research-article

The onset of instability in a hydromagnetic channel flow of Casson fluid: : the accurate solutions

Authors:

Ramesh B. Kudenatti,

Noor-E-MisbahAuthors Info & Claims

Volume 436, Issue C

https://doi.org/10.1016/j.amc.2022.127475

Published: 01 January 2023 Publication History

Highlights

•

Linear stability of a non-Newtonian hydromagnetic Casson fluid in a channel flow is studied.

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Plane-Poiseuille flow of Casson fluid becomes unstable to a wall-mode.

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Increasing magnetic field stabilizes flow which postpones instability in a channel.

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Interesting eigenspectra are found to form a leaf-like structure.

Abstract

We study the temporal stability of linear two-dimensional disturbances of plane Poiseuille flow of a Casson fluid in a rigid parallel channel under the influence of a uniform magnetic field. When the disturbance is taken in normal mode it transforms the perturbed equations to a fourth-order eigenvalue problem which is then solved by the spectral method. We first obtain sufficient conditions for the hydrodynamic stability in the channel by analyzing the nature of the growth rate and the Reynolds number. For the chosen set of parameters, the eigenspectra of the flow exhibit the familiar Y-shaped structure with three distinct modes depending on the phase speed approach. The eigenfunctions corresponding to the least stable and most unstable eigenmodes have the symmetric and antisymmetric modes. For a certain range of Casson parameter β and the magnetic number M, instability always appears on the wall mode for which the eigenfunction is antisymmetric about the channel center-line. The neutral stability curves that correspond to various values of β and M are found to be an extension of the continuation of the Tollmien-Schlichting instability that is noticed for a Newtonian channel flow. The regions of stability are enlarged for small β and large M.

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Index Terms

The onset of instability in a hydromagnetic channel flow of Casson fluid: the accurate solutions
1. Applied computing
  1. Physical sciences and engineering
    1. Physics
2. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations
      2. Partial differential equations
    2. Numerical analysis
      1. Computations on matrices

Index terms have been assigned to the content through auto-classification.

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Published In

cover image Applied Mathematics and Computation

Applied Mathematics and Computation Volume 436, Issue C

Jan 2023

378 pages

ISSN:0096-3003

Issue’s Table of Contents

Copyright © 2022.

Publisher

Elsevier Science Inc.

United States

Publication History

Published: 01 January 2023

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