https://doi.org/10.1140/epjp/s13360-026-07340-1
Regular Article
Circular couette flow with radial mass transfer using a recursive approach
1
CFisUC, Departamento de Física, Universidade de Coimbra, 3004-516, Coimbra, Portugal
2
State University of São Paulo - UNESP, Rio Claro-SP, Brazil
3
Polytechnic School, University of Pernambuco, Recife, PE, Brazil
a
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Received:
9
December
2025
Accepted:
18
January
2026
Published online:
24
January
2026
Abstract
The dynamics of a fluid confined between two concentric cylinders are investigated using a novel approach based on recursive equations. First, for a system constrained by no radial mass transfer, an exact analytical solution is formulated. When compared against the classical solution derived from the Navier–Stokes equations, our model shows increasing deviation as the ratio of the outer-to-inner radii grows. Subsequently, the model is extended to permit a radial mass flow, and a corresponding solution is proposed. The solution is enhanced by proposing a variable radial mass flow model, where a comparison with experiment provides the rate of variation. A primary advantage of this methodology is its enhanced accuracy in describing the steady flow profile near the inner cylinder, a region where both Navier–Stokes and our previous obtained solutions with no radial mass transfer can be less precise. The proposed framework is readily applicable and extendable, holding promise for theoretical studies of similar confined flow phenomena.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
