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In this study, the thermal and hydraulic performances of an air-cooled planar heat sink with cross-connected alternating converging-diverging channels were investigated. The commercial CFD solver ANSYS Fluent was used to solve the fluid flow and heat transfer from the fins to the air flow for a range of converging-diverging channel expansion ratios, heat generation rates and Reynolds numbers. The converging and diverging channel sections create high and low pressure zones, respectively, in the flow domain and this pressure difference induces secondary flows from the converging channel sections to the diverging channel sections through the cross connections. The observed heat transfer enhancement results from two different phenomena: (1) thermal boundary layer disruption and re-initialization at the cross connections and (2) fluid mixing; where the former reduces the convection resistance in the vicinity of the fin walls by reducing the thermal boundary layer thickness, while the latter allows a more uniform temperature build-up of air in the streamwise direction. Despite the fact that the pressure drop penalty increases due to flow restriction compared to the straight channel heat sinks, it is possible to enhance the Nusselt number for up to 100% with the proposed heat sink design.