HUGHMARK

Computes a laminar two-phase heat transfer coefficient in tube flow using the Hughmark correlation, which is based on entry-region behavior and void-fraction-adjusted liquid contribution.

The model returns heat transfer coefficient from the Nusselt relationship:

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

with Nu formed from empirical dependence on mass flow, liquid thermal properties, tube length, and optional viscosity correction.

Excel Usage

=HUGHMARK(m, x, alpha, D, L, Cpl, kl, mu_b, mu_w)

m (float, required): Mass flow rate (kg/s).
x (float, required): Quality at the tube interval (-).
alpha (float, required): Void fraction in the tube (-).
D (float, required): Tube diameter (m).
L (float, required): Tube length (m).
Cpl (float, required): Liquid heat capacity at constant pressure (J/kg/K).
kl (float, required): Liquid thermal conductivity (W/m/K).
mu_b (float, optional, default: null): 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: Hughmark example

Inputs:

m	x	alpha	D	L	Cpl	kl	mu_b	mu_w
1	0.9	0.9	0.3	0.5	2300	0.6	0.001	0.0012

Excel formula:

=HUGHMARK(1, 0.9, 0.9, 0.3, 0.5, 2300, 0.6, 0.001, 0.0012)

Expected output:

212.741

Example 2: Without wall viscosity correction

Inputs:

m	x	alpha	D	L	Cpl	kl	mu_b
0.6	0.4	0.7	0.05	1	4180	0.6	0.001

Excel formula:

=HUGHMARK(0.6, 0.4, 0.7, 0.05, 1, 4180, 0.6, 0.001)

Expected output:

778.145

Example 3: Lower void fraction

Inputs:

m	x	alpha	D	L	Cpl	kl	mu_b	mu_w
0.4	0.2	0.4	0.04	0.8	3900	0.55	0.0011	0.0013

Excel formula:

=HUGHMARK(0.4, 0.2, 0.4, 0.04, 0.8, 3900, 0.55, 0.0011, 0.0013)

Expected output:

509.305

Example 4: Longer tube length

Inputs:

m	x	alpha	D	L	Cpl	kl	mu_b	mu_w
0.8	0.6	0.8	0.06	2	3600	0.52	0.0009	0.001

Excel formula:

=HUGHMARK(0.8, 0.6, 0.8, 0.06, 2, 3600, 0.52, 0.0009, 0.001)

Expected output:

591.242

Python Code

Show Code

from ht.conv_two_phase import Hughmark as ht_Hughmark

def Hughmark(m, x, alpha, D, L, Cpl, kl, mu_b=None, mu_w=None):
    """
    Calculate two-phase laminar heat transfer coefficient using the Hughmark 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 (-).
        alpha (float): Void fraction in the tube (-).
        D (float): Tube diameter (m).
        L (float): Tube length (m).
        Cpl (float): Liquid heat capacity at constant pressure (J/kg/K).
        kl (float): Liquid thermal conductivity (W/m/K).
        mu_b (float, optional): Liquid viscosity at bulk conditions (Pa*s). Default is None.
        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_Hughmark(
            m=m,
            x=x,
            alpha=alpha,
            D=D,
            L=L,
            Cpl=Cpl,
            kl=kl,
            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 (-).

alpha *

Void fraction in the tube (-).

D *

Tube diameter (m).

L *

Tube length (m).

Cpl *

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

kl *

Liquid thermal conductivity (W/m/K).

mu_b

Liquid viscosity at bulk conditions (Pa*s).

mu_w

Liquid viscosity at wall temperature (Pa*s).