A finite-difference numerical analysis was conducted in [3] to investigate laminar transport phenomena in constricted parallel ducts with fully developed flow and temperature profiles. The same numerical procedure is employed to determine laminar transfer phenomena in parallel channels with a short flow constriction within which the flow is still developing. Two limiting thermal conditions are treated: uniform surface temperature and uniform surface heat flux. Theoretical results are obtained for the pressure, streamline, velocity and temperature distributions, the loss coefficients, the Fanning friction factor, and the local and average heat transfer coefficients. Two new dimensionless parameters are derived which describe the transfer performance in the ducts with a short flow constriction. Both the hydrodynamic and thermo-hydrodynamic effects at the entrance as well as the exit of the constricted flow geometry are determined. The numerical scheme is capable of treating high velocity flows up to the transition Reynolds number.