Abstract
Convective stability is studied for an infinite horizontal porous layer containing a vertical porous segment of different properties. The critical Rayleigh number depends on the aspect ratio of the nonhomogeneous region and the ratios of permeability, thermal conductivity, and thermal diffusivity of the matrix. Incipient streamlines may be either symmetric or antisymmetric.
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Abbreviations
- a 1,a 2 :
-
constants defined by equations (26, 28)
- A 1,A 2,B 1,B 2 :
-
constant amplitudes
- b 1,b 2 :
-
constants defined by equations (26, 28)
- c :
-
constant defined by equation (24)
- C 1,C 2,C 3 :
-
constants defined by equation (35)
- F :
-
function ofx
- g :
-
gravitational acceleration
- G :
-
function ofx
- H :
-
height of layer
- k :
-
thermal conductivity of matrix
- K :
-
permeability
- m :
-
integer defined by equation (39)
- p :
-
pressure
- R:
-
Rayleigh number defined by equation (12)
- R c :
-
critical Rayleigh number
- S 1,S 2,S 3 :
-
constants defined by equation (35)
- T :
-
temperature
- T 0 :
-
bottom surface temperature
- u, v :
-
lateral and vertical velocities
- x, y :
-
Cartesian coordinates
- α :
-
thermal diffusivity of matrix
- β :
-
coefficient of thermal expansion of fluid
- γ :
-
ratio of permeabilitiesK 2/K 1
- δ :
-
ratio of conductivitiesk 1/k 2
- Δ:
-
difference
- λ :
-
ratio of width to height of inhomogeneity
- μ :
-
viscosity
- ν :
-
kinematic viscosity
- ρ :
-
density of fluid
- σ :
-
ratio of diffusivitiesα 1/α 2
- ÷ :
-
stream function
- ▽2 :
-
Laplace operator
- ′:
-
dimensional
- 1:
-
inhomogeneous segment
- 2:
-
infinite lamina
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Wang, C.Y. Thermal convective instability of a horizontal saturated porous layer with a segment of inhomogeneity. Appl. Sci. Res. 52, 147–160 (1994). https://doi.org/10.1007/BF00868056
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DOI: https://doi.org/10.1007/BF00868056