Abstract
The steady forced convection flow of a power-law fluid over a horizontal plate embedded in a saturated Darcy-Brinkman porous medium is considered. The flow is driven by a constant pressure gradient. In addition to the convective inertia, also the “porous Forchheimer inertia” effects are taken into account. The pertinent boundary value problem is investigated analytically, as well as numerically by a finite difference method. It is found that far away from the leading edge, the velocity boundary layer always approaches an asymptotic state with identically vanishing transverse component. This holds for pseudoplastic (0 < n < 1), Newtonian (n = 1), and dilatant (n > 1) fluids as well. The asymptotic solution is given for several particular values of the power-law index n in an exact analytical form. The main flow characteristics of physical and engineering interest are discussed in the paper in some detail.
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Abbreviations
- C F :
-
Forchheimer coefficient
- Da :
-
Darcy number
- F :
-
Forchheimer number
- K :
-
permeability (m2)
- K*:
-
modified permeability (mn+1)
- L :
-
length unit (m)
- n :
-
power-law index
- p :
-
pressure (Pa)
- S :
-
dimensionless skin friction
- u :
-
horizontal velocity (ms−1)
- u ∞ :
-
free stream velocity (ms−1)
- U :
-
dimensionless horizontal velocity
- v :
-
vertical velocity (ms−1)
- V :
-
dimensionless vertical velocity
- x :
-
horizontal coordinate (m)
- X :
-
dimensionless horizontal coordinate
- y :
-
vertical coordinate (m)
- Y :
-
dimensionless vertical coordinate
- δ :
-
displacement thickness
- \({\varepsilon}\) :
-
porosity
- μ :
-
consistency index (kgsn-2m−1)
- ρ :
-
density (kgm−3)
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Pantokratoras, A., Magyari, E. Forced Convection Flow of Power-Law Fluids Over a Flat Plate Embedded in a Darcy-Brinkman Porous Medium. Transp Porous Med 85, 143–155 (2010). https://doi.org/10.1007/s11242-010-9551-6
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DOI: https://doi.org/10.1007/s11242-010-9551-6