Phase change materials are vastly used in thermal engineering applications. The model studies reduce the experimental time and cost and gives insight into the physical process and and provides relation between the process outcomes and the influencing parameters on the process. One of the challenges in the model study related to the phase change problem is setting the appropriate boundary conditions across the phases. This is because of the fictitious definition of the mush zone across the phases. This situation becomes complicated when setting the boundary conditions across the odd geometric shapes. In this study, mathematical formulation of the condition for energy-balance at the interface of the phase changing is investigated using the curvilinear coordinate system without requiring the coordinate system. The proposed arrangement enables to create a curvilinear system via transformation equations from another curvilinear coordinate system. It also provides mathematical formulation of the interfacial boundary conditions across the phases.