Conditional stability for thermal convection in a rotating couple-stress fluid saturating a porous medium with temperature and pressure dependent viscosity

Sunil, .; Choudhary, Shalu; Mahajan, Amit

doi:10.1088/1742-2132/10/4/045013

Cited by 8 publications

(2 citation statements)

References 40 publications

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“…This can be seen for Poiseuille 10 flow through circular pipes (Stokes, 1966(Stokes, , 1984, where the velocity profile and stresses depend on both viscous parameters  and  . It turns out in some three-dimensional cases with velocity boundary conditions the results for velocities may look fine (Sunil et al, 2011(Sunil et al, , 2013Hayat et al, 2015;Hayat et al,2017). However, the couple-stress distribution inside the fluid depends on  .…”

Section:  22mentioning

confidence: 99%

An Assessment of Couple Stress Theories

Hadjesfandiari¹,

Dargush²

2018

Preprint

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In this paper, we examine the mathematical and physical consistencies of the three primary couple stress theories: original Mindlin-Tiersten-Koiter couple stress theory (MTK-CST), modified couple stress theory (M-CST) and consistent couple stress theory (C-CST).  As has been known for many years, MTK-CST suffers from some fundamental inconsistencies, such as the indeterminacy of the couple-stress tensor.  Therefore, despite the fact that MTK-CST has a fundamental position in the evolution of size-dependent continuum mechanics, it is not a reliable theory within continuum mechanics, for example, in developing new size-dependent multi-physics formulations.  We also observe that M-CST not only inherits all inconsistences from the original MTK-CST, but also suffers from new additional inconsistencies, such as the introduction of a new non-physical governing equation.  These inconsistencies refute the claim of those who state that the couple-stress tensor may be chosen symmetric.  Therefore, the apparent success of MTK-CST and M-CST in describing a size-effect for some problems, such as two-dimensional plate and beam bending, is not enough to justify these theories as suitable for general cases.  In fact, the symmetric couple-stresses in M-CST create torsional or anticlastic deformation, not bending.  On the other hand, C-CST, with a skew-symmetric couple-stress tensor, is the consistent continuum mechanics suitable for solving different size-dependent solid, fluid and multi-physics problems. 

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Section:  22mentioning

confidence: 99%

An Assessment of Couple Stress Theories

Hadjesfandiari¹,

Dargush²

2018

Preprint

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“…An interesting problem on double‐diffusive convection is studied using the energy method of Hameed and Harfash 28 by considering viscosity as a function of temperature. Sunil et al 29‐32 applied the linear and nonlinear energy stability theories on a layer of fluid with viscosity as a function of temperature and pressure.…”

Section: Introductionmentioning

confidence: 99%

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

Mahajan

Tripathi

2020

Heat Trans

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A linear and nonlinear stability analyses are carried out for a double‐diffusive chemically reactive fluid layer with viscosity being a function of temperature and pressure. The linear stability analysis is studied when the stabilizing salt gradient acts against the destabilizing thermal gradient. The effect of reaction parameters and variable viscosity on the stability of the system is studied for heated below, salted above, and the heated and salted below models with Rigid–Rigid boundary conditions. Chebyshev pseudospectral method is applied to determine the numerical solutions.

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Internal Natural Convection: Heating from Below

Nield

Bejan

2017

Convection in Porous Media

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Conditional stability for thermal convection in a rotating couple-stress fluid saturating a porous medium with temperature and pressure dependent viscosity

Cited by 8 publications

References 40 publications

An Assessment of Couple Stress Theories

An Assessment of Couple Stress Theories

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

Internal Natural Convection: Heating from Below

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