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Numerical investigation of power-law non-Newtonian fluid flow in concentric annular geometry using finite difference method with convergence analysis

Radius: Journal of Science and Technology

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Volume 3, Issue 1, Article Number: 261004 (2026)

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Prahlad Singh1,*  |  Neeraj Kumar1,*  ORCID logo

1Department of Mathematics, Govt Degree College Agra Cantt, Agra – 282001, U.P. (India)

1Department of Mathematics, Government Degree College, Goverdhan, Mathura – 281502, U.P. (India)

*Corresponding Author: neerajmath2010@gmail.com

Received: 07 April 2026 | Revised: 04 May 2026

Accepted: 15 May 2026 | Published Online: 27 May 2026

DOI: https://doi.org/10.5281/zenodo.20404218

© 2026 The Authors, under a Creative Commons license, Published by Scholarly Publication

Abstract

Through a detailed numerical study, the steady, laminar, incompressible power-law non-Newtonian fluid flow in concentric annular geometry is discussed. A FDM with Picard iterative scheme is used to solve the non-linear momentum equation in cylindrical coordinate under “No Slip” conditions to study the motion of the system. The computational domain is divided into 100 radial nodes, and has a tolerance of 10-6. The flow behaviour index is analysed for 0.6, 1.0 and 1.4 corresponding to shear-thinning fluid, Newtonian fluid & shear-thickening fluid respectively. A trend of increasing flow resistance is seen for shear-thickening fluids with the results showing a reduction in the maximum speed from 0.260 m/s to 0.138 m/s as flow behaviour index increases from 0.6 to 1.4. Just as in the previous example, the volumetric flow rate has a nonlinear decrease for an increasing n. The numerical solution of the Newtonian case (n=1) is able to confirm the accuracy of the numerical method proposed, indicating acceptable agreement with the analytical solution of the same. In addition, smooth and stable velocity and shear stress distributions indicate that the numerical scheme is robust. The influence of the rheological characteristics on the characteristics of flow is significant and hence the study clarifies the important role of the rheological parameters during analyzing the non-Newtonian annular flow for engineering applications.

Keywords

Non-Newtonian fluid, Annular flow, Finite difference method, Velocity profile, Shear stress, Numerical simulation

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Cite This Article

P. Singh and N. Kumar, “Numerical investigation of power-law non-Newtonian fluid flow in concentric annular geometry using finite difference method with convergence analysis,” Radius: Journal of Science and Technology 3(1) (2026) 261004. https://doi.org/10.5281/zenodo.20404218

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