Introduction & Context

The extruder heat balance calculation is a fundamental procedure in polymer processing and process engineering. It defines the energy distribution within the metering section of a single-screw extruder, where mechanical energy from the screw drive is converted into thermal energy through viscous dissipation. This calculation is critical for determining the required cooling duty of the barrel jacket to maintain a stable melt temperature and prevent thermal degradation of the polymer. It is typically used during the design phase of extrusion lines, process optimization, and troubleshooting thermal instability in high-shear applications.

Methodology & Formulas

The methodology relies on a steady-state energy balance within the control volume of the extruder barrel. The total mechanical energy input is partitioned into sensible heat gain (raising the polymer temperature) and the cooling duty required to maintain the set point, after accounting for external heat losses and auxiliary heating.

The mass flow rate is converted to SI units:

\[ \dot{m} = \frac{\dot{m}_{\text{hr}}}{3600} \]

The sensible heat gain of the polymer melt (in kW) is calculated using the specific heat capacity in kJ/kg·K:

\[ \dot{Q}_{\text{sensible}} = \dot{m} \cdot C_{p} \cdot \Delta T \]

The required cooling duty is determined by the energy balance equation:

\[ \dot{Q}_{\text{cooling}} = \dot{W}_{\text{mech}} + \dot{Q}_{\text{heating}} - \dot{Q}_{\text{loss}} - \dot{Q}_{\text{sensible}} \]

The thermal efficiency ratio, which validates the energy distribution, is defined as:

\[ \eta_{\text{th}} = \frac{\dot{Q}_{\text{sensible}}}{\dot{W}_{\text{mech}}} \]

Parameter	Condition/Threshold	Interpretation
Specific Heat (C_p)	1.0 ≤ C_p ≤ 3.0 kJ/kg·K	Standard empirical range for polymer materials.
Thermal Efficiency (η_th)	η_th < 0.05	Potential screw design issue or flow restriction/plugging.
Thermal Efficiency (η_th)	0.05 ≤ η_th ≤ 0.30	Normal operating range for high-shear extrusion.
Thermal Efficiency (η_th)	η_th > 0.30	Model assumptions may be violated; check input data.
Cooling Duty (Q̇_cooling)	Q̇_cooling < 0	System is heating-dominated; cooling duty is not required.

To determine the heat balance, you must account for both energy input and energy dissipation. The calculation involves the following components:

Sum of thermal energy from barrel heaters.
Mechanical energy input derived from motor torque and screw speed.
Heat loss through radiation and convection from the barrel surface.
Enthalpy change of the polymer melt based on mass flow rate and specific heat capacity.

Viscous dissipation, often referred to as shear heating, is a significant source of internal heat generation in high-viscosity polymers. Ignoring this term in your heat balance will lead to:

Overestimation of required external heating power.
Inaccurate prediction of melt temperature at the die exit.
Potential thermal degradation of the material due to localized overheating.

Reducing heat loss is essential for maintaining a stable thermal profile and improving energy efficiency. Consider these engineering controls:

Install high-performance thermal insulation jackets around the barrel segments.
Ensure proper calibration of the barrel temperature control loops.
Minimize air drafts in the production area that accelerate convective cooling.
Monitor the delta between the setpoint and the actual melt temperature to identify insulation degradation.

Worked Example: Extruder Heat Balance (Cooling Duty)

A single-screw extruder processes LDPE at steady state. The metering section is the control volume, and the barrel is under PID cooling control (heaters off). The screw rotation dissipates shaft work as heat in the viscous melt. We calculate the required cooling duty to maintain the barrel set point.

Knowns

Throughput, \(\dot{m}\): 150.0 kg/hr (0.0417 kg/s after unit conversion)
Polymer specific heat, \(C_{p}\): 2.5 kJ/kg·K (2500 J/kg·K)
Melt temperature rise, \(\Delta T\): 20.0 K
Motor mechanical power, \(\dot{W}_{\text{mech}}\): 22.0 kW
Barrel heat loss, \(\dot{Q}_{\text{loss}}\): 1.5 kW
Heater net power, \(\dot{Q}_{\text{heating}}\): 0.0 kW (controller calling for cooling)

Step-by-Step Calculation

Define control volume: The fully filled melt zone in the extruder metering section, where the polymer is completely molten and subject to uniform shear.
Gather process data: Use the mass flow rate in kg/s, specific heat in kJ/kg·K, temperature rise, mechanical power, and heat loss as listed above.
Calculate sensible heat gain (heat absorbed by the polymer to raise its temperature): \[ \dot{Q}_{\text{sensible}} = \dot{m} \cdot C_{p} \cdot \Delta T \] Substituting the known values (using \(C_{p}=2.5\ \text{kJ/kg·K}\) or \(2500\ \text{J/kg·K}\)): \[ \dot{Q}_{\text{sensible}} = 0.0417\ \text{kg/s} \cdot 2.5\ \text{kJ/kg·K} \cdot 20.0\ \text{K} = 2.083\ \text{kW} \]
Apply the energy balance to find the cooling duty: \[ \dot{Q}_{\text{cooling}} = \dot{W}_{\text{mech}} + \dot{Q}_{\text{heating}} - \dot{Q}_{\text{loss}} - \dot{Q}_{\text{sensible}} \] Using the numbers: \[ \dot{Q}_{\text{cooling}} = 22.0\ \text{kW} + 0.0\ \text{kW} - 1.5\ \text{kW} - 2.083\ \text{kW} = 18.417\ \text{kW} \]
Check thermal efficiency ratio (sensible heat fraction of mechanical power): \[ \eta_{\text{th}} = \frac{\dot{Q}_{\text{sensible}}}{\dot{W}_{\text{mech}}} = \frac{2.083\ \text{kW}}{22.0\ \text{kW}} = 0.095 \ (9.5\%) \] This value lies within the expected empirical range (5–30%), confirming the screw design is efficient and the system is not plugged.

Final Answer

The cooling system must remove 18.417 kW of heat to maintain the barrel set point. This cooling duty is typical for high-shear extrusion where viscous dissipation dominates. The result can be used to size the cooling jacket flow rate and surface area.

"Un projet n'est jamais trop grand s'il est bien conçu." — André Citroën

"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise." — Charles de Gaulle