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Nowadays, the heat transfer enhancement in electronic cabinets with heat-generating elements can be achieved using the phase change materials and finned heat sink. The latter allows to improve the energy transference surface and to augment the cooling effects for the heat sources. The present research deals with numerical analysis of phase change material behavior in an electronic cabinet with an energy-generating element. For an intensification of heat removal, the complex finned heat sink with overall width of 10 cm was introduced, having the complicated shape of the fins with width of 0.33 cm and height H = 5 cm. The fatty acid with melting temperature of 46 °C was considered as a phase change material. The considered two-dimensional challenge was formulated employing the non-primitive variables and solved using the finite difference method. Impacts of the volumetric heat flux of heat-generating element and sizes of the fins on phase change material circulation and energy transference within the chamber were studied. It was shown that the presence of transverse ribs makes it possible to accelerate the melting process and reduce the source temperature by more than 12 °C at a heat load of 1600 W/m. It should also be noted that the nature of melting depends on the hydrodynamics of the melt, so the horizontal partitions reduce the intensity of convective heat transfer between the upper part of the region and the lower part.