A computational study examines the fully developed laminar flow and heat transfer characteristics of a parallel-plate channel with internal, longitudinal, rectangular fins. The fins are integrally attached to the channel top wall, whose outer surface is heated uniformly. The bottom wall is adiabatic. The study determines the effects of varying the fin height, the fin thickness, the fin pitch, and the wall-to-fluid thermal conductivity ratio on the pressure drop in the channel and the heat transfer from the exposed channel wall and fin surfaces. The results of the conjugate heat transfer study, which are applicable to the design of heat exchangers, include the overall heat transfer, the channel pressure drop, the heat transfer per unit pumping power, and the distributions of the local temperature and velocity.