The drive for small and compact electronic components with higher processing capabilities is limited by their ability to dissipate the associated heat generated during operations, and hence, more advanced heat sink designs are required. Recently, the emergence of additive manufacturing techniques facilitated the fabrication of complex structures and overcame the limitation of traditional techniques such as milling, drilling, and casting. Therefore, complex heat sink designs are now easily realizable. In this study, we propose a design procedure for mathematically realizable architected heat sinks and investigate their performance using the computational fluid dynamics (CFD) approach. The proposed heat sinks are mathematically designed with topologies based on triply periodic minimal surfaces (TPMSs). Three-dimensional CFD models are developed using the starccm+ platform for uniform heat sinks and topologically graded heat sinks to study the heat transfer performance in forced convection domains. The overall heat transfer coefficient, surface temperature, and pressure drop versus the input heat sources as well as the Reynolds number are used to evaluate the heat sink performance. Moreover, temperature contours and velocity streamlines were examined to analyze the fluid flow behavior within the heat sinks. Results showed that the tortuosity and channel complexity of the Diamond solid-networks heat sink result in a 32% increase in convective heat transfer coefficient compared with the Gyroid solid-network heat sink which has the comparable surface area under the examined flow conditions. This increase is at the expense of increased pressure drops which increases by the same percentage. In addition, it was found that expanding channel size along flow direction using the porosity grading approach results in significant pressure drop (27.6%), while the corresponding drop in convective heat transfer is less significant (15.7%). These results show the importance of employing functional grading in the design of heat sinks. Also, the manufacturability of the proposed designs was assessed using computerized tomography (CT) scan and scanning electron microscopy (SEM) imaging performed on metallic samples fabricated using powder bed fusion techniques. A visible number of internal manufacturing defects can affect the performance of the proposed heat sinks.