Engineering & Science
Shah In-Tube Two-Phase Condensation Heat-Transfer Correlation Formula
Calculate local annular/shear-driven condenser tube heat-transfer coefficient h_TP = h_L * ((1 - x)^0.8 + (3.8 * x^0.76 * (1 - x)^0.04) / p_r^0.38) across refrigerants and steam.
Sizing HVAC refrigerant condensers and steam surface tubes across vapor quality x = 0.05 to 0.95!
Inside horizontal or vertical condenser tubes, high-velocity vapor shear thins the liquid condensate annulus dramatically—boosting heat transfer 3× to 10× above single-phase liquid flow! Mohammed M. Shah (International Journal of Heat and Mass Transfer, 1979) correlated 474 experimental datasets across water, R-11/R-22/R-134a refrigerants, methanol, and benzene using ONLY all-liquid heat-transfer coefficient h_L, local vapor quality x, and reduced pressure p_r = P_sat / P_crit: h_TP = h_L * ((1 - x)^0.8 + (3.8 * x^0.76 * (1 - x)^0.04) / p_r^0.38)!
Evaluate an R-134a chiller condenser at 40 °C (P_sat = 10.17 bar, P_crit = 40.59 bar -> p_r = 0.2506) with all-liquid coefficient h_L = 1,450 W/(m^2·K): at mid-tube vapor quality x = 0.50, Shah’s two-phase multiplier reaches 4.267× for h_TP = 6,187.6 W/(m^2·K)—and near the inlet at x = 0.80 it reaches 7,778.5 W/(m^2·K)!
| Condenser Tube Location (h_L = 1450, p_r = 10.17 / 40.59) | Shah Multiplier h_TP / h_L | Local Condensing h_TP (W/(m²·K)) | Flow Regime |
|---|---|---|---|
| Inlet Zone (x = 0.80 Vapor Quality) | 5.364× | 7,778.5 W/(m²·K) | High-Shear Thin Annular Film |
| Mid-Pass Zone (x = 0.50 Vapor Quality) | 4.267× | 6,187.6 W/(m²·K) | Annular-Wavy Condensation |
| Invalid x <= 0, x >= 1, or P >= P_crit | Undefined | "Invalid Condensation State" | Subcritical Two-Phase Guard |
Shah Local Two-Phase Condensing Heat-Transfer Coefficient h_TP (W/(m²·K))
Evaluates h_L * ((1 - x)^0.8 + (3.8 * x^0.76 * (1 - x)^0.04) / (P_sat / P_crit)^0.38) from all-liquid h_L (B2), vapor quality x (B3), saturation pressure B4 (bar), and critical pressure B5 (bar).
=IF(OR(B2 <= 0, B3 <= 0, B3 >= 1, B4 <= 0, B5 <= B4), "Invalid Condensation State", ROUND(B2 * (((1 - B3) ^ 0.8) + (3.8 * (B3 ^ 0.76) * ((1 - B3) ^ 0.04)) / ((B4 / B5) ^ 0.38)), 1))Dimensionless Shah Two-Phase Enhancement Multiplier h_TP / h_L
Isolates the dimensionless vapor-shear enhancement ratio above single-phase liquid flow.
=IF(OR(B3 <= 0, B3 >= 1, B4 <= 0, B5 <= B4), "Invalid Condensation State", ROUND(((1 - B3) ^ 0.8) + (3.8 * (B3 ^ 0.76) * ((1 - B3) ^ 0.04)) / ((B4 / B5) ^ 0.38), 3))Try the example
Use the original values or change them to test your understanding.