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<p>The instability of double-diffusive convection in an Oldroyd-B fluid in a vertical porous layer is investigated using a modified Darcy–Brinkman–Oldroyd model. Squire's theorem is validated, reducing the problem to two-dimensional linear instability. The Orr–Sommerfeld eigenvalue problem is solved numerically using the Chebyshev collocation method. The effects of dimensionless parameters on the neutral stability curves are examined. It is found that the Darcy–Prandtl number (<i>Pr</i><sub><i>D</i></sub>), relaxation time (<i>λ</i><sub>1</sub>), and normalized porosity (<i>η</i>) have dual effects on instability. <i>Pr</i><sub><i>D</i></sub> has two critical values: <i>Pr</i><sub><i>Dc</i>1</sub> and <i>Pr</i><sub><i>Dc</i>2</sub>. When <i>Pr</i><sub><i>Dc</i>1</sub> &lt; <i>Pr</i><sub><i>D</i></sub> &lt; <i>Pr</i><sub><i>Dc</i>2</sub>, <i>Pr</i><sub><i>D</i></sub> inhibits convection; otherwise, <i>Pr</i><sub><i>D</i></sub> promotes convection. The effect of <i>λ</i><sub>1</sub> on fluid stability is influenced by <i>Pr</i><sub><i>D</i></sub>. When <i>η</i> &gt; <i>η</i><sub><i>c</i></sub> (the critical value of <i>η</i>), it promotes flow instability; when <i>η</i> &lt; <i>η</i><sub><i>c</i></sub>, it suppresses instability. For Lewis number <i>Le</i> &gt; 2.31, two instability regions are observed, requiring three critical Darcy–Rayleigh numbers to determine flow instability. For <i>Le</i> &lt; 2.31, the finite unstable region disappears. Finally, the relaxation parameter <i>λ</i><sub>2</sub> promotes flow stability.</p>

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Instability of Double-Diffusive Convection in an Oldroyd-B Fluid-Saturated Vertical Brinkman Porous Layer

  • 期刊论文

  • 发表日期：

    2025年5月13日

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  • Yuanzhen Ren,
  • Jialu Wang,
  • Beinan Jia,
  • Yongjun Jian

摘要

The instability of double-diffusive convection in an Oldroyd-B fluid in a vertical porous layer is investigated using a modified Darcy–Brinkman–Oldroyd model. Squire's theorem is validated, reducing the problem to two-dimensional linear instability. The Orr–Sommerfeld eigenvalue problem is solved numerically using the Chebyshev collocation method. The effects of dimensionless parameters on the neutral stability curves are examined. It is found that the Darcy–Prandtl number (PrD), relaxation time (λ1), and normalized porosity (η) have dual effects on instability. PrD has two critical values: PrDc1 and PrDc2. When PrDc1 < PrD < PrDc2, PrD inhibits convection; otherwise, PrD promotes convection. The effect of λ1 on fluid stability is influenced by PrD. When η > ηc (the critical value of η), it promotes flow instability; when η < ηc, it suppresses instability. For Lewis number Le > 2.31, two instability regions are observed, requiring three critical Darcy–Rayleigh numbers to determine flow instability. For Le < 2.31, the finite unstable region disappears. Finally, the relaxation parameter λ2 promotes flow stability.