Theoretical and numerical study on heat transfer and evaporation in the vertical channel has been carried out and basic correlations have been derived for the heat transfer evaluation of PCCS. Analysis program was developed with low-Reynolds-number k-$varepsilon$ model and surface transfer rates were calculated for the turbulent natural convection in the vertical channel. In relation to dry cooling by buoyancy-driven air, first, the system parameters which govern overall heat transfer rate are determined through the adequate nondimensionalization procedure. After comparison with existing experimental data, numerical results are used to derive heat transfer correlation by sensitivity calculations. In relation to wet cooling by falling water film, numerical analysis are carried out for evaporation process with real film surface conditions and evaporation correlation is derived through analogy concept and correction factors.