Operation of the planar-flow melt-spinning process in a regime where the wheelspeed is high relative to the (average) solidification rate is studied. A distinct solidification front occurs. An analysis based on the governing energy and momentum equations shows that heal transfer and solidification are only weakly coupled to fluid flow. For long puddles and high wheelspeeds the governing equations decouple, leaving a Stefan problem for the shape of the solidification front and temperature fields. This problem has an analytic solution. The linear front corresponding to thin ribbons is a limiting case. Nonequilibrium kinetics at the freeze interface and undercooling of the melt are included in the general solution. These influences on solidification are thereby examined. Results are compared to previous solidification models and experiments.