Under high heat flux, upset or high power conditions due to several reasons, the components in various engineering applications can be damaged and its structural materials may undergo phase change such as melting and evaporation, making it difficult to maintain the integrity. Plasma transients such as vertical displace events, plasma disruption, runaway electron, etc. that may occur in a tokamak fusion reactor can be a relevant example. Plasma facing components (PFCs) can be exposed to high heat flux conditions and damaged if it occurs and therefore, thermal-hydraulic safety analysis to predict the behavior of reactor elements and structural components under high heat flux conditions is required. In this study, one-dimensional thermal-hydraulic analysis under material phase change conditions was conducted in the blanket first wall module of the Korean fusion demonstration reactor (K-DEMO). In order to simulate the melting and evaporating phenomenon, effective heat capacity method (EHCM) and Hertz-Knudsen-Langmuir theory of evaporation and condensation are used, respectively. At first, the flux of atoms leaving the surface of evaporating phase and the velocity of the receding surface were derived from the evaporation theory. Afterwards, EHCM modifies the effective heat capacity using the latent heat of fusion of the target material. However, this method has a distinctive disadvantage in convergence on mesh sizes and mushy zone sizes leading to distortion of the prediction results and lower numerical efficiency under rapid transient events. For this reason, a mesh adaptation technique using tracking the material phase change temperature (melting point) and the damaged depth (melting and evaporation depth) was implemented to the phase change calculation module to improve the calculation capability under diverse high heat flux conditions. An appropriate monitoring function for tracking the phase change temperature was selected and the re-meshing procedure was proceeded resulting in smaller meshes concentrated at the melting interface. As the mesh adaptation technique was applied to the EHCM, its numerical efficiency was improved and dependency on mesh size and required mushy zone size was decreased. For the validation of the melting model, Stefan’s problem was selected as a conceptual problem and the calculation results were compared with analytic solution for the code to code comparison. Then, the phase change calculation module involving both melting and evaporating simulations was coupled with the nuclear reactor safety analysis code, MARS to analyze the thermal-hydraulic behavior of the water cooled breeding blanket in KDEMO under several high heat flux conditions.