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MHD Flow Through a Perturbed Channel Filled with a Porous Medium

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A Correction to this article was published on 12 September 2022

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Abstract

The main aim of this paper is to investigate the effects of a slightly perturbed boundary on the MHD flow through a channel filled with a porous medium. We start from a rectangular domain and then perturb the upper part of its boundary by the product of the small parameter \(\varepsilon \) and an arbitrary smooth function h. Employing asymptotic analysis with respect to \(\varepsilon \), we derive the first-order effective model. We can clearly observe the nonlocal effects of the small boundary perturbation with respect to the Hartmann number since the asymptotic approximation is derived in explicit form. Theoretical error analysis is also provided, rigorously justifying our formally derived model.

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Acknowledgements

The first author of this work has been supported by the Croatia Science Foundation under the project AsAn (IP-2018-01-2735). The second and the third authors of this work have been supported by the Croatia Science Foundation under the project MultiFM (IP-2019-04-1140).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10000, Zagreb, Croatia

    Eduard Marušić–Paloka, Igor Pažanin & Marko Radulović

Authors
  1. Eduard Marušić–Paloka
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  2. Igor Pažanin
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  3. Marko Radulović
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Correspondence to Marko Radulović.

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Communicated by Syakila Ahmad.

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The original version of this article was revised: Equation 4.22 was corrected.

Appendix

Appendix

Fig. 6
figure 6

Velocity corrector \(V_{y}^{1}\) with Hartmann number \(M=0\) (left) and \(M=2\) (right)

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Fig. 7
figure 7

Velocity corrector \(V_{y}^{1}\) with Hartmann number \(M=4\) (left) and \(M=6\) (right)

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Fig. 8
figure 8

Pressure corrector \(Q^{1}\) with Hartmann number \(M=0\) (left) and \(M=2\) (right)

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Fig. 9
figure 9

Pressure corrector \(Q^{1}\) with Hartmann number \(M=4\) (left) and \(M=6\) (right)

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Fig. 10
figure 10

Velocity corrector \(V_{x}^{1}\) profile for fixed \(y=1\) with Hartmann number \(M=0\) (left) and \(M=2\) (right)

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Fig. 11
figure 11

Velocity corrector \(V_{x}^{1}\) profile for fixed \(y=1\) with Hartmann number \(M=4\) (left) and \(M=6\) (right)

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Fig. 12
figure 12

Velocity corrector \(V_{x}^{1}\) profile for fixed \(x=0.5\) with Hartmann number \(M=0\) (left) and \(M=2\) (right)

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Fig. 13
figure 13

Velocity corrector \(V_{x}^{1}\) profile for fixed \(x=0.5\) with Hartmann number \(M=4\) (left) and \(M=6\) (right)

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Fig. 14
figure 14

Velocity corrector \(V_{x}^{1}\) profile for fixed \(x=1\) with Hartmann number \(M=0\) (left) and \(M=2\) (right)

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Fig. 15
figure 15

Velocity corrector \(V_{x}^{1}\) profile for fixed \(x=1\) with Hartmann number \(M=4\) (left) and \(M=6\) (right)

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Fig. 16
figure 16

Velocity corrector \(V_{y}^{1}\) profile for fixed \(x=0.5\) with Hartmann number \(M=0\) (left) and \(M=2\) (right)

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Fig. 17
figure 17

Velocity corrector \(V_{y}^{1}\) profile for fixed \(x=0.5\) with Hartmann number \(M=4\) (left) and \(M=6\) (right)

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Fig. 18
figure 18

Velocity approximation (x-component) profile for fixed \(y=1\) with Hartmann number \(M=0\) (left) and \(M=2\) (right) and \(\varepsilon =0.1\)

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Fig. 19
figure 19

Velocity approximation (x-component) profile for fixed \(y=1\) with Hartmann number \(M=4\) (left) and \(M=6\) (right) and \(\varepsilon =0.1\)

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Fig. 20
figure 20

Velocity approximation (x-component) profile for fixed \(x=0.5\) with Hartmann number \(M=0\) (left) and \(M=2\) (right) and \(\varepsilon =0.1\)

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Fig. 21
figure 21

Velocity approximation (x-component) profile for fixed \(x=0.5\) with Hartmann number \(M=4\) (left) and \(M=6\) (right) and \(\varepsilon =0.1\)

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Marušić–Paloka, E., Pažanin, I. & Radulović, M. MHD Flow Through a Perturbed Channel Filled with a Porous Medium. Bull. Malays. Math. Sci. Soc. 45, 2441–2471 (2022). https://doi.org/10.1007/s40840-022-01356-3

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