Time-dependent conjugate conduction/convection direct numerical simulations of four rib configurations that differ in material composition and distribution of internal heat generation are conducted in laminar and transitional grooved-channel flows. The effect of material composition, concentration of heal generation and flow regime on the spatial distribution of temperature, heat flux and Nusselt number along the solid-fluid interface is investigated. Furthermore, the distribution of internal heat generation is found to affect strongly the convective resistance at the solid-fluid interface of the rib, leading to a nonmonotonic relationship between convective heat transport and Reynolds number for the range of parameters investigated in the configurations with local heat generation.