Summary
This article theoretically studies the conjugate film condensation and natural convection along the vertical plate between a saturated vapor porous medium and a fluid-saturated porous medium. The solution takes into consideration the effect of heat conduction along the plate. The governing equations along with their corresponding boundary conditions for film condensation and natural convection are first cast into a dimensionless form by a nonsimilar transformation, and the resulting equations are then solved by the cubic spline collocation method. The primary parameters studied include the thermal resistance ratio of film to plateA, the thermal resistance ratio of natural convection to filmB, and the Jakob numberJa of the subcooling degree in the film. The effects of these dimensionless parameters on the plate temperature distribution and the local heat transfer rate on both sides of the plate are discussed in detail. In addition, the interesting engineering results regarding the overall heat transfer rate from the film condensation side to the natural convection side are also illustrated.
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Abbreviations
- A :
-
thermal resistance ratio of film to plate
- B :
-
thermal resistance ratio of natural convection to film
- C p :
-
specific heat
- g :
-
gravitational acceleration
- h :
-
heat transfer coefficient
- h fg :
-
latent heat of condensation
- Ja :
-
Jakob number (subcooling parameter)
- K :
-
permeability
- k :
-
thermal conductivity
- L :
-
length of the plate
- m :
-
mass flow rate per unit width
- Nu x :
-
local Nusselt number
- Nu :
-
overall Nusselt number
- p :
-
pressure
- Q :
-
total heat flux
- q x :
-
local heat flux
- Ra :
-
Rayleigh number
- Ra x :
-
local Rayleigh number
- T :
-
temperature
- t :
-
thickness of the plate
- u, v :
-
velocity components alongx-,y-directions
- x, y :
-
Cartesian coordinates
- α:
-
thermal diffusivity
- δ:
-
film thickness
- η:
-
pseudo-similarity variable
- θ:
-
dimesionless temperature
- μ:
-
dynamic viscosity
- v :
-
kinematic viscosity
- ζ:
-
transformed streamwise coordinate
- ϱ:
-
density
- ψ:
-
stream function
- n :
-
false time level of n
- n+1:
-
false time level of n+1
- ′:
-
derivate with respect to η
- c :
-
natural convection side
- i, j :
-
grid point location
- l :
-
film condensation side
- s :
-
saturated condition
- ν:
-
vapor phase
- w :
-
plate
- ∞:
-
ambient condition
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Char, M.I., Lin, J.D. Conjugate film condensation and natural convection between two porous media separated by a vertical plate. Acta Mechanica 148, 1–15 (2001). https://doi.org/10.1007/BF01183665
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DOI: https://doi.org/10.1007/BF01183665