Abstract
The classical two-phase boundary layer concept was adopted to analyse the problem of combined free and forced convection film boiling over an impermeable wall embedded in a porous medium. The governing equations, namely, the equations of continuity, energy and Darcy's model, were written for both vapor and liquid layers, and were solved simultaneously by means of the similarity transformation. Similarity solutions are found for a vertical flat plate, a horizontal circular cylinder and a sphere. Numerical integrations were carried out for given sets of the parameters associated with the vapor superheating Sup, the liquid subcooling Sub, the vapor mass flow rate R and the ratio of the liquid Rayleigh number to Peclet number Ra xf /Pe xf . It is found that a significant simplification of the problem is possible by setting the liquid stream function at the interface to zero. This simplification also reveals that the solution of the problem virtually depends on only three parameters, namely, Sup, Ra xf /Pe xf and the lumped parameter Sub/R.
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Abbreviations
- f :
-
dimensionless stream function
- g :
-
acceleration due to gravity
- h fg :
-
latent heat of vaporization
- k :
-
thermal conductivity
- K :
-
permeability
- Nu x :
-
local Nusselt number
- Pe x :
-
local Peclet number
- q w :
-
local surface heat flux
- R :
-
parameter associated with the vapor buoyancy effect on film boiling
- Ra x :
-
local Rayleigh number
- Sub:
-
parameter associated with liquid subcooling
- Sup:
-
parameter associated with vapor superheating
- T :
-
temperature
- u, v :
-
Darcian velocity components
- x, y :
-
boundary layer coordinates
- α :
-
thermal diffusivity
- β :
-
coefficient of thermal expansion
- η :
-
similarity variable
- θ :
-
dimensionless temperature
- ϱ :
-
density
- ψ :
-
stream function
- e :
-
external
- f :
-
liquid
- s :
-
interface
- w :
-
wall
References
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P. Cheng and A.K. Verma: The effect of subcooled liquid on film boiling about a vertical heated surface in a porous medium, Int. J. Heat Mass Transfer 24 (1981) 1151–1160
J.C.Y. Koh: Analysis of film boiling on vertical surfaces, J. Heat Transfer 84 (1962) 55–62.
P. Cheng: Combined free and forced convection flow about inclined surfaces in porous media, Int. J. Heat Mass Transfer 20 (1977) 807–814.
J.H. Merkin: Free convection boundary layers on axisymmetric and two-dimensional bodies of arbitrary shape in a saturated porous medium, Int. J. Heat Mass Transfer 22 (1979) 1461–1462.
A. Nakayama and H. Koyama: Free convective heat transfer over a non-isothermal body of arbitrary shape embedded in a fuid-saturated porous medium, J. Heat Transfer 109 (1987) 125–130.
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Nakayama, A., Koyama, H. A similarity transformation for subcooled mixed convection film boiling in a porous medium. Applied Scientific Research 45, 129–143 (1988). https://doi.org/10.1007/BF00386208
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DOI: https://doi.org/10.1007/BF00386208