Implementing active cooling through micro-channel heat sinks integrated with printed circuit heat exchangers demands a simultaneous enhancement of thermal and hydraulic performance, all while avoiding complex designs for ease of fabrication. We propose a porous wall embedded double-layered micro-channel heat sink, aiming to decrease the necessary pumping powers while maintaining a minimal impact on the heat transfer rate. Additionally, this design simplifies geometric complexities, enhancing ease of fabrication. We assessed the feasibility of different porous embedded double-layered micro-channel heat sink configurations by evaluating their thermal and hydraulic performance. Our analysis uniquely integrates the principles of the second law of thermodynamics with traditional first law analysis, providing novel insights into heat sink design. We discovered that configuring porous walls solely in the top layer of the double-layered micro-channel heat sink is the only viable option. Furthermore, our analysis reveals that embedding porous walls exclusively in the top layer reduces irreversibility due to frictional losses by 9.13 %, with a slight increase in irreversibility due to heat transfer by 1.55 %, in comparison to the solid double-layered micro-channel heat sink at a flow rate of 1000 ml/min. Moreover, at the same flow rate, compared to configuration with porous walls in both layers, the top layer configuration exhibits improved thermal performance by 17.28 %. Next, we demonstrate that while the first law analysis indicates the viability of the top porous configuration, the second law analysis limits its viability to a certain coolant flow rate range. Finally, we optimize the heat sink design and coolant flow rates, proposing a viable design by simply incorporating porous walls in only the top layer of double layered micro-channel heat sink, which otherwise proved to be non-viable.