Mathematical models for fluid flow and heat transfer of plate falling film with low Reynolds numbers had been built in this paper. The governing equations for temperature were then discretized and calculated to obtain transient heat transfer characteristics along the whole plate. For smooth laminar falling film

the velocity field was obtained by numerically calculating the governing equations of the boundary layer flow. The governing equation for temperature was then numerically solved to obtain transient characteristics of heat transfer. For wavy falling film

body-fitted coordinate grids were used and the governing equation for temperature was transformed accordingly to deal with the irregular flow domain

which changes with time as well. The transformed temperature equation was then discretized and numerically calculated. The results for smooth laminar falling film showed that the transient period was very short due to the highly effective heat transfer of falling film. For wavy laminar flow

the results showed that the mean fluid temperature close to the entrance of the plate had the wavy characteristics both along the plate and with the time. In addition

along the plate the mean fluid temperature of wavy laminar flow apparently approached to the interface temperature much faster than that of smooth laminar flow

which indicated the enhancement of heat transfer by the wavy flow.