Engineering & Fluid Mechanics
Kandlikar Flow Boiling Correlation Formula: Convective Number Co & Two-Phase Heat Transfer
Calculate in-tube evaporator and cold-plate flow-boiling heat transfer using Satish G. Kandlikar’s 1990 Convection Number Co = ((1 - x)/x)^0.8 * (rho_g / rho_l)^0.5 and convective-dominant boiling branch h_TP = h_LO * (1.136 * Co^(-0.9) + 667.2 * Bo^0.7 * F_fl).
Unifying nucleate boiling (Bo) and annular-film evaporation (Co) inside refrigerant and water tubes!
Satish G. Kandlikar (1990, ASME Journal of Heat Transfer — calibrated on > 5,200 water and refrigerant data points) replaced empirical Chen suppression graphs with the dimensionless Convection Number Co = ((1 - x) / x)^0.8 * (rho_g / rho_l)^0.5 alongside the Boiling Number Bo = q" / (G * h_fg) and single-phase liquid-only coefficient h_LO!
Kandlikar’s correlation takes MAX(h_NBD, h_CBD) across the Nucleate-Boiling-Dominant branch and Convective-Boiling-Dominant branch! For vertical tubes (or horizontal tubes with liquid Froude Fr_LO >= 0.04) with water (fluid-surface parameter F_fl = 1.00), at vapor quality x = 0.25, density ratio rho_g/rho_l = 0.042, Bo = 0.00055, and h_LO = 1,450 W/(m^2*K), Co = 0.4935 (< 0.65, convective regime) and convective-branch h_TP = 8,166.8 W/(m^2*K)—jumping to 11,916.2 W/(m^2*K) as vapor acceleration thins the annular liquid film at x = 0.50!
| Vapor Quality x (rho_g/rho_l = 0.042, Bo = 5.5e-4) | Kandlikar Convection Number Co | Convective Flow-Boiling h_TP (W/m²·K) |
|---|---|---|
| x = 0.25 (25% Vapor Mass Quality) | 0.4935 (< 0.65 Convective) | 8,166.8 W/(m²·K) |
| x = 0.50 (Thin Annular Liquid Film) | 0.2049 | 11,916.2 W/(m²·K) (+45.9% enhancement) |
| Dryout / Single-Phase x <= 0 or x >= 1 | Outside Two-Phase Window | "Requires Vapor Quality 0 < x < 1" |
Kandlikar Dimensionless Convection Number Co = ((1 - x) / x)^0.8 * (rho_g / rho_l)^0.5
Evaluates Co across vapor quality 0 < x < 1 (B2) and vapor-to-liquid density ratio rho_g/rho_l (B3).
=IF(OR(B2 <= 0, B2 >= 1, B3 <= 0, B3 >= 1, B4 <= 0, B5 <= 0), "Requires Vapor Quality 0 < x < 1", ROUND((((1 - B2) / B2) ^ 0.8) * (B3 ^ 0.5), 4))Kandlikar Convective-Boiling-Dominant Heat Transfer Coefficient h_TP,CBD (W/m²·K, Water F_fl = 1)
Computes h_LO * (1.136 * Co^(-0.9) + 667.2 * Bo^0.7) for water/vertical-tube flow boiling.
=IF(OR(B2 <= 0, B2 >= 1, B3 <= 0, B3 >= 1, B4 <= 0, B5 <= 0), "Requires Vapor Quality 0 < x < 1", ROUND(B5 * (1.136 * (((((1 - B2) / B2) ^ 0.8) * (B3 ^ 0.5)) ^ (-0.9)) + 667.2 * (B4 ^ 0.7)), 1))Try the example
Use the original values or change them to test your understanding.