Natural convection in a vertical porous enclosure with internal heat generation

Haajizadeh, Masoud; Özgüç, A.; Tien, C. L.

doi:10.1016/0017-9310(84)90171-6

Cited by 71 publications

(37 citation statements)

References 2 publications

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“…Onset of convection in a fluid saturating a horizontal layer of an anisotropic porous medium with internal heat source subjected to inclined temperature gradient is studied by Parthiban and Palil (1997). Effects of uniform heat generation across an enclosure with isothermal vertical walls and adiabatic horizontal walls were studied by Rao and Wang (1991) and Haajizadeh et al (1984). An analytic solution for small Rayleigh number in a finite container with isothermal walls and uniform heat generation within the porous medium has been given by Joshi et al (2006).…”

Section: Introductionmentioning

confidence: 99%

Natural convection in a rotating anisotropic porous layer with internal heat generation

Bhadauria

Kumar

et al. 2011

Transp Porous Med

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In this article, linear and nonlinear thermal instability in a rotating anisotropic porous layer with heat source has been investigated. The extended Darcy model, which includes the time derivative and Coriolis term has been employed in the momentum equation. The linear theory has been performed by using normal mode technique, while nonlinear analysis is based on minimal representation of the truncated Fourier series having only two terms. The criteria for both stationary and oscillatory convection is derived analytically. The rotation inhibits the onset of convection in both stationary and oscillatory modes. Effects of parameters on critical Rayleigh number has also been investigated. A weak nonlinear analysis based on the truncated representation of Fourier series method has been used to find the Nusselt number. The transient behavior of the Nusselt number has also been investigated by solving the finite amplitude equations using a numerical method. Steady and unsteady streamlines, and isotherms have been drawn to determine the nature of flow pattern. The results obtained during the analysis have been presented graphically.

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Section: Introductionmentioning

confidence: 99%

Natural convection in a rotating anisotropic porous layer with internal heat generation

Bhadauria

Kumar

et al. 2011

Transp Porous Med

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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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“…Recently, Mealey and Merkin (2009) moved away from the study of uniform internal heating to that of non-uniform internal heating and solved the problem numerically and analytically. However, Haajizadeh et al (1984), Rao and Wang (1991), Joshi et al (2006) and Mealey and Merkin (2009) considered the steady flow only.…”

Section: Introductionmentioning

confidence: 98%

“…Numerical treatment usually used to solve the equations or if possible by an analytic method. Numerical investigation of natural convection in porous enclosure having uniform internal heating firstly conducted by Haajizadeh et al (1984). Then continued by Rao and Wang (1991) and analytically by Joshi et al (2006).…”

Section: Introductionmentioning

confidence: 99%

Effect of Time Periodic Boundary Conditions on Convective Flows in a Porous Square Enclosure with Non-Uniform Internal Heating

2010

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The problem of unsteady natural convection in a square region filled with a fluid-saturated porous medium having non-uniform internal heating and heated laterally is considered. The heated wall surface temperature varies sinusoidally with the time about fixed mean temperature. The opposite cold wall is maintained at a constant temperature. The top and bottom horizontal walls are kept adiabatic. The flow field is modelled with the Darcy model and is solved numerically using a finite difference method. The transient solutions obtained are all periodic in time. The effect of Rayleigh number, internal heating parameters, heating amplitude and oscillating frequency on the flow and temperature field as well as the total heat generated within the convective region are presented. It was found that strong internal heating can generate significant maximum fluid temperatures above the heated wall. The location of the maximum fluid temperature moves with time according to the periodically changing heated wall temperature. The augmentation of the space-averaged temperature in the cavity strongly depends on the heating amplitude and rather insensitive to the oscillating frequency.

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Natural convection in a vertical porous enclosure with internal heat generation

Cited by 71 publications

References 2 publications

Natural convection in a rotating anisotropic porous layer with internal heat generation

Natural convection in a rotating anisotropic porous layer with internal heat generation

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

Effect of Time Periodic Boundary Conditions on Convective Flows in a Porous Square Enclosure with Non-Uniform Internal Heating

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