Evaporation is a complex process that, among others, involves the change of phase from liquid to vapour. Although have been extensively studied, the evaporation process has yet to be fully understood. To assist in this, a numerical model had been developed to simulate the process in which various fluid flow governing equations are integrated together and solved. In order to validate the developed model, the well-known 1-dimensional Stefan diffusion problem is solved as it has a known analytical solution. The Stefan diffusion problem is simulated for both water and the fluorinate compound FC-72, each representing the case for a non-volatile and volatile fluid, respectively. The mass flow rates obtained from the simulation are compared to the existing analytical solution while the concentration and velocity profiles are compared to theories and experimental findings from other researchers. The comparisons showed good agreement between the numerical model, the analytical solution and experimental findings thereby validating the developed evaporation model.