Flow of Fluids with Pressure-Dependent Viscosity in Between Intersecting Planes

The flow of an incompressible power-law fluid through a convergent channel is considered, where the viscosity is chosen to be pressure dependent. Instead of utilizing the classical similarity transformation traditionally employed when considering Jeffery-Hamel flow, allowing for purely radial soluti...

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Main Authors: Rhameez S. Herbst, Charis Harley, Kumbakonam R. Rajagopal
Format: Article
Language:English
Published: MDPI AG 2025-01-01
Series:Fluids
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Online Access:https://www.mdpi.com/2311-5521/10/2/33
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author Rhameez S. Herbst
Charis Harley
Kumbakonam R. Rajagopal
author_facet Rhameez S. Herbst
Charis Harley
Kumbakonam R. Rajagopal
author_sort Rhameez S. Herbst
collection DOAJ
description The flow of an incompressible power-law fluid through a convergent channel is considered, where the viscosity is chosen to be pressure dependent. Instead of utilizing the classical similarity transformation traditionally employed when considering Jeffery-Hamel flow, allowing for purely radial solutions for the velocity field, we allow for flow in both the radial and angular directions. We develop a numerical scheme that conserves the pressure-dependent viscosity at each cell in the computational grid. We recover the classical solution to the problem, and through our numerical solutions, we observe not only that the tangential velocities are not negligible, but also that flow reversal occurs, as illustrated by solutions with varying flow regimes. Decreasing the angle of the channel causes the magnitude of the velocity to decrease, while shorter channels lead to an increase in the magnitude of the radial and tangential velocities. In the case of the latter, this could indicate that in shorter channels, the tangential velocity has a larger impact on the occurrence of flow reversal. For more varied flow regimes, the magnitude of the radial and tangential velocities increases.
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spelling doaj-art-e1abf7654cc047bda0088d00afdc1eb92025-08-20T02:44:49ZengMDPI AGFluids2311-55212025-01-011023310.3390/fluids10020033Flow of Fluids with Pressure-Dependent Viscosity in Between Intersecting PlanesRhameez S. Herbst0Charis Harley1Kumbakonam R. Rajagopal2Department of Mathematics and Applied Mathematics, Faculty of Science, University of Johannesburg, Johannesburg 2006, South AfricaDepartment of Electrical and Electronic Engineering Science, Faculty of Engineering and the Built Environment, University of Johannesburg, Johannesburg 2006, South AfricaDepartment of Mechanical Engineering, Texas A&M University, College Station, TX 77840, USAThe flow of an incompressible power-law fluid through a convergent channel is considered, where the viscosity is chosen to be pressure dependent. Instead of utilizing the classical similarity transformation traditionally employed when considering Jeffery-Hamel flow, allowing for purely radial solutions for the velocity field, we allow for flow in both the radial and angular directions. We develop a numerical scheme that conserves the pressure-dependent viscosity at each cell in the computational grid. We recover the classical solution to the problem, and through our numerical solutions, we observe not only that the tangential velocities are not negligible, but also that flow reversal occurs, as illustrated by solutions with varying flow regimes. Decreasing the angle of the channel causes the magnitude of the velocity to decrease, while shorter channels lead to an increase in the magnitude of the radial and tangential velocities. In the case of the latter, this could indicate that in shorter channels, the tangential velocity has a larger impact on the occurrence of flow reversal. For more varied flow regimes, the magnitude of the radial and tangential velocities increases.https://www.mdpi.com/2311-5521/10/2/33incompressible fluidJeffery–Hamel flowpressure-dependent viscosityflow reversal
spellingShingle Rhameez S. Herbst
Charis Harley
Kumbakonam R. Rajagopal
Flow of Fluids with Pressure-Dependent Viscosity in Between Intersecting Planes
Fluids
incompressible fluid
Jeffery–Hamel flow
pressure-dependent viscosity
flow reversal
title Flow of Fluids with Pressure-Dependent Viscosity in Between Intersecting Planes
title_full Flow of Fluids with Pressure-Dependent Viscosity in Between Intersecting Planes
title_fullStr Flow of Fluids with Pressure-Dependent Viscosity in Between Intersecting Planes
title_full_unstemmed Flow of Fluids with Pressure-Dependent Viscosity in Between Intersecting Planes
title_short Flow of Fluids with Pressure-Dependent Viscosity in Between Intersecting Planes
title_sort flow of fluids with pressure dependent viscosity in between intersecting planes
topic incompressible fluid
Jeffery–Hamel flow
pressure-dependent viscosity
flow reversal
url https://www.mdpi.com/2311-5521/10/2/33
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