KUDIRKA_GROSH_MCF

Computes the two-phase tube-flow heat transfer coefficient using the Kudirka-Grosh-McFadden empirical correlation. The model combines gas-liquid velocity ratio effects, viscosity ratio effects, and liquid thermal scaling.

The output coefficient is formed through:

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

with Nu determined by the correlation’s empirical exponents and optional viscosity correction using bulk and wall liquid viscosities.

Excel Usage

=KUDIRKA_GROSH_MCF(m, x, D, rhol, rhog, Cpl, kl, mug, mu_b, mu_w)

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).

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

Example 1: Kudirka-Grosh-McFadden 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:

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

Expected output:

303.994

Example 2: Without wall viscosity correction

Inputs:

m	x	D	rhol	rhog	Cpl	kl	mug	mu_b
0.7	0.3	0.05	980	2.2	4180	0.6	0.00002	0.001

Excel formula:

=KUDIRKA_GROSH_MCF(0.7, 0.3, 0.05, 980, 2.2, 4180, 0.6, 0.00002, 0.001)

Expected output:

5582.84

Example 3: Small diameter tube

Inputs:

m	x	D	rhol	rhog	Cpl	kl	mug	mu_b	mu_w
0.4	0.6	0.02	990	1.8	3800	0.55	0.000015	0.0011	0.0013

Excel formula:

=KUDIRKA_GROSH_MCF(0.4, 0.6, 0.02, 990, 1.8, 3800, 0.55, 0.000015, 0.0011, 0.0013)

Expected output:

11395.1

Example 4: Lower quality flow

Inputs:

m	x	D	rhol	rhog	Cpl	kl	mug	mu_b	mu_w
0.9	0.15	0.04	970	2.7	3600	0.5	0.000012	0.0014	0.0016

Excel formula:

=KUDIRKA_GROSH_MCF(0.9, 0.15, 0.04, 970, 2.7, 3600, 0.5, 0.000012, 0.0014, 0.0016)

Expected output:

3676

Python Code

Show Code

from ht.conv_two_phase import Kudirka_Grosh_McFadden as ht_Kudirka_Grosh_McFadden

def Kudirka_Grosh_McF(m, x, D, rhol, rhog, Cpl, kl, mug, mu_b, mu_w=None):
    """
    Calculate two-phase heat transfer coefficient using the Kudirka-Grosh-McFadden 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.

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

Online Calculator

m *

Mass flow rate (kg/s).

x *

Quality at the tube interval (-).

D *

Tube diameter (m).

rhol *

Liquid density (kg/m^3).

rhog *

Gas density (kg/m^3).

Cpl *

Liquid heat capacity at constant pressure (J/kg/K).

kl *

Liquid thermal conductivity (W/m/K).

mug *

Gas viscosity (Pa*s).

mu_b *

Liquid viscosity at bulk conditions (Pa*s).

mu_w

Liquid viscosity at wall temperature (Pa*s).