A typical solar air heaters (SAHs) are used to heat the air, however their small convective heat coefficient and thermal efficiency due to the creation of a viscous sub-layer between flowing air and the collector plate. By adding artificial roughness to the collector plate with an appropriate design, we can interrupt the shear layer and enhance the convective coefficient. This study investigated the analytical thermohydraulic performance of a multi-ribbed, rough, arc-shaped SAH. The thermal performance of the rough SAH is compared to that of the smooth duct in this paper. The thermal efficiency of the arc-shaped collector is significantly higher than that of the smooth duct, at around 40% average increment. This work presents a novel exergy efficiency analysis, which shows that smooth ducts have an average 47% reduction in exergy efficiency when compared to arc-shape roughness. The optimal values for thermal performance are relative pitch height (P/e) = 10, relative rib height (e/D) = 0.043, and attack angle (α) = 30°.