Your observation is astute. While many flow equations for polymer extrusion don't explicitly include temperature as a variable, its influence is significant and indirectly accounted for in several ways:

1. Viscosity:

• Temperature-dependent viscosity: The most direct effect of temperature is on the viscosity of the polymer. Higher temperatures reduce viscosity, making the polymer flow more easily.
• Indirect inclusion in flow equations: While viscosity might not appear explicitly in some equations, it's often a key parameter that influences the flow rate and pressure.

2. Pressure Compensation:

• Extruder head flow: As you correctly noted, an increase in temperature can lead to a slight increase in pressure due to the reduced viscosity. However, the extruder head is designed to compensate for this by adjusting its flow rate.
• Dynamic equilibrium: The system reaches a new equilibrium where the increased pressure from the extruder is balanced by the increased flow rate through the head.

3. Screw RPM and Flow Rate:

• Constant RPM: While maintaining a constant screw RPM generally results in a constant flow rate, temperature can influence the specific characteristics of the flow.
• Flow profile: The flow profile within the extruder can change due to temperature-induced viscosity variations, potentially affecting factors like mixing and distribution of additives.

4. Energy Consumption:

• Reduced power consumption: The primary reason for operating at higher temperatures is to reduce the power consumption of the extruder. Lower viscosity means less energy is required to overcome the resistance to flow.

In essence, while temperature isn't explicitly included in many flow equations, its impact is significant and is accounted for indirectly through factors like viscosity, pressure compensation, and flow profile.

Thank you very much, I have come out of this doubt and the truth is interesting the conclusion that higher temperature does not make us have higher flow, it is somewhat counterintuitive. But since the extruder follows the flow equations the temperature does not affect the flow rate, but it does affect the energy consumption of the motor.

The Temperature in the extrusion process is most of the times a constant since is dependent and fixed by the melting point of the extrudate or master batch.