Global stability of natural convection in internally heated inclined fluid layer

Arora, Manisha; Bajaj, Renu

doi:10.1007/s10665-021-10127-1

Cited by 9 publications

(4 citation statements)

References 29 publications

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“…Kumar et al 25 revisited and reworked the problem previously examined by Matta and Hill 22 to conduct a nonlinear stability analysis. Recently, Arora and Bajaj 31 utilized the energy method to analyze the nonlinear stability of a fluid layer heated internally with an inclined configuration. Tlau and Ontela investigated entropy generation in a sloping channel filled with a porous medium during magnetohydrodynamic nanofluid flow with a heat source/sink 26 .…”

Section: Introductionmentioning

confidence: 99%

Influence of a magnetic field on double‐diffusive convection in an inclined porous layer

Ragoju

2024

Heat Trans

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The present study investigates the impact of a magnetic field on double‐diffusive convection in an inclined porous layer, employing linear instability theory. The perturbed state is solved using the normal mode technique, and the stability eigenvalue problem is numerically analyzed for longitudinal and traveling rolls using the Runge‐Kutta method coupled with the shooting method. Various dimensionless physical parameters, including solutal and thermal Rayleigh numbers, inclination angle, Hartmann number, and Lewis number, are examined for their influence on system stability. The findings reveal that, for , the Hartmann number, solute Rayleigh number, and inclination angle act as stabilizing factors, with greater stability observed for traveling rolls compared to longitudinal rolls. In the case of , the critical Rayleigh number shows a monotonic relationship with the solute Rayleigh number and inclination angle, while its relationship with the Hartmann number is non‐monotonic for traveling rolls. Moreover, for , the Hartmann number stabilizes the system by raising the onset threshold value, favouring longitudinal modes. The solute Rayleigh number also contributes to system stability. The impact of the inclination angle on system stability is contingent upon its magnitude, with small angles favouring the stability of longitudinal rolls and larger angles leading to an initial transition from traveling to longitudinal rolls, indicating a complex non‐monotonic behavior.

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Section: Introductionmentioning

confidence: 99%

Influence of a magnetic field on double‐diffusive convection in an inclined porous layer

Ragoju

2024

Heat Trans

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“…All realized perturbations are cellular. Arora et al [15] studied the nonlinear stability of natural convection in a tilted layer of liquid that has a uniform internal source (or, on the contrary, a sink) of heat, while a constant temperature is maintained at the boundaries of the layer. It has been established that the stability region is significantly determined by the layer tilt angle and the value of the Prandtl number.…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Convection in an Inclined Porous Layer Subjected to a Vertical Temperature Gradient

Shubenkov,

Lyubimova,

Sadilov

2024

FDMP

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In this paper, we study the onset and development of three-dimensional convection in a tilted porous layer saturated with a liquid. The layer is subjected to a gravitational field and a strictly vertical temperature gradient. Typically, problems of thermal convection in tilted porous media saturated with a liquid are studied by assuming constant different temperatures at the boundaries of the layer, which prevent these systems from supporting conductive (non-convective) states. The boundary conditions considered in the present work allow a conductive state and are representative of typical geological applications. In an earlier work, we carried out a linear stability analysis of the conductive state. It was shown that at any layer tilt angles, the most dangerous type of disturbances are longitudinal rolls. Moreover, a non-zero velocity component exists in z-direction. In the present work, threedimensional non-linear convection regimes are studied. The original three-dimensional problem is reduced to two-dimensional one with an analytical expression for the velocity z-component v z ¼ v z x; y ð Þ. It is shown that the critical Rayleigh number values obtained through numerical solutions of the obtained 2D problem by a finite difference method for different layer inclination angles, are in a good agreement with those predicted by the linear theory. The number of convective rolls realized in nonlinear calculations also fits the linear theory predictions for a given cavity geometry. Calculations carried out at low supercriticalities show that a direct bifurcation takes place. With increasing supercriticality, no transitions to other convective regimes are detected. The situation studied in this problem can be observed in oil-bearing rock formations under the influence of a geothermal temperature gradient, where the ensuing fluid convection can affect the distribution of oil throughout the layer.

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“…Their studies consider longitudinal and transverse rolls (TRs), and the solutions are obtained using numerical methods. A few nonlinear stability studies on inclined layer convection have been done using numerical methods like the shooting method [18,34] or artificial neural network prediction [35]. RBC in mono and hybrid nanoliquids in an inclined geometry using shooting method is an unexplored area of study.…”

Section: Introductionmentioning

confidence: 99%

Rayleigh–Bénard convection in mono and hybrid nanoliquids in an inclined slot

Gayathri,

Pranesh,

Siddheshwar

2023

J. Phys. A: Math. Theor.

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Linear stability analysis is conducted to investigate the longitudinal and transverse rolls (TRs) generated in Rayleigh–Bénard convection in mono and hybrid nanoliquids confined between two infinite inclined parallel slots. Thermophysical properties of six mono nanoliquids and fifteen hybrid nanoliquids are calculated for different volume fractions (0.5%, 1%, 2%) using phenomenological laws and mixture theory. The shooting method is used to solve boundary eigenvalue problems to obtain the eigenvalues for 16 different boundary conditions. It is observed that as the inclination angle is increased, it delays the onset of longitudinal rolls in the case of all boundary conditions. However, it advances the onset of TRs except when the lower plate is adiabatic. The addition of mono and hybrid nanoparticles results in the advancement of the onset of convection. The addition of SWCNT and SWCNT— Al 2 O 3 accelerates the onset of convection the most while Cu and Cu-Ag accelerates the onset of convection the least amongst the mono and hybrid nanoparticles considered in the study.

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Global stability of natural convection in internally heated inclined fluid layer

Cited by 9 publications

References 29 publications

Influence of a magnetic field on double‐diffusive convection in an inclined porous layer

Influence of a magnetic field on double‐diffusive convection in an inclined porous layer

Three-Dimensional Convection in an Inclined Porous Layer Subjected to a Vertical Temperature Gradient

Rayleigh–Bénard convection in mono and hybrid nanoliquids in an inclined slot

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