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Double-diffusive convection in a Darcy–Brinkman porous layer with higher-order thermal and solutal diffusion.

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Title: Double-diffusive convection in a Darcy–Brinkman porous layer with higher-order thermal and solutal diffusion.
Authors: Khalaf, Sanaa L.1 (AUTHOR) sanaasanaa1978@yahoo.com, Harfash, Akil Jassim1 (AUTHOR) akilharfash@gmail.com
Source: International Journal of Numerical Methods for Heat & Fluid Flow. 2026, Vol. 36 Issue 5, p1993-2026. 34p.
Subjects: Stability of linear systems, Stability of nonlinear systems, Thermal instability, Porous materials, Numerical analysis, Concentration gradient, Thermal conductivity
Abstract: Purpose: The purpose of this study is to analyse double-diffusive convection in a fluid-saturated porous layer using an extended Darcy–Brinkman model with higher-order (bi-Laplacian) thermal and solutal diffusion and to determine linear and nonlinear stability thresholds. Design/methodology/approach: The governing equations are nondimensionalised and linearised about the conduction state to obtain the perturbation equations. Linear instability analysis was performed, and a nonlinear energy stability analysis was developed to determine unconditional decay thresholds for perturbations. The instability and nonlinear thresholds are computed using two high-accuracy Chebyshev collocation methods (standard and boundary-fitted). Findings: Brinkman viscous diffusion and higher-order thermal/solutal diffusion act predominantly as stabilising mechanisms: they increase the critical Rayleigh numbers, reshape the neutral curves and shift the stationary–oscillatory transition in parameter space. The nonlinear (energy) threshold is consistently lower than the linear threshold, identifying a conditional-stability interval RaE < Ra < RaL in which linear stability holds but unconditional nonlinear decay is not guaranteed by the present energy estimate. In the top-heavy solutal configuration, higher-order solutal diffusion provides the strongest suppression of solutal-driven fingering. Both numerical schemes exhibit spectral convergence; however, the boundary-fitted method achieves smaller residuals at the same truncation order, indicating improved accuracy and efficiency. Originality/value: To the best of the authors' knowledge, this is the first combined linear/energy stability study of thermosolutal convection in a Darcy–Brinkman porous layer with higher-order thermal and solutal diffusion, supported by spectrally accurate Chebyshev collocation schemes for the associated high-order eigenvalue problems. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Numerical Methods for Heat & Fluid Flow is the property of Emerald Publishing Limited and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 193119260
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PubType: Academic Journal
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  Label: Title
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  Data: Double-diffusive convection in a Darcy–Brinkman porous layer with higher-order thermal and solutal diffusion.
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  Data: &lt;searchLink fieldCode=&quot;AR&quot; term=&quot;%22Khalaf%2C+Sanaa+L%2E%22&quot;&gt;Khalaf, Sanaa L.&lt;/searchLink&gt;&lt;relatesTo&gt;1&lt;/relatesTo&gt; (AUTHOR)&lt;i&gt; sanaasanaa1978@yahoo.com&lt;/i&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;AR&quot; term=&quot;%22Harfash%2C+Akil+Jassim%22&quot;&gt;Harfash, Akil Jassim&lt;/searchLink&gt;&lt;relatesTo&gt;1&lt;/relatesTo&gt; (AUTHOR)&lt;i&gt; akilharfash@gmail.com&lt;/i&gt;
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– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Purpose: The purpose of this study is to analyse double-diffusive convection in a fluid-saturated porous layer using an extended Darcy–Brinkman model with higher-order (bi-Laplacian) thermal and solutal diffusion and to determine linear and nonlinear stability thresholds. Design/methodology/approach: The governing equations are nondimensionalised and linearised about the conduction state to obtain the perturbation equations. Linear instability analysis was performed, and a nonlinear energy stability analysis was developed to determine unconditional decay thresholds for perturbations. The instability and nonlinear thresholds are computed using two high-accuracy Chebyshev collocation methods (standard and boundary-fitted). Findings: Brinkman viscous diffusion and higher-order thermal/solutal diffusion act predominantly as stabilising mechanisms: they increase the critical Rayleigh numbers, reshape the neutral curves and shift the stationary–oscillatory transition in parameter space. The nonlinear (energy) threshold is consistently lower than the linear threshold, identifying a conditional-stability interval RaE &lt; Ra &lt; RaL in which linear stability holds but unconditional nonlinear decay is not guaranteed by the present energy estimate. In the top-heavy solutal configuration, higher-order solutal diffusion provides the strongest suppression of solutal-driven fingering. Both numerical schemes exhibit spectral convergence; however, the boundary-fitted method achieves smaller residuals at the same truncation order, indicating improved accuracy and efficiency. Originality/value: To the best of the authors&#39; knowledge, this is the first combined linear/energy stability study of thermosolutal convection in a Darcy–Brinkman porous layer with higher-order thermal and solutal diffusion, supported by spectrally accurate Chebyshev collocation schemes for the associated high-order eigenvalue problems. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: &lt;i&gt;Copyright of International Journal of Numerical Methods for Heat &amp; Fluid Flow is the property of Emerald Publishing Limited and its content may not be copied or emailed to multiple sites without the copyright holder&#39;s express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.&lt;/i&gt; (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
  BibEntity:
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 34
        StartPage: 1993
    Subjects:
      – SubjectFull: Stability of linear systems
        Type: general
      – SubjectFull: Stability of nonlinear systems
        Type: general
      – SubjectFull: Thermal instability
        Type: general
      – SubjectFull: Porous materials
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Concentration gradient
        Type: general
      – SubjectFull: Thermal conductivity
        Type: general
    Titles:
      – TitleFull: Double-diffusive convection in a Darcy–Brinkman porous layer with higher-order thermal and solutal diffusion.
        Type: main
  BibRelationships:
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      – PersonEntity:
          Name:
            NameFull: Khalaf, Sanaa L.
      – PersonEntity:
          Name:
            NameFull: Harfash, Akil Jassim
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 05
              Text: 2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 09615539
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            – Type: volume
              Value: 36
            – Type: issue
              Value: 5
          Titles:
            – TitleFull: International Journal of Numerical Methods for Heat & Fluid Flow
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