On the Stability of Convection in a Non-Newtonian Vertical Fluid Layer in the Presence of Gold Nanoparticles: Drug Agent for Thermotherapy
We consider the effect of gold nanoparticles on the stability properties of convection in a vertical fluid layer saturated by a Jeffreys fluid. The vertical boundaries are rigid and hold at uniform but different temperatures. Brownian diffusion and thermophoresis effects are considered. Due to numer...
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MDPI AG
2021-06-01
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| Series: | Mathematics |
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| author | Khaled S. Mekheimer Bangalore M. Shankar Shaimaa F. Ramadan Hosahalli E. Mallik Mohamed S. Mohamed |
| author_facet | Khaled S. Mekheimer Bangalore M. Shankar Shaimaa F. Ramadan Hosahalli E. Mallik Mohamed S. Mohamed |
| author_sort | Khaled S. Mekheimer |
| collection | DOAJ |
| description | We consider the effect of gold nanoparticles on the stability properties of convection in a vertical fluid layer saturated by a Jeffreys fluid. The vertical boundaries are rigid and hold at uniform but different temperatures. Brownian diffusion and thermophoresis effects are considered. Due to numerous applications in the biomedical industry, such a study is essential. The linear stability is investigated through the normal mode disturbances. The resulting stability problem is an eighth-order ordinary differential complex eigenvalue problem that is solved numerically using the Chebyshev collection method. Its solution provides the neutral stability curves, defining the threshold of linear instability, and the critical parameters at the onset of instability are determined for various values of control parameters. The results for Newtonian fluid and second-grade fluid are delineated as particular cases from the present study. It is shown that the Newtonian fluid has a more stabilizing effect than the second-grade and the Jeffreys fluids in the presence of gold nanoparticles and, Jeffreys fluid is the least stable. |
| first_indexed | 2024-03-10T10:40:17Z |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T10:40:17Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-aa93b37bf5e1440f90dc1cb4dd4f6cd22023-11-21T23:01:50ZengMDPI AGMathematics2227-73902021-06-01911130210.3390/math9111302On the Stability of Convection in a Non-Newtonian Vertical Fluid Layer in the Presence of Gold Nanoparticles: Drug Agent for ThermotherapyKhaled S. Mekheimer0Bangalore M. Shankar1Shaimaa F. Ramadan2Hosahalli E. Mallik3Mohamed S. Mohamed4Department of Mathematics, Faculty of Science (Men), Al-Azhar University, Cairo 11884, EgyptDepartment of Mathematics, PES University, Bangalore 560085, IndiaDepartment of Mathematics, Faculty of Science (Girls), Al-Azhar University, Cairo 11884, EgyptDepartment of Mathematics, PES University, Bangalore 560085, IndiaDepartment of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaWe consider the effect of gold nanoparticles on the stability properties of convection in a vertical fluid layer saturated by a Jeffreys fluid. The vertical boundaries are rigid and hold at uniform but different temperatures. Brownian diffusion and thermophoresis effects are considered. Due to numerous applications in the biomedical industry, such a study is essential. The linear stability is investigated through the normal mode disturbances. The resulting stability problem is an eighth-order ordinary differential complex eigenvalue problem that is solved numerically using the Chebyshev collection method. Its solution provides the neutral stability curves, defining the threshold of linear instability, and the critical parameters at the onset of instability are determined for various values of control parameters. The results for Newtonian fluid and second-grade fluid are delineated as particular cases from the present study. It is shown that the Newtonian fluid has a more stabilizing effect than the second-grade and the Jeffreys fluids in the presence of gold nanoparticles and, Jeffreys fluid is the least stable.https://www.mdpi.com/2227-7390/9/11/1302linear stabilitygold nanoparticlesJeffreys fluidradiationeigenvalue problem |
| spellingShingle | Khaled S. Mekheimer Bangalore M. Shankar Shaimaa F. Ramadan Hosahalli E. Mallik Mohamed S. Mohamed On the Stability of Convection in a Non-Newtonian Vertical Fluid Layer in the Presence of Gold Nanoparticles: Drug Agent for Thermotherapy Mathematics linear stability gold nanoparticles Jeffreys fluid radiation eigenvalue problem |
| title | On the Stability of Convection in a Non-Newtonian Vertical Fluid Layer in the Presence of Gold Nanoparticles: Drug Agent for Thermotherapy |
| title_full | On the Stability of Convection in a Non-Newtonian Vertical Fluid Layer in the Presence of Gold Nanoparticles: Drug Agent for Thermotherapy |
| title_fullStr | On the Stability of Convection in a Non-Newtonian Vertical Fluid Layer in the Presence of Gold Nanoparticles: Drug Agent for Thermotherapy |
| title_full_unstemmed | On the Stability of Convection in a Non-Newtonian Vertical Fluid Layer in the Presence of Gold Nanoparticles: Drug Agent for Thermotherapy |
| title_short | On the Stability of Convection in a Non-Newtonian Vertical Fluid Layer in the Presence of Gold Nanoparticles: Drug Agent for Thermotherapy |
| title_sort | on the stability of convection in a non newtonian vertical fluid layer in the presence of gold nanoparticles drug agent for thermotherapy |
| topic | linear stability gold nanoparticles Jeffreys fluid radiation eigenvalue problem |
| url | https://www.mdpi.com/2227-7390/9/11/1302 |
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