A Review of Some Recent Results on the Thermal Instability of a Plane Porous Layer with an Inclined Temperature Gradient

2013 ◽  
Vol 1 (2) ◽  
pp. 35
Author(s):  
Antonio Barletta
Keyword(s):  
Temperature Gradient ◽  
Porous Layer ◽  
Thermal Instability ◽  
Inclined Temperature Gradient

Effect of a Variable Gravity Field on Convection in an Anisotropic Porous Medium With Internal Heat Source and Inclined Temperature Gradient

2001 ◽  
Vol 124 (1) ◽  
pp. 144-150 ◽  
Author(s):  
Sherin M. Alex ◽  
Prabhamani R. Patil
Keyword(s):  
Temperature Gradient ◽  
Heat Source ◽  
Gravity Field ◽  
Convective Instability ◽  
Opposite Effect ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Anisotropic Porous Medium ◽  
Variable Gravity ◽  
Inclined Temperature Gradient

The convective instability of a horizontal fluid-saturated anisotropic porous layer, with internal heat source and inclined temperature gradient, subject to a gravity field varying with distance in the layer, is investigated. A linear stability analysis is performed and the resulting eigenvalue problem solved using a Galerkin technique. In the absence of an inclined temperature gradient, an increase in the variable gravity parameter above −1 destabilizes the system. In its presence interesting developments occur. An increase in the heat generation destabilizes the system when the variable gravity parameter is nonnegative. When it is negative the opposite effect is seen.

Thermal Instability of a Fluid-Saturated Porous Medium Bounded by Thin Fluid Layers

1987 ◽  
Vol 109 (3) ◽  
pp. 677-682 ◽  
Author(s):  
G. Pillatsis ◽  
M. E. Taslim ◽  
U. Narusawa
Keyword(s):  
Porous Medium ◽  
Porous Layer ◽  
Thermal Instability ◽  
Numerical Solutions ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Convective Motion ◽  
Wave Number ◽  
Thermal Conductivity Ratio ◽  
Fluid Layers

A linear stability analysis is performed for a horizontal Darcy porous layer of depth 2dm sandwiched between two fluid layers of depth d (each) with the top and bottom boundaries being dynamically free and kept at fixed temperatures. The Beavers–Joseph condition is employed as one of the interfacial boundary conditions between the fluid and the porous layer. The critical Rayleigh number and the horizontal wave number for the onset of convective motion depend on the following four nondimensional parameters: dˆ ( = dm/d, the depth ratio), δ ( = K/dm with K being the permeability of the porous medium), α (the proportionality constant in the Beavers–Joseph condition), and k/km (the thermal conductivity ratio). In order to analyze the effect of these parameters on the stability condition, a set of numerical solutions is obtained in terms of a convergent series for the respective layers, for the case in which the thickness of the porous layer is much greater than that of the fluid layer. A comparison of this study with the previously obtained exact solution for the case of constant heat flux boundaries is made to illustrate quantitative effects of the interfacial and the top/bottom boundaries on the thermal instability of a combined system of porous and fluid layers.

Low-frequency modulation of thermal instability

1970 ◽  
Vol 43 (2) ◽  
pp. 385-398 ◽  
Author(s):  
S. Rosenblat ◽  
D. M. Herbert
Keyword(s):  
Temperature Gradient ◽  
Asymptotic Solution ◽  
Frequency Modulation ◽  
Thermal Instability ◽  
Low Frequency ◽  
Experimental Results ◽  
Stability Criteria ◽  
The Stability ◽  
Boussinesq Fluid

A Boussinesq fluid is heated from below. The applied temperature gradient is the sum of a steady component and a low-frequency sinusoidal component. An asymptotic solution is obtained which describes the behaviour of infinitesimal disturbances to this configuration. The solution is discussed from the viewpoint of the stability or otherwise of the basic state, and possible stability criteria are analyzed. Some comparison is made with known experimental results.

Thermal instability of a nonhomogeneous power-law nanofluid in a porous layer with horizontal throughflow

2014 ◽  
Vol 213 ◽  
pp. 50-56 ◽  
Author(s):  
Jianhong Kang ◽  
Fubao Zhou ◽  
Wenchang Tan ◽  
Tongqiang Xia
Keyword(s):  
Porous Layer ◽  
Power Law ◽  
Thermal Instability ◽  
Power Law Nanofluid
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