The main issue of this thesis is an investigation of mathematical, numerical, and physical foundations for the thermal-hydraulic and chemical analysis of the steam generator of the nuclear power plant. Two-tools of a best estimate three-dimensional code named as FAUST(Flow Analysis of U-tube Steam generator) and a dynamic scaling method are developed here. FAUST is based on the two-fluid model derived with the distribution function. The effect of the interfacial pressure force on the mathematical characteristics is studied to assure the well-posedness of the two-fluid model. Physical models used in FAUST are the wall-friction model on the basis of the SU(2) group representation, the one-dimensional representative tube model for heat transfer, a steam dome model for asymmetric distribution of feedwater, the interfacial mass transfer model based on the penetration theory for the water chemistry, and the loading model based on the singular point analysis. Nonlinear equations having the above physical models are finitely differenced and efficiently solved by developing a numerical logic named as SETS-WM whose stability is greatly enhanced by the interfacial drag force. The simulation results are well fitted by the experimental data of BUGEY-4 power plant within a 10\% error and PH distribution due to AVT(allvolatile treatment) is compared with the dynamic equilibrium model used conventionally. The thermal-gradient between the hot-leg side and the cold-leg side results in circulating liquid which forms countercurrent flow in the upper part of the U-bend. For the experiment of the steam generator, a dynamic scaling method is developed. This scaling method is successfully used to design a test rig and justified by USODA. It is shown that the one-dimensional lumped parameter model for the dynamic scaling method well represents the dynamics of the water level.