A mathematical simulation to the cooling process of a flat moving surface using a weak concentration micropolar-nanofluid as a cooling medium has been investigated. The modelling based on the conservation equations of the unsteady case for the momentum and thermal boundary layer taking into consider the effect of suction process and thermal radiation. Using similarity transformation technique, the conservation equations have been transformed to ordinary differential equations that are solved numerically for general case and analytically for the steady case. Surface shear stress, couple shear stress, and the rate of heat transfer are deduced, and the impact of these physical characteristics on the final quality and the mechanical properties of the surface to be cooled discussed.