The momentum and thermal boundary layer equations are solved numerically to assess the effects of filament drawdown on aerodynamic drag and heat transfer in melt fiber spinning. It is found that, relative to the case without drawdown (constant filament velocity and diameter), the aerodynamic drag on the filament increases substantially, but the heat transfer rate is suppressed. Moreover, the air velocity profile eventually becomes fully developed (unlike the, zero drawdown case), and the (velocity) boundary layer thickness, rather than continuing to grow with distance beneath the spinneret, eventually becomes proportional to the filament diameter, and thus decreases with increasing axial distance. Quantitative results are presented for the dimensionless drag force per unit length along the filament (the Drag number) and the Nusselt number as functions of the dimensionless axial distance and a new dimensionless parameter, the Drawdown Reynolds number. (C) 2004 American Institute of Chemical Engineers AIChE J, 50: 898-905, 2004