Fully developed laminar flow heat transfer in a plate-fin heat exchanger with interfin core channels of trapezoidal cross section and by extension, its limiting rectangular and triangular cross section geometries, is considered. With heating or cooling at the partition plates of the core given by the constant wall temperature, or , and uniform heat flux, or , conditions, the fin effectiveness is modeled to be zero. This condition is representative of poor contact between the fin and partition plate, encountered in mass-produced compact cores and/or low conductivity fin materials. Computational solutions, obtained by second-order accurate control-volume schemes, highlight the effects of geometry and thermal condition on the Nusselt number ( and ), and the results complement and extend the literature on compact-channel internal forced convection. Also, as a design and optimization tool for the practicing engineer, polynomial functions of the flow cross section aspect ratio are presented to predict both the friction factor and the Nusselt number for the different trapezoidal and triangular fin core geometries considered.