A study of fractional Oldroyd-B fluid flow in a ciliated tube

Maqbool, Khadija; Ansar, Hajra; Mann, Amer Bilal; Poncet, Sebastien

doi:10.24200/sci.2025.63613.8527

A study of fractional Oldroyd-B fluid flow in a ciliated tube

Articles in Press

Document Type : Research Article

Authors

Khadija Maqbool ¹

Hajra Ansar ¹

Amer Bilal Mann ²

Sebastien Poncet ³

¹ Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan

² Department of Mathematical Sciences, Federal Urdu University of Arts, Sciences & Technology, Near Bahria Enclave, Sector C-2, Islamabad 44000, Pakistan

³ Mechanical Engineering Department, Universite de Sherbrooke, Sherbrooke (QC), J1K2R1 Canada

10.24200/sci.2025.63613.8527

Abstract

This study presents a mathematical model for the fractional Oldroyd-B fluid flow through a ciliated tube. The proposed model simulates the movement of mucus (fractional Oldroyd-B fluid) within the respiratory tract, where symplectic and antiplectic metachronal wave patterns are generated by ciliary motion. The model, though intricate, is simplified using the lubrication approach, and the resulting partial differential Equations (pdes) are solved using the fractional Adomian Decomposition Method (ADM). For the analysis of fluid flow, mathematical expressions for the pressure gradient, pressure rise, frictional force, and streamlines are derived, plotted, and discussed. The graphical results demonstrate that the symplectic wave pattern is more effective than the antiplectic wave pattern in transporting mucus through the respiratory tract.

Keywords

Fractional Oldroyd-B fluid

Ciliated cylinder

Metachronal waves

Fractional differential equations

Adomian decomposition method

Subjects