Double-Diffusive Convection in a Saturated Anisotropic Porous Layer with Internal Heat Source

Bhadauria, B. S.

doi:10.1007/s11242-011-9903-x

Cited by 84 publications

(41 citation statements)

References 34 publications

(30 reference statements)

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“…The literature on internal heating is much less extensive than that on external heating. Some latest studies are due to Bhadauria et al [22], Bhadauria [23] and Bhadauria et al ([24], [25], [26]). …”

Section: Introductionmentioning

confidence: 99%

Nonlinear thermal convection in a layer of nanofluid under G-jitter and internal heating effects

Bhadauria

Kiran

Belhaq

2014

MATEC Web of Conferences

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Abstract. This paper deals with a mathematical model of controlling heat transfer in nanofluids. The time-periodic vertical vibrations of the system are considered to effect an external control of heat transport along with internal heating effects. A weakly non-linear stability analysis is based on the five-mode Lorenz model using which the Nusselt number is obtained as a function of the thermal Rayleigh number, nano-particle concentration based Rayleigh number, Prandtl number, Lewis number, modified diffusivity ratio, amplitude and frequency of modulation. It is shown that modulation can be effectively used to control convection and thereby heat transport. Further, it is found that the effect of internal Rayleigh number is to enhance the heat and nano-particles transport.

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Section: Introductionmentioning

confidence: 99%

Nonlinear thermal convection in a layer of nanofluid under G-jitter and internal heating effects

Bhadauria

Kiran

Belhaq

2014

MATEC Web of Conferences

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“…However, there are relatively very few studies available in which the effect of internal heating on convective flow has been investigated. Some of these studies are; Bhattacharya and Jena (1984), Haajizadeh et al (1984), Rionero and Straughan (1990), Rao and Wang (1991), Parthiban andPatil (1997), Herron Isom (2001), Khalili and Huettel (2002), Joshi et al (2006), Bhadauria et al (2011), andBhadauria (2012).…”

Section: Introductionmentioning

confidence: 99%

Study of Heat Transport in a Porous Medium Under G-jitter and Internal Heating Effects

2012

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In this article we study the combined effect of internal heating and time-periodic gravity modulation on thermal instability in a closely packed anisotropic porous medium, heated from below and cooled from above. The time-periodic gravity modulation, considered in this problem can be realized by vertically oscillating the porous medium. A weak non-linear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number has been obtained in terms of the amplitude of convection which is governed by the non-autonomous Ginzburg-Landau equation derived for the stationary mode of convection. The effects of various parameters such as; internal Rayleigh number, amplitude and frequency of gravity modulation, thermo-mechanical anisotropies, and Vadász number on heat transport has been analyzed. It is found that the response of the convective system to the internal Rayleigh number is destabilizing. Further it is found that the heat transport can also be controlled by suitably adjusting the external parameters of the system.

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“…Capone et al [43] carried -27 -DOI: 10.5963/AMSA0301004 out the linear and nonlinear stability analysis of double-diffusive penetrative convection in an anisotropic porous layer with a constant throughflow via internal heat source. Recently Bhadauria group [44][45][46][47] have studied the problem of thermal instability in porous media with internal heating, considering various physical models. Double diffusive convection occurs in many systems in industry and nature, and in the present context, is of particular interest in the study of extraction of metals from ores where a mushy layer is formed during solidification of a metalic alloy.…”

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Effect of Internal Heating on Double Diffusive Convection in a Couple Stress Fluid Saturated Anisotropic Porous Medium

Srivastava¹,

Bhadauria²,

Hashim³

2014

AMSA

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Abstract-The effect of internal heat source on double diffusive convection in a couple stress fluid saturated horizontal anisotropic porous layer was studied analytically by performing linear and nonlinear stability analyses. For linear stability analysis, normal mode technique was used, whereas for nonlinear stability analysis a minimal representation of Fourier series upto two terms was used. Effects of anisotropic parameter, couple stress parameter, solute Rayleigh number, Vadász number, Lewis number, internal heat source parameter on stationary, oscillatory and finite amplitude convection were obtained and shown graphically. Also the graphs for heat and mass transport, streamlines, isotherms, isohalines for steady and unsteady cases were drawn. It was found that internal heat source parameter had destabilizing effect on all modes of convection. Heat transport increased and mass transport decreased with the increase in internal heat source parameter.

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Double-Diffusive Convection in a Saturated Anisotropic Porous Layer with Internal Heat Source

Cited by 84 publications

References 34 publications

Nonlinear thermal convection in a layer of nanofluid under G-jitter and internal heating effects

Nonlinear thermal convection in a layer of nanofluid under G-jitter and internal heating effects

Study of Heat Transport in a Porous Medium Under G-jitter and Internal Heating Effects

Effect of Internal Heating on Double Diffusive Convection in a Couple Stress Fluid Saturated Anisotropic Porous Medium

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