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Flow Stability of Nanofluid Thin Films on Non-Uniformly Heated Porous Slopes.

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Title: Flow Stability of Nanofluid Thin Films on Non-Uniformly Heated Porous Slopes.
Authors: Li, Jiawei1 (AUTHOR), Li, Xia1,2 (AUTHOR), Yue, Liqing1 (AUTHOR), Li, Xinshan1,2 (AUTHOR), Ding, Zhaodong1,2 (AUTHOR)
Source: Nanomaterials (2079-4991). Feb2026, Vol. 16 Issue 4, p247. 24p.
Subjects: Flow stability (Fluid dynamics), Flow instability, Nanofluidics, Marangoni effect, Nonlinear analysis, Temperature control equipment, Porous materials, Nanofluids
Abstract: Thin liquid film flows of nanofluids over porous surfaces are central to applications ranging from microfluidic thermal management to precision coating technologies. This study investigates the hydrodynamic and thermal stability of a nanofluid flowing down a non-uniformly heated inclined porous plane subject to the Beavers-Joseph slip boundary condition. Using the long-wave approximation, a nonlinear evolution equation governing the film thickness is derived. The stability characteristics are systematically analyzed via linear stability theory, weakly nonlinear analysis, and fast Fourier transform (FFT) numerical simulations. Quantitative results indicate that the porous medium permeability, density difference, and Marangoni number act as destabilizing factors; specifically, increasing the porous parameter β (from 0 to 0.3), the density ratio ζ 0 (from 0 to 5), and the Marangoni number M n (from 0 to 0.3) significantly reduces the critical Reynolds number and accelerates the onset of interfacial instabilities. In contrast, increasing the nanoparticle volume fraction ϕ from 0 to 0.3 exerts a dominant stabilizing effect by elevating the critical Reynolds number and shrinking the unstable wavenumber domain. Furthermore, nonlinear simulations confirm that higher nanoparticle concentrations effectively suppress the saturation amplitude of disturbances, promoting the eventual stabilization of the liquid film. [ABSTRACT FROM AUTHOR]
Copyright of Nanomaterials (2079-4991) is the property of MDPI 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.)
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Items – Name: Title
  Label: Title
  Group: Ti
  Data: Flow Stability of Nanofluid Thin Films on Non-Uniformly Heated Porous Slopes.
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  Data: <searchLink fieldCode="AR" term="%22Li%2C+Jiawei%22">Li, Jiawei</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Li%2C+Xia%22">Li, Xia</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Yue%2C+Liqing%22">Yue, Liqing</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Li%2C+Xinshan%22">Li, Xinshan</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Ding%2C+Zhaodong%22">Ding, Zhaodong</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Nanomaterials+%282079-4991%29%22">Nanomaterials (2079-4991)</searchLink>. Feb2026, Vol. 16 Issue 4, p247. 24p.
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  Data: <searchLink fieldCode="DE" term="%22Flow+stability+%28Fluid+dynamics%29%22">Flow stability (Fluid dynamics)</searchLink><br /><searchLink fieldCode="DE" term="%22Flow+instability%22">Flow instability</searchLink><br /><searchLink fieldCode="DE" term="%22Nanofluidics%22">Nanofluidics</searchLink><br /><searchLink fieldCode="DE" term="%22Marangoni+effect%22">Marangoni effect</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+analysis%22">Nonlinear analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Temperature+control+equipment%22">Temperature control equipment</searchLink><br /><searchLink fieldCode="DE" term="%22Porous+materials%22">Porous materials</searchLink><br /><searchLink fieldCode="DE" term="%22Nanofluids%22">Nanofluids</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Thin liquid film flows of nanofluids over porous surfaces are central to applications ranging from microfluidic thermal management to precision coating technologies. This study investigates the hydrodynamic and thermal stability of a nanofluid flowing down a non-uniformly heated inclined porous plane subject to the Beavers-Joseph slip boundary condition. Using the long-wave approximation, a nonlinear evolution equation governing the film thickness is derived. The stability characteristics are systematically analyzed via linear stability theory, weakly nonlinear analysis, and fast Fourier transform (FFT) numerical simulations. Quantitative results indicate that the porous medium permeability, density difference, and Marangoni number act as destabilizing factors; specifically, increasing the porous parameter β (from 0 to 0.3), the density ratio ζ 0 (from 0 to 5), and the Marangoni number M n (from 0 to 0.3) significantly reduces the critical Reynolds number and accelerates the onset of interfacial instabilities. In contrast, increasing the nanoparticle volume fraction ϕ from 0 to 0.3 exerts a dominant stabilizing effect by elevating the critical Reynolds number and shrinking the unstable wavenumber domain. Furthermore, nonlinear simulations confirm that higher nanoparticle concentrations effectively suppress the saturation amplitude of disturbances, promoting the eventual stabilization of the liquid film. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Nanomaterials (2079-4991) is the property of MDPI 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.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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        Value: 10.3390/nano16040247
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      – Code: eng
        Text: English
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      – SubjectFull: Flow stability (Fluid dynamics)
        Type: general
      – SubjectFull: Flow instability
        Type: general
      – SubjectFull: Nanofluidics
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      – SubjectFull: Marangoni effect
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      – SubjectFull: Temperature control equipment
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      – SubjectFull: Porous materials
        Type: general
      – SubjectFull: Nanofluids
        Type: general
    Titles:
      – TitleFull: Flow Stability of Nanofluid Thin Films on Non-Uniformly Heated Porous Slopes.
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            NameFull: Li, Jiawei
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            NameFull: Li, Xia
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            NameFull: Yue, Liqing
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              Text: Feb2026
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              Y: 2026
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