Process Thermal Engineering & Heat Exchangers
TEMA Heat Exchanger Fouling & Dirty U-Value Formula
Calculate Outer-Area-Referenced Total Fouling Resistance R_f_tot = R_f_in * (D_o / D_i) + R_f_out, Service Dirty Overall Conductance U_dirty, Cleanliness Factor, and Surface Overdesign Fraction.
Scale inner tube-side fouling resistance by D_o / D_i when U is referenced to outer tube area!
Shell-and-tube heat-exchanger datasheets under Tubular Exchanger Manufacturers Association (TEMA) standards specify Overall Heat Transfer Coefficient U on the OUTER tube surface area A_o. Consequently, adding inner tube-side scale/biofilm resistance R_f_in directly to outer shell-side fouling R_f_out without multiplying R_f_in by the outer-to-inner tube diameter ratio (D_o / D_i) understates thermal resistance! Exact TEMA series thermal addition gives R_f_total = R_f_in * (D_o / D_i) + R_f_out, Service Dirty Conductance U_dirty = 1 / (1 / U_clean + R_f_total), HEI Cleanliness Factor CF = U_dirty / U_clean, and Required Excess Tube Area Overdesign Fraction (A_dirty - A_clean) / A_clean = U_clean * R_f_total!
Verify on Clean_Conductance U_clean = 1,000 W/(m^2*K) (B2), Tube_Side_Cooling_Water_Rf = 0.00020 m^2*K/W (B3), Tube_OD_ID_Ratio = 1.25 (25 mm OD / 20 mm ID, B4 -> Outer-Referenced Inner Rf = 0.00025), and Shell_Side_Process_Rf = 0.00025 m^2*K/W (B5): Total Outer-Referenced Fouling Resistance is 0.00050 m^2*K/W (E2); Service Dirty U-Value is 1 / (0.00100 + 0.00050) = 666.67 W/(m^2*K) (E3); Cleanliness Factor is 0.6667 (66.67% in E4); and Required Excess Surface Overdesign is 1,000 * 0.00050 = 0.5000 (+50.0% extra bundle area in E5)!
| TEMA Exchanger Fouling Metric (U_clean=1,000, Rf_in=0.0002, OD/ID=1.25, Rf_out=0.00025) | Formula | Verified Output |
|---|---|---|
| Outer-Referenced Total R_f | R_f_in * (D_o / D_i) + R_f_out | 0.00050 m^2*K/W |
| Service Dirty Overall U_dirty | 1 / (1 / U_clean + R_f_total) | 666.67 W/(m^2*K) |
| Exchanger Cleanliness Factor | U_dirty / U_clean | 0.6667 (1.0000 when clean) |
| Required Excess Area Fraction | U_clean * R_f_total | 0.5000 (+50% @ U=1k; +100% @ U=2k) |
TEMA Outer-Referenced Service Dirty U-Value Formula
Validate U_clean > 0, R_f_in >= 0, D_o / D_i > 1 (outer diameter strictly exceeds inner bore!), and R_f_out >= 0!
=LET(u_cl, B2, rf_i, B3, d_rt, B4, rf_o, B5, IF(OR(u_cl <= 0, rf_i < 0, d_rt <= 1, rf_o < 0), "Invalid TEMA Geometry", LET(rf_t, rf_i * d_rt + rf_o, ROUND(1 / (1 / u_cl + rf_t), 2))))High-Conductance Fouling Sensitivity Check (U_clean = 2,000)
Double U_clean to 2,000 W/(m^2*K) (condenser/plate regime) at the exact same 0.00050 fouling resistance: Excess Area Fraction jumps from 0.50 (+50%) to 1.00 (+100% doubling of area)!
=IF(ISTEXT(E3), E3, ROUND(B2 * E2, 4))Try the example
Use the original values or change them to test your understanding.