This paper addresses the output regulation of flow systems described by a class of two-time-scale nonlinear PDE systems. Within the framework of singular perturbation, the reduced-order slow model comprised of first-order PDEs coupled with ODEs is obtained. Based on the numerical approximation technique and the solvability of an inertial manifold, the finite-dimensional nonlinear model with nonlinear input is developed in this paper. Extending from the geometric control method, the non-distributed nonlinear controller can be synthesized. A combination of the state-space internal model control scheme, the reduced observer-based controller can asymptotically attenuate the effect of external disturbances. Finally, the developed methodologies are successfully applied to the development of a PFR system asscociated with the cooling coil apparatus.