A revised model for the effect of nanoparticle mass flux on the thermal instability of a nanofluid layer
A revised model of the nanoparticle mass flux is introduced and used to study the thermal instability of the Rayleigh-Benard problem for a horizontal layer of nanofluid heated from below. The motion of nanoparticles is characterized by the effects of thermophoresis and Brownian diffusion. The nanofl...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2021-12-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2021-0045 |
| _version_ | 1819001756078571520 |
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| author | Alharbi Ozwah S. Abdullah Abdullah A. |
| author_facet | Alharbi Ozwah S. Abdullah Abdullah A. |
| author_sort | Alharbi Ozwah S. |
| collection | DOAJ |
| description | A revised model of the nanoparticle mass flux is introduced and used to study the thermal instability of the Rayleigh-Benard problem for a horizontal layer of nanofluid heated from below. The motion of nanoparticles is characterized by the effects of thermophoresis and Brownian diffusion. The nanofluid layer is confined between two rigid boundaries. Both boundaries are assumed to be impenetrable to nanoparticles with their distribution being determined from a conservation condition. The material properties of the nanofluid are allowed to depend on the local volume fraction of nanoparticles and are modelled by non-constant constitutive expressions developed by Kanafer and Vafai based on experimental data. The results show that the profile of the nanoparticle volume fraction is of exponential type in the steady-state solution. The resulting equations of the problem constitute an eigenvalue problem which is solved using the Chebyshev tau method. The critical values of the thermal Rayleigh number are calculated for several values of the parameters of the problem. Moreover, the critical eigenvalues obtained were real-valued, which indicates that the mode of instability is via a stationary mode. |
| first_indexed | 2024-12-20T22:54:16Z |
| format | Article |
| id | doaj.art-712d8fd64c0b49f290c58a253fcc291e |
| institution | Directory Open Access Journal |
| issn | 2391-4661 |
| language | English |
| last_indexed | 2024-12-20T22:54:16Z |
| publishDate | 2021-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-712d8fd64c0b49f290c58a253fcc291e2022-12-21T19:24:10ZengDe GruyterDemonstratio Mathematica2391-46612021-12-0154148849910.1515/dema-2021-0045A revised model for the effect of nanoparticle mass flux on the thermal instability of a nanofluid layerAlharbi Ozwah S.0Abdullah Abdullah A.1Department of Mathematical Sciences, Umm Al-Qura University, Makkah, Saudi ArabiaDepartment of Mathematical Sciences, Umm Al-Qura University, Makkah, Saudi ArabiaA revised model of the nanoparticle mass flux is introduced and used to study the thermal instability of the Rayleigh-Benard problem for a horizontal layer of nanofluid heated from below. The motion of nanoparticles is characterized by the effects of thermophoresis and Brownian diffusion. The nanofluid layer is confined between two rigid boundaries. Both boundaries are assumed to be impenetrable to nanoparticles with their distribution being determined from a conservation condition. The material properties of the nanofluid are allowed to depend on the local volume fraction of nanoparticles and are modelled by non-constant constitutive expressions developed by Kanafer and Vafai based on experimental data. The results show that the profile of the nanoparticle volume fraction is of exponential type in the steady-state solution. The resulting equations of the problem constitute an eigenvalue problem which is solved using the Chebyshev tau method. The critical values of the thermal Rayleigh number are calculated for several values of the parameters of the problem. Moreover, the critical eigenvalues obtained were real-valued, which indicates that the mode of instability is via a stationary mode.https://doi.org/10.1515/dema-2021-0045linear stabilityrayleigh-benard convectionnanofluidthermophoresisbrownianchebyshev tau method76e06 |
| spellingShingle | Alharbi Ozwah S. Abdullah Abdullah A. A revised model for the effect of nanoparticle mass flux on the thermal instability of a nanofluid layer Demonstratio Mathematica linear stability rayleigh-benard convection nanofluid thermophoresis brownian chebyshev tau method 76e06 |
| title | A revised model for the effect of nanoparticle mass flux on the thermal instability of a nanofluid layer |
| title_full | A revised model for the effect of nanoparticle mass flux on the thermal instability of a nanofluid layer |
| title_fullStr | A revised model for the effect of nanoparticle mass flux on the thermal instability of a nanofluid layer |
| title_full_unstemmed | A revised model for the effect of nanoparticle mass flux on the thermal instability of a nanofluid layer |
| title_short | A revised model for the effect of nanoparticle mass flux on the thermal instability of a nanofluid layer |
| title_sort | revised model for the effect of nanoparticle mass flux on the thermal instability of a nanofluid layer |
| topic | linear stability rayleigh-benard convection nanofluid thermophoresis brownian chebyshev tau method 76e06 |
| url | https://doi.org/10.1515/dema-2021-0045 |
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