Global stability for thermal convection in a couple-stress fluid

Sunil, .; Devi, Reeta; Mahajan, Amit

doi:10.1016/j.icheatmasstransfer.2011.03.030

Cited by 43 publications

(17 citation statements)

References 33 publications

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“…Majority of the investigations are concerned with buoyancy driven convection in a horizontal couple stress fluid layer [26][27][28][29][30] . Recently, Shivakumara et al [31] presented the effect of velocity and temperature boundary conditions on electrothermal convection in a rotating dielectric fluid layer considering the variation in the dielectric constant with the nonhomogeneous temperature gradient in the bulk flow.…”

Section: Introductionmentioning

confidence: 99%

Stability of natural convection in a vertical dielectric couple stress fluid layer in the presence of a horizontal AC electric field

Shankar

Kumar

Shivakumara

2016

Applied Mathematical Modelling

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a b s t r a c tThe combined effect of couple stresses and a uniform horizontal AC electric field on the stability of buoyancy-driven parallel shear flow of a vertical dielectric fluid between vertical surfaces maintained at constant but different temperatures is investigated. Applying linear stability theory, stability equations are derived and solved numerically using the Galerkin method with wave speed as the eigenvalue. The critical Grashof number G c , the critical wave number a c and the critical wave speed c c are computed for wide ranges of couple stress parameter c , AC electric Rayleigh number R ea and the Prandtl number Pr . Based on these parameters, the stability characteristics of the system are discussed in detail. The value of Prandtl number at which the transition from stationary to travelling-wave mode takes place is found to be independent of AC electric Rayleigh number even in the presence of couple stresses but increases significantly with increasing c . Moreover, the effect of increasing R ea is to instill instability, while the couple stress parameter shows destabilizing effect in the stationary mode but it exhibits a dual behavior if the instability is via travelling-wave mode. The streamlines and isotherms presented demonstrate the development of complex dynamics at the critical state.

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Section: Introductionmentioning

confidence: 99%

Stability of natural convection in a vertical dielectric couple stress fluid layer in the presence of a horizontal AC electric field

Shankar

Kumar

Shivakumara

2016

Applied Mathematical Modelling

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“…Jain and Stokes [14] studied the effect of couple stresses in fluids on the hydrodynamic stability of plane Poiseuille flow, while effect of couple stresses on thermal convective instability is analyzed by many researchers ( [15][16][17][18][19]). Rudraiah et al [20] investigated electrohydrodynamic stability of couple stress fluid flow in a horizontal channel occupied by a porous medium using energy method.…”

Section: Introductionmentioning

confidence: 99%

Stability of natural convection in a vertical couple stress fluid layer

Shankar

Kumar

Shivakumara

2014

International Journal of Heat and Mass Transfer

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a b s t r a c tThe stability of buoyancy-driven parallel shear flow of a couple stress fluid confined between vertical plates is investigated by performing a classical linear stability analysis. The plates are maintained at constant but different temperatures. A modified Orr-Sommerfeld equation is derived and solved numerically using the Galerkin method with wave speed as the eigenvalue. The critical Grashof number G c ; critical wave number a c and critical wave speed c c are computed for wide ranges of couple stress parameter K c and the Prandtl number Pr. Based on these parameters, the stability characteristics of the system are discussed in detail. The value of Prandtl number, at which the transition from stationary to travelling-wave mode takes place, increases with increasing K c . The couple stress parameter shows destabilising effect on the convective flow against stationary mode, while it exhibits a dual behaviour if the instability is via travelling-wave mode. The streamlines and isotherms presented demonstrate the development of complex dynamics at the critical state.

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“…Malashetty et al [40] investigated the onset of convection in a Couple-stress fluid in a porous medium, using a thermal non-equilibrium model. Sunil et al [41] studied global stability for thermal convection in a Couple-stress fluid and found that the linear and nonlinear stability Rayleigh number are the same.…”

Section: Introductionmentioning

confidence: 99%

Thermal Instability in a Layer of Couple Stress Nanofluid Saturated Porous Medium

Chand¹,

Rana²,

Yadav³

2017

Journal of Theoretical and Applied Mechanics

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Thermal instability in a horizontal layer of Couple-stress nanofluid in a porous medium is investigated. Darcy model is used for porous medium. The model used for nanofluid incorporates the effect of Brownian diffusion and thermophoresis. The flux of volume fraction of nanoparticle is taken to be zero on the isothermal boundaries. Normal mode analysis and perturbation method is employed to solve the eigenvalue problem with the Rayleigh number as eigenvalue. Oscillatory convection cannot occur for the problem. The effects of Couple-stress parameter, Lewis number, modified diffusivity ratio, concentration Rayleigh number and porosity on stationary convection are shown both analytically and graphically.

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Global stability for thermal convection in a couple-stress fluid

Cited by 43 publications

References 33 publications

Stability of natural convection in a vertical dielectric couple stress fluid layer in the presence of a horizontal AC electric field

Stability of natural convection in a vertical dielectric couple stress fluid layer in the presence of a horizontal AC electric field

Stability of natural convection in a vertical couple stress fluid layer

Thermal Instability in a Layer of Couple Stress Nanofluid Saturated Porous Medium

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