This article describes the optimal design of a flat-plate solar collector with fins, based on the minimum entropy generation criterion. The design parameters were optimized, considering entropy generation due to heat transfer and airflow. The latter has not been considered in previous works. The flat plate in the collector is assimilated to a finned heat sink. The dimensionless entropy generation variation is analyzed to increase values of the number of fins, as well as for different plate thicknesses and heights. We also considered variations in airflow velocity. Our data shows that airflow velocity greatly influences entropy generation. Values other than the optimum found, caused a considerable growth of total entropy. For a collector area of 4 m2, and an outlet temperature of 50°C, the optimum parameters that minimize the entropy generation rate were: 9 fins on each side of the collector plate, a height of 5 x10-2 m, a thickness of 25x10-3m, and an air velocity variable between 0.015 and 0.046 m/s. This development is relevant to the design of flat plate solar collectors, for grain drying applications.