Conservation of mass for a two dimensional film in a three dimensional domain is:

(17–1)

where is the liquid density, h the film height, the surface gradient operator, the mean film velocity and the mass source per unit wall area due to droplet collection, film separation, film stripping, and phase change.

Conservation of film momentum is given,

(17–2)

where

The terms on the left hand side of Equation 17–2 represent transient and convection effects, respectively, with tensor denoting the differential advection term computed on the basis of the quadratic film velocity profile representation [287], [288]. On the right hand side, the first term includes the effects of gas-flow pressure, the gravity component normal to the wall surface (known as spreading), and surface tension; the second term represents the effect of gravity in the direction parallel to the film; the third and fourth terms represent the net viscous shear force on the gas-film and film-wall interfaces, based on the quadratic film velocity profile representation; the fifth term is associated with droplet collection or separation; and the last term is the surface force due to film liquid surface tension and contact angle. Note that in arriving at the shear and viscous terms on the RHS, a parabolic film velocity profile has been assumed.

Conservation of film energy is given as:

(17–3)

In the above equation, is the average film temperature, and vector is the differential advection term computed using the representation of quadratic film velocity and temperature profiles. On the right hand side, the first term inside the bracket represents the net heat flux on the gas-film and film-wall interfaces, with and as the film surface and wall temperatures, respectively, and as the film half depth temperature, all computed from the film temperature profile representation and thermal boundary conditions at gas-film and film-wall interfaces. is the source term due to liquid impingement from the bulk flow to the wall. is the mass vaporization or condensation rate and is the latent heat associated with the phase change.

Equation 17–1 and Equation 17–2 form the foundation of EWF modeling, with the solution of Equation 17–3 being optional only when thermal modeling is desired. These equations are solved on the surface of a wall boundary. Since the film considered here is thin, the lubrication approximation (parallel flow) is valid and therefore these equations are solved in local coordinates that are parallel to the surface.

Subsequent sections present the EWF sub-models and numerical solution procedures adopted in Ansys Fluent.