• The effect of sintered porous copper structure thickness on pool boiling heat transfer was investigated. • The additional contribution of graphene coating to further HTC enhancement was presented. • Increased wetted area and nucleation sites enhanced heat transfer on sintered porous surfaces. • Liquid supply mechanism and thermal conductivity with graphene coatings further enhanced heat transfer. • Effective heat dissipation underneath bubbles and prevention of hot spots are possible with Graphene coatings. Phase change heat transfer via pool boiling is an effective and low-cost method for applications such as electronics cooling and noticeably depends on bubble dynamics behavior. Porous copper surfaces provide a larger heat transfer area and more nucleation sites at the liquid-surface interface and improve heat transfer compared to bare copper surfaces. In addition, the capability of copper foams in surface replenishment and capillary wicking prevents surface dry-out at elevated heat fluxes. Graphene has recently attracted increasing attention in thermal management applications due to its exceptional thermal and mechanical properties. This study focuses on the effects of foam thickness (i.e., 0.5 mm, 1 mm, 1.5 mm, and 2 mm) and graphene-coating on pool boiling heat transfer on sintered porous surfaces by combining the porous structure with graphene coating. According to the obtained results, thinner samples (i.e., 0.5 mm and 1 mm) exhibited a better performance due to their lower vapor resistance and efficient liquid supply compared to thicker samples (i.e., 1.5 mm and 2 mm). The optimum surface configuration depends on the operating condition. Graphene-coating affects bubble dynamics and leads to further enhancement in boiling heat transfer by increasing the thermal conductivity and wicking rate. The maximum heat transfer enhancement was recorded for the thickness of 0.5 mm on graphene-coated sintered porous copper surfaces as 161% compared to the bare copper surface, while the maximum enhancement with graphene coating was 24% relative to the porous copper surface of the same thickness. Thus, the contribution of graphene coating on sintered porous copper surfaces to further boiling heat transfer enhancement was proven in this study.