversible and irreversible reactions
• finite difference method

2010 AMS SUBJECT CLASSIFICATIONS:

• Physiological flows: 76Z05 (2010)
• Biomechanics: 92C10 (2010)
• Non-Newtonian fluids: 76A05 (2010)
• PDEs in connection with fluid mechanics: 35Q35 (2010)
• Finite difference methods: 65M06 (2010)

Acknowledgments

The authors greatly acknowledge the valuable suggestions and comments of editor and reviewers.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

S. Debnath is thankful to the National Institute of Technology, Agartala, India for financial support for pursuing this work.