Thermal performance enhancement in microchannel heat sinks has recently become a challenge due to advancements in modern microelectronics, which demand compatibility with heat sinks able to dissipate ever-increasing amounts of heat. Recent advancements in manufacturing techniques, such as additive manufacturing, have made the modification of the microchannel heat sink geometry possible well beyond the conventional rectangular model to improve the cooling capacity of these devices. One such modification in microchannel geometry includes the introduction of secondary flow channels in the walls between adjacent mainstream microchannels. The present study computationally models secondary flow channels in regular trapezoidal and parallel orientations for fluid circulation through the microchannel walls in a heat sink design. The heat sink is made of silicon wafer, and water is used as the circulating fluid in this study. Continuity, momentum, and energy equations are solved for the fluid flow through the regular trapezoidal secondary flow and parallel secondary flow designs in the heat sink with I-type, C-type, and Z-type inlet–outlet configurations. Plots of velocity contours show that I-type geometry creates optimal flow disruption in the heat sink. Therefore, for this design, the pressure drop and base plate temperatures are plotted for a volumetric flow rate range, and corresponding contour plots are obtained. The results are compared with corresponding trends for the conventional rectangular microchannel design, and associated trends are explained. The study suggests that the flow phenomena such as flow impingement onto the microchannel walls and formation of vortices inside the secondary flow passages coupled with an increase in heat transfer area due to secondary flow passages may significantly improve the heat sink performance.