Unconditional nonlinear stability for double‐diffusive convection with temperature‐ and pressure‐dependent viscosity

The thermorheological effect on the onset of Rayleigh–Bénard convection in a biviscous Bingham fluid in the presence of a horizontal magnetic field is investigated considering rough boundary conditions on velocity and Robin boundary conditions on temperature. The viscosity of the electrically conducting fluid is assumed to be sensitive to temperature variation. Linear and global nonlinear stability analyses are performed using the Chebyshev pseudospectral method to determine the existence of instability or otherwise. A general interpretation is made from the results to show the effects of the magnetic field and the variable viscosity on the system's stability. The biviscous Bingham parameter and the Chandrasekhar number are shown to have a delay in the onset of convection, while the effect of temperature sensitivity is to advance the onset. It is found that the results of linear and global nonlinear stability are not in agreement, so the region of subcritical instability exists. Also, the results obtained for Rayleigh–Bénard convection agree pretty well with those of Platten and Legros and Siddheshwar et al. for the limiting cases.

Section: Introductionmentioning

confidence: 99%

Thermorheological effect on Rayleigh–Bénard magnetoconvection in a biviscous Bingham fluid with rough boundary condition on velocity and Robin boundary condition on temperature

Nandal

Siddheshwar

2023

“…Mulone and Rionero 13 and Lombardo et al 14 used modified generalized energies to estimate additional strong nonlinear stability limitations for the thermosolutal penetrative convective motion. Mahajan and Tripathi 15 investigated the effects of nonuniform thermophoresis gradients with variable viscosity on the stability of a configuration that involves heat diffusion as well as mass diffusion.…”

Section: Introductionmentioning

confidence: 99%

Effects of throughflow on thermosolutal penetrative convection in a fluid layer with variable gravity field

Gangadharaiah¹,

Ananda²,

Aruna

2022

In this study, the start of thermosolutal penetrative convection in a horizontal fluid layer heated and salted from below was investigated analytically and graphically in the presence of throughflow and changeable gravity field effects. The normal mode technique is used to test the system's stability properties. The mathematical expressions for stationary and oscillatory Rayleigh numbers are obtained as a function of the governing parameters. The analysis demonstrates that the vertical throughflow, gravity parameter, and heat source effect all have a considerable influence on the beginning of convective motion in double‐diffusive flow. The impacts of variable gravity, vertical throughflow, and heat source parameters, as well as other physical parameters such as Solutal Rayleigh numbers and Lewis numbers, on stationary and oscillatory convection, are studied and illustrated graphically, and some previously published results are recovered in the limiting cases.

“…To name a few, oceanography, magma chambers, solar ponds, solidification of alloys, cooling towers, drying technologies, solar collector, pin-fin devices, insulation of nuclear reactor, solar plate collector, cooling process of electronic devices, and so forth. [1][2][3][4][5][6][7][8][9][10] On the other hand, the deviation from the idealized conditions (i.e., uniform temperature and concentration) is quite frequently found in the pragmatic conditions. Therefore, an in-depth study of heat and mass transfer (HMT) characteristics in such systems subjected to nonuniform heating and concentration conditions is of prime essence.…”

Section: Introductionmentioning

confidence: 99%

“…DDC has all‐embracing findings in different natural and man‐made activities. To name a few, oceanography, magma chambers, solar ponds, solidification of alloys, cooling towers, drying technologies, solar collector, pin‐fin devices, insulation of nuclear reactor, solar plate collector, cooling process of electronic devices, and so forth 1–10 . On the other hand, the deviation from the idealized conditions (i.e., uniform temperature and concentration) is quite frequently found in the pragmatic conditions.…”

Section: Introductionmentioning

confidence: 99%

Effect of the aspect ratio of the shallow enclosure and built‐in rectangular blockage on MHD double‐diffusive free convection subjugated to non‐uniform boundary conditions

Kumar

Gangawane

2022

In this study, the lattice Boltzmann method is used to explore the double‐diffusive natural convection within a shallow enclosure with a built‐in rectangular blockage at its geometric center. The enclosure is exposed to an external magnetic field. One of the enclosure walls is subjected to linearly/sinusoidal heating and concentration conditions. The rectangular blockage is at higher temperature and concentration conditions. Numerical experimentation is executed for a range of parameters such as Rayleigh number MathClass-open( 1 0 3 ≤ R a ≤ 1 0 5 MathClass-close) $(1{0}^{3}\le Ra\le 1{0}^{5})$, Lewis number MathClass-open( 2 ≤ L e ≤ 10 MathClass-close) $(2\le Le\le 10)$, buoyancy ratio MathClass-open( − 2 ≤ N ≤ 2 MathClass-close) $(-2\le N\le 2)$, aspect ratio of the enclosure MathClass-open( 2 ≤ A R ≤ 4 MathClass-close) $(2\le AR\le 4)$, aspect ratio of the built‐in blockage MathClass-open( 2 ≤ a r ≤ 4 MathClass-close) $(2\le ar\le 4)$, and Hartmann number MathClass-open( 0 ≤ H a ≤ 100 MathClass-close) $(0\le Ha\le 100)$. The working fluid is assumed to be liquid metal (sodium–potassium alloy, P r = 0.054 $Pr=0.054$). The complex interaction of flow parameters with the nonuniform heating and concentration conditions has been explored. Higher heat and mass transfer (HMT) rates are noticed for the sinusoidal temperature and concentration profile compared to linear for a given R a $Ra$. N u t o t a l $N{u}_{total}$ and S h t o t a l $S{h}_{total}$ showed enhancement by 22 % $22 \% $, and 21 % $21 \% $ for sinusoidal temperature and concentration profile of the enclosure as compared to linear for A R = 2 $AR=2$. The increase in the blockage and the enclosure aspect ratio shows augmentation in the HMT rate. The consequences of the study are also summarized in terms of empirical correlations of the N u t o t a l $N{u}_{total}$ and S h t o t a l $S{h}_{total}$ numbers showing functional dependence on the considered range of parameters.