A numerical investigation of five surface transport within a hollow glass ampule with feed-in boundary conditions is presented. The glass ampule is treated as a vertical film with a finite pressure difference across the film, with applied influx on the upper boundary, and with applied heat flux at the outer free surface. Two different sizes of glass ampules, along with different influx values art investigated. A finite element method with full consideration of surface tension and viscosity effects is used to solve the transient Navier-Stokes equations in cyclindrical coordinates. Radiative and connective boundary conditions are incorporated when solving the energy equation. The movement of the inner and outer free surfaces with the specified feed-in velocity for different dimensions and temporal temperature distribution are analyzed. It is found that the feed-in mechanism rather than the pressure difference provides the more dominant driving forces. Also studied is the effect of using different feed-in velocities on the flow and temperature fields. The results presented in this work illustrate the basic effects of the feed-in mechanism of the free surface transport phenomenon.