The use of phase change materials in modern electronic technologies expands the range of problems of heat and mass transfer in systems with phase transitions. One of these tasks is the cooling of electronic units by the PCM heat sinks. Studying the effectiveness of PCM based systems is one of the most relevant topics in passive cooling. From the point of view of heat and mass transfer modeling, such systems are complex and, as a rule, are studied experimentally. The present numerical study is devoted to the impact of the geometric configuration of a copper profile on the phase change of lauric acid in the presence of volumetric heat generation element. Several profile models have been considered to increase the effective thermal conductivity of the system, including horizontal flat fins, vertical flat fins, and a profile divided into cells by vertical and horizontal plate fins, each cell is filled with the same volume of lauric acid. It should be noted that such analysis allows understanding the influence of vertical and horizontal orientations of fins on heat transfer enhancement within the heat sink. Moreover, a presence of a heater of constant volumetric heat generation illustrates features of heat removal from such an element. To obtain the most accurate solution, the equations of conjugate natural convection are formulated with the melting/solidification processes employing the non-primitive variables like stream function and vorticity. The finite difference technique is applied in modeling the thermohydrodynamic processes with phase transitions. The impact of the profile shape on the development of convective energy transport and phase transitions is analyzed. The novelty of the present study can be described by the following results. It has been shown that vertical plate fins promote faster thermal dissipation than horizontal fins within the metal structure, however, during phase transformations in cavities, the area enhancement ratio of the heat sink becomes the most important. A large number of cells increases the effective heat capacity of the system and reduces its temperature difference.