Solar air heater (SAH) ducts have poor thermal efficiency, which can be improved by introducing ribs. This study is focused on the numerical investigation of heat transfer and pressure drop of a permissible ribbed SAH duct. The flow domains for three different permissible rib geometries, i.e. horizontal slit, 30° inclined slit and 30° inclined split slit, were analysed. Different turbulence models based on two equations were compared with the experimental results for the solid rib model. The realisable, k-ε turbulence model obtained the less error of enhancement heat transfer when compared with the experimental work for solid rib. An increase in heat transfer was noted for permissible rib geometry due to secondary vortices. An increase of 12.4%, 7.4% and 1.6% was observed in average heat transfer for horizontal, 30° inclined slit and 30° inclined split slit configurations for the Reynolds number value of 12800, respectively. Inclined split slit gave the maximum friction factor when compared to other permissible rib cases. An improvement of 14%, 8.6% and 3.3% was observed in thermal performance for 30° inclined split, 30° inclined and horizontal slit at the Reynolds number value of 12800.