Onset of convection in a porous layer with net through-flow and internal heat generation

1998 ◽  
Vol 10 (1) ◽  
pp. 315-317 ◽  
Author(s):  
A. Khalili ◽  
I. S. Shivakumara
Keyword(s):  
Porous Layer ◽  
Heat Generation ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Onset Of Convection ◽  
Through Flow

scholarly journals Onset of Convection in an Inclined Anisotropic Porous Layer with Internal Heat Generation

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 75 ◽  
Author(s):  
Leiv Storesletten ◽  
D. Andrew S. Rees
Keyword(s):  
Porous Layer ◽  
Heat Generation ◽  
Internal Heat ◽  
Convective Motion ◽  
Linear Instability ◽  
Internal Heat Generation ◽  
Anisotropy Ratio ◽  
Heat Sources ◽  
Onset Of Convection ◽  
Set Up

The onset of convection in an inclined porous layer which is heated internally by a uniform distribution of heat sources is considered. We investigate the combined effects of inclination, anisotropy and internal heat generation on the linear instability of the basic parallel flow. When the Rayleigh number is sufficiently large, instability occurs and a convective motion is set up. It turns out that the preferred motion at convection onset depends quite strongly on the anisotropy ratio, ξ , and the inclination angle. When ξ < 1 the preferred motion is in the form of longitudinal rolls for all inclinations. When ξ > 1 transverse rolls are preferred for small inclinations but, at high inclinations, longitudinal rolls are preferred. At intermediate inclinations the preferred roll orientation varies smoothly between these two extremes.

scholarly journals Vadasz Number Effects on Convection in a Horizontal Porous Layer Subjected to Internal Heat Generation and G-Jitter

Fluids ◽  
2020 ◽  
Vol 5 (3) ◽  
pp. 124
Author(s):  
Saneshan Govender
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Porous Layer ◽  
Heat Generation ◽  
Critical Rayleigh Number ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Onset Of Convection ◽  
Vadasz Number ◽  
The Impact

Flow and heat transfer in a horizontal porous layer subjected to internal heat generation and g-jitter is considered for the Dirichlet thermal boundary condition. A linear stability analysis is used to determine the convection threshold in terms of the critical Rayleigh number. For the low amplitude, high frequency approximation, the results show that vibration has a stabilizing effect on the onset of convection when the porous layer is heated from below. When the porous layer is cooled from below and heated from above, the vibration has a destabilizing effect in the presence of internal heat generation. It is also demonstrated that when the top and bottoms walls are cooled and rigid/impermeable, the critical Rayleigh number is infinitely large and conduction is the only possible mode of heat transfer. The impact of increasing the Vadasz number is to stabilize the convection, in addition to reducing the transition point from synchronous to subharmonic solutions.

The Onset of Brinkman-Benard Ferroconvection in a Saturated Porous Layer With Internal Heat Generation

2010 ◽  
Author(s):  
C. E. Nanjundappa ◽  
H. N. Prakash
Keyword(s):  
Porous Layer ◽  
Heat Generation ◽  
Lower Boundary ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Darcy Number ◽  
Internal Heat Generation ◽  
Fluid Viscosity ◽  
Thermomagnetic Convection ◽  
Saturated Porous Layer

The effect of internal heat generation on the criterion for the onset of thermomagnetic convection in a horizontal ferrofluid saturated porous layer in the presence of a uniform magnetic field is studied using the Brinkman-Lapwood extended Darcy flow model with fluid viscosity different from effective viscosity. The lower boundary is taken to be rigid – insulating and the upper surface is free and subject to the general thermal condition. The resulting eigenvalue problem is solved numerically using the Galerkin method with the Rayleigh number as the eigenvalue. The effect of increase in the value of dimensionless internal heat source strength Ns, magnetic number M1 and the non-linearity of fluid magnetization parameter M3 is to hasten, while increase in the value of inverse of Darcy number Da−1, viscosity ratio Λ, Biot number Bi and magnetic susceptibility χ is to delay the onset of thermomagnetic convection in a ferrofluid saturated porous layer. Further, increase in the value of Bi, Da−1 and Ns as well as decrease in Λ M1> and M3 is to diminish the dimension of convection cells.

scholarly journals Vadasz Number Effects on Convection in a Vertical Rotating Porous Layer, Placed Far from Axis of Rotation, and Subjected to Internal Heat Generation and Centrifugal Jitter

Physics ◽  
2021 ◽  
Vol 3 (3) ◽  
pp. 728-738
Author(s):  
Saneshan Govender
Keyword(s):  
Porous Layer ◽  
Heat Generation ◽  
Critical Rayleigh Number ◽  
Time Derivative ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Stability Criteria ◽  
Axis Of Rotation ◽  
Vadasz Number ◽  
The Impact

The flow and heat transfer in a rotating vertical porous layer, placed far from the axis of rotation, and subjected to internal heat generation and centrifugal jitter, is considered. The linear stability theory is used to determine the convection threshold, in terms of the critical Rayleigh number. Typical liquids used in engineering applications and heavy liquid metals are used to demonstrate conditions at which the Vadasz number is sufficiently small to warrant the retention of the time derivative in the momentum equation. When considering low amplitude and high frequency approximation, the results show that vibration has a stabilizing effect on the onset of convection. The impact of increasing the Vadasz number is to stabilize the convection, in addition to reducing the transition point from synchronous to subharmonic solutions. In summary, when the Vadasz number is large, centrifugal jitter has no impact on the convection stability criteria. In contrast, when the Vadasz number is small, centrifugal jitter impacts the convection stability criteria.

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