Thermal Process Engineering, Gasketed Plate Heat Exchangers & Anti-Fouling Design
Plate Heat Exchanger (PHE) Velocity & Wall Shear Formula
Calculate Parallel Channels Per Fluid, Enlargement-Adjusted Hydraulic Diameter D_h (mm), Inter-Plate Channel Velocity (m/s), and Self-Cleaning Wall Shear Stress tau_w (Pa).
Why PHE hydraulic diameter equals (2 * b) / Phi—and keeping chevron wall shear tau_w above 50 Pa prevents biofouling!
In a symmetric single-pass gasketed Plate Heat Exchanger (PHE) containing N_p total corrugated plates (giving N_ch = INT((N_p - 1) / 2) parallel flow channels per fluid), herringbone chevron pressings increase wetted heat-transfer area by the Surface Enlargement Factor Phi (typically 1.15–1.25) without expanding free-flow cross-sectional gap b (mm)! Consequently, PHE Hydraulic Diameter is D_h = (4 * Cross_Section) / Wetted_Perimeter = (2 * b) / Phi (NOT 2 * b!), Inter-Plate Superficial Channel Velocity is v_ch = (Q_m3_hr / 3,600) / (N_ch * W_m * (b / 1,000)), and Force Balance across port-to-port length L_p (m) under channel pressure drop Delta_P (kPa) yields Wall Shear Stress tau_w = ((Delta_P * 1,000) * (b / 1,000)) / (2 * Phi * L_p) Pa—where process engineers target tau_w >= 50 Pa so turbulent chevron vortices continuously scour scale and biofilm off the stainless plates!
Verify on a 41-Plate District-Cooling / Pasteurizer PHE—Volumetric_Flow = 72.0 m³/hr (0.02 m³/s, B2), Total_Plates N_p = 41 (B3 -> 20 channels per fluid in E2), Plate_Width W = 0.50 m (B4), Mean_Channel_Gap b = 3.00 mm (B5), Chevron_Enlargement_Factor Phi = 1.18 (B6), Channel_Pressure_Drop = 60.0 kPa (B7), and Port_Length L_p = 1.20 m (B8): Chevron Hydraulic Diameter equals (2 * 3.00) / 1.18 = 5.085 mm (E3), Channel Velocity hits 0.67 m/s (E4), and Wall Shear Stress reaches 63.56 Pa (E5, comfortably above the 50 Pa self-cleaning threshold)!
| Chevron PHE Hydraulic KPI (72 m³/h, 41 Plates, W=0.5 m, b=3 mm, Phi=1.18, 60 kPa) | Formula | Verified Output |
|---|---|---|
| Parallel Channels Per Fluid Nch | INT((Total_Plates_Np - 1) / 2) | 20 channels |
| Chevron Hydraulic Diameter Dh | (2 * Gap_b_mm) / Enlargement_Phi | 5.085 mm |
| Inter-Plate Channel Velocity (m/s) | (Flow_m3_h / 3600) / (Nch * W * (b/1000)) | 0.67 m/s (0.33 m/s @ 50% turndown) |
| Wall Shear Stress tau_w (Pa) | (dP_Pa * Gap_b_m) / (2 * Phi * Length_m) | 63.56 Pa (21.19 Pa @ 20 kPa fouling!) |
Chevron PHE Hydraulic Diameter, Velocity & Wall Shear Stress Formula
Validate Flow > 0, Total_Plates >= 3, Width > 0, Gap b > 0.5 mm, Chevron_Enlargement Phi in [1.00, 1.50], Pressure_Drop > 0, and Port_Length > 0!
=LET(qw_h, B2, np_t, B3, wp_m, B4, gb_m, B5, ph_i, B6, dp_k, B7, lp_m, B8, IF(OR(qw_h <= 0, np_t < 3, wp_m <= 0, gb_m <= 0.5, ph_i < 1, ph_i > 1.5, dp_k <= 0, lp_m <= 0), "Invalid PHE Input", ROUND(((dp_k * 1000) * (gb_m / 1000)) / (2 * ph_i * lp_m), 2)))50% Pump Turndown Low-Shear Fouling Risk Check (Set Flow = 36 m³/h & dP = 20 kPa)
Throttle pump flow to 50% winter turndown (Flow B2 = 36.0 m³/hr, dropping Channel_Pressure_Drop B7 to 20.0 kPa): Inter-Plate Velocity E4 halves to 0.33 m/s and Wall Shear Stress E5 plunges from 63.56 Pa down to 21.19 Pa—falling below the 50 Pa anti-fouling threshold!
=IF(ISTEXT(E5), E5, ROUND((B2 / 3600) / (INT((B3 - 1) / 2) * B4 * (B5 / 1000)), 2))Try the example
Use the original values or change them to test your understanding.