Heat transfer coefficients were investigated by insertion of a probe into melting polymers under laminar flow at 200-240degreesC and a flow velocity of 0.5-2.7 mm/sec. The average heat transfer coefficients of melting polypropylene (PP) and polystyrene (PS) were found to be 160-220 W/m.degreesC and 180-270 W/m.degreesC, respectively. These coefficients show remarkable dependence on flow velocity, and the average heat transfer coefficient of PS is about 13%-23% higher than that of PP. When the flow velocity of flowing melting PP and PS exceeds about 0.078mm/sec, heat transfer by convection becomes dominant, whereas under lower flow velocities, since the equivalent conduction layer thickness delta' in which the quiescent state without flow approaches infinity, heat transfer by conduction becomes dominant. The Prandtl number (Pr) and Nusselt number (Nu) of melting PP are 125-133 X 10(6) and 38.6-51.4, respectively, and those of melting PS are 63-64 X 10(6) and 42.3-61.3. In the case of constant flow velocity, the Peclet number (Pe) and Stanton number (St) are dependent on the specific heat of melting polymer.