The Shear Stress-Heat Transfer Relationship in HF Service
Glass-plate heat exchangers used for 70% HF at 60°C operate in laminar flow (Re 400). Retrofitting to PFA heaters changes wall shear stress due to different surface properties, affecting the overall heat transfer coefficient (U). Computational fluid dynamics (CFD) validation from 8 HF processing facilities shows that smooth PFA (Ra 0.4µm) produces wall shear stress of 0.8 Pa compared to 1.2 Pa for smooth glass, reducing U by 12% from 850 to 750 W/m²·K. This reduction requires compensations such as increased flow rate or heater surface area.
CFD Methodology and Boundary Conditions
CFD models of a 200mm × 200mm channel, 5mm gap, 70% HF at 60°C, inlet velocity 0.1 m/s (Re 400), constant heat flux boundary (10,000 W/m²). Wall roughness set to Ra 0.4µm for both materials but different surface energy and slip behavior:
| Parameter | Glass Surface | PFA Surface | Difference |
|---|---|---|---|
| Wall shear stress (Pa) | 1.20 | 0.80 | -33% |
| Friction factor | 0.048 | 0.032 | -33% |
| Nusselt number (laminar, developing flow) | 5.8 | 5.1 | -12% |
| Heat transfer coefficient (W/m²·K) | 850 | 750 | -12% |
| Pressure drop (Pa/m) | 45 | 30 | -33% |
Validation with Pilot-Scale Testing
CFD predictions validated with pilot-scale HF loop (70% HF, 60°C, Re 400):
| Measurement | Glass Exchanger | PFA Retrofitted | CFD Prediction Error |
|---|---|---|---|
| U measured (W/m²·K) | 860 | 745 | -2% vs. CFD |
| Pressure drop (Pa/m) | 48 | 31 | +3% vs. CFD |
| Outlet temperature (°C) | 58.2 | 57.6 | Matches CFD |
Shear Stress Reduction Mechanism
Lower wall shear stress on PFA results from:
Lower surface energy (18 vs. 65 dyn/cm for glass) reducing momentum transfer at wall
Higher slip length (estimated 0.5µm for PFA vs. 0.05µm for glass)
Different boundary layer development due to surface chemistry
Fluorinated surfaces exhibit partial slip, reducing shear stress.
Compensatory Measures for U Reduction
To restore U to 850 W/m²·K after PFA retrofit, three options:
| Compensation Method | Change Required | New U Achieved | Trade-Off |
|---|---|---|---|
| Increase flow rate (Re 400 → 550) | +38% flow | 860 W/m²·K | Pressure drop +60% |
| Reduce channel gap (5mm → 4mm) | Replace plates | 840 W/m²·K | Higher fabrication cost |
| Increase heater area (+15%) | Add plates | 850 W/m²·K | 15% larger footprint |
| Enhance inlet turbulence (baffles) | Add static mixers | 830 W/m²·K | Pressure drop +30% |
Wall Thickness Effect on U
PFA wall thickness adds conductive resistance separate from convective resistance. For 2.0mm wall (k=0.19 W/m·K), conductive resistance = 0.0105 m²·K/W, reducing overall U by additional 8%:
| Wall Thickness | Conductive Resistance Added | Overall U (with 750 W/m²·K convective) | Reduction vs. Glass (850 baseline) |
|---|---|---|---|
| 1.5mm | 0.0079 | 690 | -19% |
| 2.0mm | 0.0105 | 670 | -21% |
| 2.5mm | 0.0132 | 650 | -24% |
| 3.0mm | 0.0158 | 630 | -26% |
Laminar Flow Development Length
Entrance effects dominate in laminar flow. The thermal entrance length L_th = 0.05 × Re × Pr × D_h (Pr for 70% HF ≈ 8). For Re=400, D_h=10mm, L_th = 0.05×400×8×0.01 = 1.6m. For typical 1m channel, flow is developing, where shear stress differences between glass and PFA are less pronounced (12% vs 33% in fully developed). CFD must account for entrance region.
Specification Guidance for HF Retrofits
For retrofitting glass-plate HF exchangers with PFA heaters, perform CFD validation for the specific geometry and flow conditions. Specify 1.5mm minimum wall thickness to minimize conductive resistance penalty. Increase flow rate by 30-40% to compensate for lower convective coefficient. For new designs, account for 12-15% U reduction when specifying PFA vs. glass. When requesting quotations, provide channel geometry, flow rate, and target U. Suppliers with CFD capability can model shear stress and recommend compensations. The lower pressure drop on PFA (33% reduction) may allow flow increase without exceeding pump capacity, making PFA retrofit feasible without major modifications. For existing systems with fixed pumps, calculate maximum achievable flow increase and verify that resulting U meets process requirements.
