A simplified method, successfully tested previously for flow in circular pipes, is used in this work to estimate the friction factor and Nusselt number in fully-developed laminar flow between parallel plates of non-Newtonian fluids. Both constant wall temperature and constant wall heat flux cases are considered. The methodology was tested using several constitutive equations, including generalized Newtonian fluids, such as the Herschel-Bulkley, Bingham, Casson, and Carreau-Yasuda models, and also the simplified Phan-Thien-Tanner viscoelastic model. The error of the approximate methodology was found to be small, below 3.4%, except for the fluids with yield stress for which the maximum error increased to 8.4% for the cases analyzed, which cover a wide range of shear viscosity curves.