Systems based on PCM rely not only on the capacity of the system to absorb or release energy but also on the rate at which these processes are carried out. The design and optimization of thermal management systems require understanding the phase change process under different conditions. In this work, the time-dependent phase change process is studied numerically. Gallium, contained in a thin cell, is considered the working fluid. Numerical modeling is done by ANSYS Fluent in two dimensions. This model is validated against reported experimental results. Subsequently, two conditions are systematically investigated: (i) inclination, considering five angles (−45,−22.5,0,22.5, and 45°), and (ii) partial heating, considering four relative heater sizes (0.25,0.50,0.75 and 1.00). Both cases are studied for three aspect ratios (A=0.50,0.75, and 1.00). Results show that small aspect ratios and positive tilting angles could modify flow dynamics, which ultimately affects the melting process and the Nusselt number. Moreover, partial heating reduces up to 38% the melting time compared to the case in which the heat flux is distributed homogeneously along the entire length of the wall. These results could be used as guidelines to address the “rate problem” for practical applications.