The ribbed three-dimensional solar air heater (SAH) model is numerically investigated to estimate flow and heat transfer through it. The numerical analysis is based on finite volume approach, and the set of flow governing equations has been solved to determine the heat transfer and flow field through the SAH. For detailed analysis, rib chamfer height ratio (e′/e) and rib aspect ratio (e/w), two innovative parameters, have been created and considered along with the commonly used roughness parameter, i.e., relative roughness height, e/D. The parameters e′/e, e/w, and e/D are varied from 0.0 to 1, 0.1 to 1.5, and 0.18 to 0.043, respectively, but the value of P/e is kept constant for the entire investigation at 12. A good match is seen in Nusselt number (Nu) and friction factor (f) by comparing the predicted results with the experimental ones. With the variation of roughness parameters, distinguishable change in Nu and f is obtained. The highest value of thermohydraulic performance parameter (TPP) observed is 2.08 for P/e, e′/e, e/w, and e/D values of 12, 0.75, 1.5, and 0.043, respectively, at Re of 17,100. The developed generalized equation for Nu and f has shown acceptable percentage deviation under the studied range of parameters.