In this study, a comprehensive analysis of flow and thermal characteristics within channels featuring periodic grooves was conducted, emphasizing pulsatile and reverse flow conditions. The investigation spanned Reynolds numbers from 50 to 200, with concave-convex ratios of 0.5, 1, and 2. These controlled variations provided insights into the influence of geometric configurations on fluid dynamics and heat transfer processes. To ensure robustness and reliability, the computational model is validated against established literature results. A grid independence test further affirmed the consistency and reliability of the outcomes, confirming that the conclusions remained unaffected by variations in mesh sizes. Notably, despite a significant increase in pressure drop for the R = 2 configuration, this particular setup exhibited the highest Nusselt number and efficiency. Such findings highlight the intricate relationship between geometric attributes, fluid dynamics, and heat transfer mechanisms. These insights have substantial implications for enhancing and optimizing thermal systems, especially in renewable energy, suggesting avenues for the design of next-generation heat exchangers and furthering advancements in energy efficiency and sustainability.