Abstract
A boundary-layer analysis is presented for the mixed convection flow which is produced when a horizontal line heat source, which is embedded in an infinite fluid-saturated porous medium, generates heat at a constant rate. It is shown that the governing equations can be non-dimensionalized so that they do not involve any parameters and thus just one solution of the transformed boundary-layer equations is required. Series solutions which are valid both near the line source and far downstream are obtained and compared with the numerical solution of the full boundary-layer equations.
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Abbreviations
- A :
-
constant, equation (29)
- c :
-
specific heat
- g :
-
acceleration due to gravity
- k :
-
thermal conductivity
- K :
-
permeability of the porous medium
- L :
-
characteristic length
- Pe :
-
Peclet number, equation (7)
- q :
-
the constant rate of heat released from the line source,
- Ra :
-
modified Rayleigh number for a porous medium, equation (7)
- T :
-
temperature
- u, v :
-
non-dimensional velocity components in thex- andy-directions
- x, y :
-
non-dimensional coordinates
- α :
-
thermal diffusivity
- Β :
-
coefficient of thermal expansion
- θ :
-
non-dimensional temperature
- η,\(\hat \eta \),ξ,ζ :
-
similarity variables
- Μ :
-
dynamic viscosity
- v :
-
kinematic viscosity
- ψ :
-
non-dimensional stream function
- ξ :
-
a similarity variable
- -:
-
dimensional variables,
- ′:
-
differentiation with respect toη,\(\hat \eta \) orζ
- Ω :
-
centreline condition
- ∞:
-
ambient condition
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Pop, I., Ingham, D.B. & Miskin, I. Mixed convection in a porous medium produced by a line heat source. Transp Porous Med 18, 1–13 (1995). https://doi.org/10.1007/BF00620657
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DOI: https://doi.org/10.1007/BF00620657