Abstract
We consider a horizontal static liquid layer on a planar solid boundary. The layer is evaporating when the plate is heated. Vapor recoil and thermo-capillary are discussed along with the effect of mass loss and vapor convection due to evaporating liquid and non-equilibrium thermodynamic effects. These coupled systems of equations are reduced to a single evolution equation for the local thickness of the liquid layer by using a long-wave asymptotics. The partial differential equation is solved numerically.
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Abbreviations
- C :
-
Capillary number
- D :
-
Distance between solid surface and water pipe
- D ρ :
-
Ratio of the liquid density and vapor density
- D v :
-
Ratio of the liquid kinematic viscosity and vapor kinematic viscosity
- d b :
-
Mean film thickness
- d b :
-
Dimensionless solid plate thickness
- E :
-
Evaporation number
- G :
-
Non-dimensional measure of gravityg
- H :
-
Curvature
- h :
-
Liquid depth
- h r :
-
Heat transfer coefficient of vapor
- Ĩ:
-
Identity tensor
- J :
-
Mass flux
- K :
-
The degree of non-equilibrium at the evaporating interface
- L :
-
Latent heat
- α:
-
Normal vector at liquid surface
- M :
-
Maragoni number
- p :
-
Pressure
- Pr:
-
Prandtl number
- R s :
-
Ratio for the thermal conductive coefficient of solid and vapor
- S :
-
Non-dimensional surface tension
- T:
-
Stress tensor
- T :
-
Temperature
- T d :
-
Temperature atz=D
- T sat :
-
Saturated temperature
- \(\vec t\) :
-
Tangential vector at liquid surface
- \(\vec v\) :
-
Velocity vector for
- t :
-
Time
- κ :
-
Thermal diffusivity
- σ0 :
-
Surface tension at the reference temperature
- Γ :
-
Ratio of thermal diffusivity
- θ r :
-
Rupture time
- Φ :
-
Non-dimensional temperature
- \(\bar \tau \) :
-
The ratio of deformation tensors
- ρ:
-
Density
- μ :
-
Dynamic viscosity
- ν :
-
Kinematic viscosity
- b :
-
Bottom of solid plate
- s :
-
Ratio of solid property and liquid property
- v :
-
Ratio of vapor property and liquid property
- v :
-
Vapor phase
- s :
-
Solid phase
- I :
-
Liquid-vapor interface
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Joo, S.W., Park, M.S. & Kim, M.S. Heat transfer of an evaporating liquid on a horizontal plate. J Mech Sci Technol 19, 1649–1661 (2005). https://doi.org/10.1007/BF03023941
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DOI: https://doi.org/10.1007/BF03023941