Soret Effect on the Instability of Double-Diffusive Convection in a Saturated Vertical Brinkman Porous Layer of Oldroyd-B Fluid
The instability of the double-diffusive convection of an Oldroyd-B fluid in a vertical Brinkman porous layer caused by temperature and solute concentration differences with the Soret effect is studied. Based on perturbation theory, an Orr–Sommerfeld eigenvalue problem is derived and numerically solv...
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2024-12-01
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| author | Yuanzhen Ren Yongjun Jian |
| author_facet | Yuanzhen Ren Yongjun Jian |
| author_sort | Yuanzhen Ren |
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| description | The instability of the double-diffusive convection of an Oldroyd-B fluid in a vertical Brinkman porous layer caused by temperature and solute concentration differences with the Soret effect is studied. Based on perturbation theory, an Orr–Sommerfeld eigenvalue problem is derived and numerically solved using the Chebyshev collocation method. The effects of dimensionless parameters on the neutral stability curves and the growth rate curves are examined. It is found that Lewis number <i>Le</i>, Darcy–Prandtl number <i>Pr<sub>D</sub></i>, and normalized porosity <i>η</i> have critical values: When below these thresholds, the parameters promote instability, whereas exceeding them leads to suppression of instability. In addition, for <i>Le</i> < <i>Le<sub>c</sub></i><sub>2</sub> (a critical value of <i>Le</i>), <i>S<sub>r</sub></i> strengthens the instability of the flow, while for <i>Le</i> > <i>Le<sub>c</sub></i><sub>2</sub>, <i>S<sub>r</sub></i> suppresses it. These results highlight the complex coupling of heat and mass transfer in Oldroyd-B fluids within porous media. |
| format | Article |
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| institution | Kabale University |
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| language | English |
| publishDate | 2024-12-01 |
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| spelling | doaj-art-80cbb236d68a47b384e710f287e1ecc52025-01-10T13:18:15ZengMDPI AGMathematics2227-73902024-12-0113110010.3390/math13010100Soret Effect on the Instability of Double-Diffusive Convection in a Saturated Vertical Brinkman Porous Layer of Oldroyd-B FluidYuanzhen Ren0Yongjun Jian1School of Mathematical Science, Inner Mongolia University, Hohhot 010021, ChinaSchool of Mathematics and Statistics, Donghua University, Shanghai 201620, ChinaThe instability of the double-diffusive convection of an Oldroyd-B fluid in a vertical Brinkman porous layer caused by temperature and solute concentration differences with the Soret effect is studied. Based on perturbation theory, an Orr–Sommerfeld eigenvalue problem is derived and numerically solved using the Chebyshev collocation method. The effects of dimensionless parameters on the neutral stability curves and the growth rate curves are examined. It is found that Lewis number <i>Le</i>, Darcy–Prandtl number <i>Pr<sub>D</sub></i>, and normalized porosity <i>η</i> have critical values: When below these thresholds, the parameters promote instability, whereas exceeding them leads to suppression of instability. In addition, for <i>Le</i> < <i>Le<sub>c</sub></i><sub>2</sub> (a critical value of <i>Le</i>), <i>S<sub>r</sub></i> strengthens the instability of the flow, while for <i>Le</i> > <i>Le<sub>c</sub></i><sub>2</sub>, <i>S<sub>r</sub></i> suppresses it. These results highlight the complex coupling of heat and mass transfer in Oldroyd-B fluids within porous media.https://www.mdpi.com/2227-7390/13/1/100Soret effectOldroyd-B fluidBrinkman porous layerdouble-diffusive convectioninstability |
| spellingShingle | Yuanzhen Ren Yongjun Jian Soret Effect on the Instability of Double-Diffusive Convection in a Saturated Vertical Brinkman Porous Layer of Oldroyd-B Fluid Mathematics Soret effect Oldroyd-B fluid Brinkman porous layer double-diffusive convection instability |
| title | Soret Effect on the Instability of Double-Diffusive Convection in a Saturated Vertical Brinkman Porous Layer of Oldroyd-B Fluid |
| title_full | Soret Effect on the Instability of Double-Diffusive Convection in a Saturated Vertical Brinkman Porous Layer of Oldroyd-B Fluid |
| title_fullStr | Soret Effect on the Instability of Double-Diffusive Convection in a Saturated Vertical Brinkman Porous Layer of Oldroyd-B Fluid |
| title_full_unstemmed | Soret Effect on the Instability of Double-Diffusive Convection in a Saturated Vertical Brinkman Porous Layer of Oldroyd-B Fluid |
| title_short | Soret Effect on the Instability of Double-Diffusive Convection in a Saturated Vertical Brinkman Porous Layer of Oldroyd-B Fluid |
| title_sort | soret effect on the instability of double diffusive convection in a saturated vertical brinkman porous layer of oldroyd b fluid |
| topic | Soret effect Oldroyd-B fluid Brinkman porous layer double-diffusive convection instability |
| url | https://www.mdpi.com/2227-7390/13/1/100 |
| work_keys_str_mv | AT yuanzhenren soreteffectontheinstabilityofdoublediffusiveconvectioninasaturatedverticalbrinkmanporouslayerofoldroydbfluid AT yongjunjian soreteffectontheinstabilityofdoublediffusiveconvectioninasaturatedverticalbrinkmanporouslayerofoldroydbfluid |