Introduction & Context

Cold extrusion of pasta is a low-temperature forming process in which hydrated semolina is compacted and shaped under vacuum without exceeding the starch gelatinisation threshold. The purpose of the calculation sheet is to size the cooling jacket of a single-screw extruder so that the dough leaves the die below a safe temperature while maintaining the target throughput and vacuum level. The same logic is used by process engineers when retro-fitting water-cooled barrels on traditional “bronze” pasta lines, when scaling-up from pilot (20–50 kg h^-1) to industrial (400–1200 kg h^-1) units, or when verifying that an existing chiller has enough reserve capacity for a new product recipe.

Methodology & Formulas

Residence time
The average time available for heat removal is set by the free barrel volume and the volumetric throughput: \[ t_{\text{res}} = \frac{V_{\text{barrel}}}{Q_{\text{L}}} \] where \( Q_{\text{L}} = \frac{\dot{m}}{\rho_{\text{dough}}} \).
Cooling duty
The thermal load to be extracted from the dough is: \[ \dot{Q} = \dot{m}\,C_{p,\text{dough}}\,\Delta T_{\text{dough}} \] with \( \Delta T_{\text{dough}} = T_{\text{dough,max}} - T_{\text{dough,in}} \).
Log-mean temperature difference
For counter-current flow between the dough (assumed well mixed at \(T_{\text{dough,max}}\)) and the cooling water: \[ \Delta T_{\text{lm}} = \frac{\Delta T_{1}-\Delta T_{2}}{\ln\left(\dfrac{\Delta T_{1}}{\Delta T_{2}}\right)} \] where \( \Delta T_{1} = T_{\text{dough,max}} - T_{\text{water,in}} \) and \( \Delta T_{2} = T_{\text{dough,max}} - T_{\text{water,out}} \).
Required heat-transfer area
The jacket area is obtained from: \[ A = \frac{\dot{Q}}{U\,\Delta T_{\text{lm}}} \] The overall coefficient \(U\) is correlated against the water-side Reynolds number: \[ Re = \frac{4\,\dot{m}_{\text{water}}}{\pi\,D\,\mu_{\text{water}}} \]
Die pressure drop
The head built by the screw is dissipated across the die plate: \[ \Delta P = k_{\text{D}}\,Q_{\text{L}} \] where \(k_{\text{D}}\) is the die resistance coefficient.

Operating limits and validity ranges
Parameter	Minimum	Maximum	Remark
Residence time	60 s	—	Below 60 s cooling may be incomplete
Die resistance \(k_{\text{D}}\)	0.5 bar s L^-1	2.0 bar s L^-1	Outside range, screw torque rises sharply
Vacuum (absolute)	0.2 bar	0.3 bar	Lower vacuum gives bubbles; higher is unnecessary
Overall coefficient \(U\)	0.35 kW m^-2 °C^-1	0.55 kW m^-2 °C^-1	Valid only for turbulent water side (Re > 4000)
Dough temperature	—	50 °C	Above 50 °C starch gelatinises and product browns

Target 25–32 °C at the die face. Achieve this by:

Chilling water/glycol to 5 °C and circulating it through the die jacket at ≥ 1.5 m s^-1
Using a screw with 1.5–2.0 compression ratio to minimise viscous heating
Installing a variable-frequency drive so residence time can be trimmed to < 90 s

Keep moisture ≥ 32 % and use 1.8–2.2 % added oil. Additional measures:

Polish die land to Ra ≤ 0.2 µm to lower wall friction
Apply 0.05 mm PTFE-based release coating refreshed every 48 h
Maintain 80–90 bar back-pressure so the dough consolidates without temperature rise

A single-flight, 3-zone screw with 1.6 L/D feed, 0.8 compression, and 0.3 mm flight-to-barrel clearance. Run at 15–25 rpm to keep specific mechanical energy < 0.08 kWh kg^-1.

Extrude at 34 % moisture, then stabilise:

Pass strands through 12 °C, 85 % RH tunnel for 25 min to equilibrate surface and core
Use vacuum post-extrusion at –0.6 bar for 40 s to pull off 1–1.5 % water
Package immediately in high-barrier film; target a_w 0.45–0.50 for shelf-stable fresh pasta

Worked Example – Sizing the Cooling Jacket for a Cold-Extrusion Pasta Line

A small artisan pasta plant runs 400 kg h^-1 of durum-wheat dough through a 6 L single-screw cold extruder. To keep the product below 45 °C, chilled water is circulated through the barrel jacket. Determine the required heat-transfer area and check that the water-side Reynolds number is high enough for turbulent flow.

Knowns

Mass flow rate of dough: \(\dot{m}\) = 0.111 kg s^-1 (400 kg h^-1)
Dough specific heat: \(C_{p,\text{dough}}\) = 1.8 kJ kg^-1 K^-1
Inlet dough temperature: \(T_{\text{dough,in}}\) = 38 °C
Maximum allowable dough temperature: \(T_{\text{dough,max}}\) = 45 °C
Chilled-water inlet temperature: \(T_{\text{w,in}}\) = 12 °C
Chilled-water outlet temperature: \(T_{\text{w,out}}\) = 20 °C
Water volumetric flow rate: 5 m³ h^-1 → 1.389 kg s^-1
Overall heat-transfer coefficient (jacketed single screw): \(U\) = 0.45 kW m^-2 K^-1
Barrel inner diameter (flow path): \(D\) = 0.0254 m
Water dynamic viscosity: \(\mu_{\text{w}}\) = 0.001 Pa s

Step-by-step calculation

Heat to be removed from the dough
\[ Q_{\text{dough}} = \dot{m}\,C_{p,\text{dough}}\,\Delta T_{\text{dough}} = 0.111 \times 1.8 \times (45 - 38) = 1.4\ \text{kW} \]
Log-mean temperature difference
Hot side: 38 → 45 °C Cold side: 12 → 20 °C
\[ \Delta T_1 = 38 - 20 = 18\ \text{K}, \quad \Delta T_2 = 45 - 12 = 33\ \text{K} \] \[ \Delta T_{\text{lm}} = \frac{\Delta T_2 - \Delta T_1}{\ln(\Delta T_2/\Delta T_1)} = \frac{33 - 18}{\ln(33/18)} = 24.6\ \text{K} \]
Required heat-transfer area
\[ A = \frac{Q_{\text{dough}}}{U\,\Delta T_{\text{lm}}} = \frac{1.4}{0.45 \times 24.6} = 0.127\ \text{m}^2 \]
Water-side Reynolds number
\[ Re = \frac{4\,\dot{m}_{\text{w}}}{\pi\,D\,\mu_{\text{w}}} = \frac{4 \times 1.389}{\pi \times 0.0254 \times 0.001} = 69\,622 \] Since \(Re \gg 4000\), the flow is fully turbulent and the assumed \(U\) is valid.

Final Answer

A stainless-steel jacket with 0.127 m² of wetted surface is sufficient to hold the dough temperature below 45 °C. The cooling water will leave the jacket at 20 °C with a Reynolds number of 69,600, ensuring efficient heat removal.

"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