Numerical solution for film evaporation of a spherical liquid droplet on an isothermal and adiabatic surfacet

A numerical solution for the problem of film evaporation of a liquid droplet on a horizontal surface is presented. The droplets are small enough to be assumed spherical. Two principal cases are considered : (1) the horizontal surface is maintained at a constant temperature (case I), and (2) the surface is insulated while the ambience is hot (case II). The complete set of equations governing this problem were solved under the following assumptions : (1) evaporation is quasi-steady, (2) no internal liquid circulation, (3) constant properties, and (4) the droplet temperature is spatially uniform but temporally varying. The Lewis number is not assumed to be unity ; gas phase viscous effects, Stefan type convection, and gas phase inertia are included in the analysis. The total droplet evaporation time was found to decrease with increasing plate (I) or ambient (II) temperature as expected, and the droplet progressively moves away from the plate as it evaporates. The numerical results agree with the analytical solution for film evaporation of a droplet above an adiabatic surface in a hot ambience in the limit of large effective Reynolds number (i.e. potential flow).