GROOTHUIS_HENDAL

Estimates the two-phase convective heat transfer coefficient for gas-liquid flow in tubes using the Groothuis-Hendal correlation. The model supports two calibration forms, including a dedicated option for water-air systems.

The coefficient is returned via the Nusselt conversion:

h = \frac{Nu\,k_l}{D}

where Nu is computed from empirical powers of a mixture Reynolds term, liquid Prandtl number, and optional viscosity correction factor.

Excel Usage

=GROOTHUIS_HENDAL(m, x, D, rhol, rhog, Cpl, kl, mug, mu_b, mu_w, water)
  • m (float, required): Mass flow rate (kg/s).
  • x (float, required): Quality at the tube interval (-).
  • D (float, required): Tube diameter (m).
  • rhol (float, required): Liquid density (kg/m^3).
  • rhog (float, required): Gas density (kg/m^3).
  • Cpl (float, required): Liquid heat capacity at constant pressure (J/kg/K).
  • kl (float, required): Liquid thermal conductivity (W/m/K).
  • mug (float, required): Gas viscosity (Pa*s).
  • mu_b (float, required): Liquid viscosity at bulk conditions (Pa*s).
  • mu_w (float, optional, default: null): Liquid viscosity at wall temperature (Pa*s).
  • water (bool, optional, default: false): Use the water-air correlation instead of gas-oil (-).

Returns (float): Heat transfer coefficient (W/m^2/K).

Example 1: Groothuis-Hendal example

Inputs:

m x D rhol rhog Cpl kl mug mu_b mu_w
1 0.9 0.3 1000 2.5 2300 0.6 0.00001 0.001 0.0012

Excel formula:

=GROOTHUIS_HENDAL(1, 0.9, 0.3, 1000, 2.5, 2300, 0.6, 0.00001, 0.001, 0.0012)

Expected output:

1192.95

Example 2: Water-air correlation

Inputs:

m x D rhol rhog Cpl kl mug mu_b mu_w water
0.6 0.5 0.04 998 1.2 4180 0.6 0.000018 0.001 0.0011 true

Excel formula:

=GROOTHUIS_HENDAL(0.6, 0.5, 0.04, 998, 1.2, 4180, 0.6, 0.000018, 0.001, 0.0011, TRUE)

Expected output:

79603.3

Example 3: Without wall viscosity correction

Inputs:

m x D rhol rhog Cpl kl mug mu_b
0.8 0.3 0.05 900 2 3500 0.5 0.00002 0.002

Excel formula:

=GROOTHUIS_HENDAL(0.8, 0.3, 0.05, 900, 2, 3500, 0.5, 0.00002, 0.002)

Expected output:

8712.04

Example 4: Lower quality flow

Inputs:

m x D rhol rhog Cpl kl mug mu_b mu_w
0.4 0.1 0.02 970 3 3800 0.55 0.000015 0.0013 0.0015

Excel formula:

=GROOTHUIS_HENDAL(0.4, 0.1, 0.02, 970, 3, 3800, 0.55, 0.000015, 0.0013, 0.0015)

Expected output:

16587

Python Code

Show Code 
from ht.conv_two_phase import Groothuis_Hendal as ht_Groothuis_Hendal

def Groothuis_Hendal(m, x, D, rhol, rhog, Cpl, kl, mug, mu_b, mu_w=None, water=False):
    """
    Calculate two-phase heat transfer coefficient using the Groothuis-Hendal correlation.

    See: https://ht.readthedocs.io/en/latest/ht.conv_two_phase.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        m (float): Mass flow rate (kg/s).
        x (float): Quality at the tube interval (-).
        D (float): Tube diameter (m).
        rhol (float): Liquid density (kg/m^3).
        rhog (float): Gas density (kg/m^3).
        Cpl (float): Liquid heat capacity at constant pressure (J/kg/K).
        kl (float): Liquid thermal conductivity (W/m/K).
        mug (float): Gas viscosity (Pa*s).
        mu_b (float): Liquid viscosity at bulk conditions (Pa*s).
        mu_w (float, optional): Liquid viscosity at wall temperature (Pa*s). Default is None.
        water (bool, optional): Use the water-air correlation instead of gas-oil (-). Default is False.

    Returns:
        float: Heat transfer coefficient (W/m^2/K).
    """
    try:
        return ht_Groothuis_Hendal(
            m=m,
            x=x,
            D=D,
            rhol=rhol,
            rhog=rhog,
            Cpl=Cpl,
            kl=kl,
            mug=mug,
            mu_b=mu_b,
            mu_w=mu_w,
            water=water,
        )
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Mass flow rate (kg/s).
Quality at the tube interval (-).
Tube diameter (m).
Liquid density (kg/m^3).
Gas density (kg/m^3).
Liquid heat capacity at constant pressure (J/kg/K).
Liquid thermal conductivity (W/m/K).
Gas viscosity (Pa*s).
Liquid viscosity at bulk conditions (Pa*s).
Liquid viscosity at wall temperature (Pa*s).
Use the water-air correlation instead of gas-oil (-).