<abstract xmlns="http://www.w3.org/1999/xhtml">

It is proved analytically that the complex growth rate <italic>n</italic> = <italic>nr</italic> + <italic>ini</italic> (<italic>nr</italic> and <italic>ni</italic> are the real and imaginary parts of <italic>n</italic> , respectively) of an arbitrary neutral or unstable oscillatory disturbance of growing amplitude in rotatory electrothermoconvection in a dielectric fluid layer saturating a sparsely distributed porous medium heated from below, for the case of free boundaries, is located inside a semicircle in the right half of the <italic>nrni</italic> − plane, whose centre is at the origin and radius = 
<inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_sgem-2024-0008_ineq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msqrt><mrow><mo>max</mo><mfenced><mrow><msub><mi>T</mi><mi>a</mi></msub><msubsup><mi>P</mi><mi>r</mi><mn>2</mn></msubsup><mo>,</mo><mfrac><mrow><msub><mi>R</mi><mrow><mi mathvariant="italic">ea</mi></mrow></msub><msub><mi>P</mi><mi>r</mi></msub></mrow><mi>A</mi></mfrac></mrow></mfenced></mrow></msqrt></mrow></math>
<tex-math>\sqrt {\max \left( {{T_a}P_r^2,{{{R_{ea}}{P_r}} \over A}} \right)} </tex-math>
</alternatives>
</inline-formula>
, where <italic>Ta</italic> is the modified Taylor’s number, <italic>Pr</italic> is the modified Prandtl number, <italic>Rea</italic> is electric Rayleigh number and <italic>A</italic> is the ratio of heat capacities. The upper limits for the case of rigid boundaries are derived separately. Furthermore, similar results are also derived for the same configuration when heated from above.
</abstract>

It is proved analytically that the complex growth rate n = nr + ini (nr and ni are the real and imaginary parts of n , respectively) of an arbitrary neutral or unstable oscillatory disturbance of growing amplitude in rotatory electrothermoconvection in a dielectric fluid layer saturating a sparsely distributed porous medium heated from below, for the case of free boundaries, is located inside a semicircle in the right half of the nrni − plane, whose centre is at the origin and radius = 



maxTaPr2,ReaPrA
\sqrt {\max \left( {{T_a}P_r^2,{{{R_{ea}}{P_r}} \over A}} \right)} 


, where Ta is the modified Taylor’s number, Pr is the modified Prandtl number, Rea is electric Rayleigh number and A is the ratio of heat capacities. The upper limits for the case of rigid boundaries are derived separately. Furthermore, similar results are also derived for the same configuration when heated from above.

On the upper limits for complex growth rate in rotatory electrothermoconvection in a dielectric fluid layer saturating a sparsely distributed porous medium

Studia Geotechnica et Mechanica

This work is licensed under the Creative Commons Attribution 4.0 International License.

It is proved analytically that the complex growth rate n = nr + ini (nr and ni are the real and imaginary parts of n , respectively) of an arbitrary neutral or...

On the upper limits for complex growth rate in rotatory electrothermoconvection in a dielectric fluid layer saturating a sparsely distributed porous medium

Article Category: Research Article

Published Online: Jul 10, 2024

Page range: -

Received: Jan 11, 2024

Accepted: May 10, 2024

DOI: https://doi.org/10.2478/sgem-2024-0008

Keywords
Linear stability analysis, Dielectric fluid, Oscillatory instability, complex growth rate, Electrothermoconvection

© 2024 Jitender Kumar et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1:

Figure 2:

Figure 3:

Figure 4:

Figure 5:

On the upper limits for complex growth rate in rotatory electrothermoconvection in a dielectric fluid layer saturating a sparsely distributed porous medium

Article Category: Research Article

Published Online: Jul 10, 2024

Page range: -

Received: Jan 11, 2024

Accepted: May 10, 2024

DOI: https://doi.org/10.2478/sgem-2024-0008

KeywordsLinear stability analysis, Dielectric fluid, Oscillatory instability, complex growth rate, Electrothermoconvection

© 2024 Jitender Kumar et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1:

Figure 2:

Figure 3:

Figure 4:

Figure 5:

Keywords
Linear stability analysis, Dielectric fluid, Oscillatory instability, complex growth rate, Electrothermoconvection