Abstract
A Prandtl number effect for natural convection in a horizontal porous layer is demonstrated to be an explanation for the difference in heat transfer between different porous systems. A Prandtl number trend in experimental data is identified and arguments are presented to substantiate a Prandtl number dependence. Finally, Nusselt number correlations of experimental data at different Prandtl numbers have been developed.
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Abbreviations
- c p :
-
specific heat
- d :
-
particle diameter
- Da:
-
Darcy number
- ê i :
-
unit vector in i direction
- g :
-
acceleration due to gravity
- h c :
-
fluid-solid heat transfer coefficient
- k :
-
thermal conductivity
- k m :
-
effective thermal conductivity of porous media
- KC:
-
Kozeny-Carman number
- l :
-
spacing between particles
- L :
-
height of layer
- Nu:
-
Nusselt number
- P :
-
pressure
- Pr m :
-
porous media Prandtl number
- Ra:
-
Rayleigh number
- Re m :
-
porous media Reynolds number
- T :
-
temperature
- u :
-
velocity
- U :
-
Darcian velocity
- u, v, w :
-
components of velocity in the x, y, and z directions, respectively
- U, V, W :
-
components of the Darcian velocity in the x, y, and z directions, respectively
- x, y, z :
-
spatial coordinates
- α m :
-
thermal diffusivity of porous media
- β :
-
thermal expansion coefficient
- ΔT :
-
applied temperature difference
- Ε:
-
porosity
- Λ:
-
dimensionless fluid-solid heat transfer coefficient
- ν :
-
kinematic viscosity
- ψ :
-
permeability
- ϕ :
-
Kozeny coefficient
- ρ :
-
density
- f :
-
pertaining to the fluid
- s :
-
pertaining to the solid
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Somerton, C.W. The Prandtl number effect in porous layer convection. Appl. Sci. Res. 40, 333–344 (1983). https://doi.org/10.1007/BF00383039
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DOI: https://doi.org/10.1007/BF00383039