KNOTT

Calculates two-phase convective heat transfer in tube flow using the Knott correlation. The method can use a supplied liquid-only coefficient or estimate it from liquid properties and tube geometry.

The two-phase enhancement is based on scaling the liquid-only coefficient:

h_{TP} = h_l\,\phi

where \phi is an empirical two-phase multiplier derived from gas-liquid flow rate effects.

Excel Usage

=KNOTT(m, x, D, rhol, rhog, Cpl, kl, mu_b, mu_w, L, hl)

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, optional, default: null): Liquid heat capacity at constant pressure (J/kg/K).
kl (float, optional, default: null): 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).
L (float, optional, default: null): Tube length (m).
hl (float, optional, default: null): Liquid-only heat transfer coefficient (W/m^2/K).

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

Example 1: Knott example

Inputs:

m	x	D	rhol	rhog	Cpl	kl	mu_b	mu_w	L
1	0.9	0.3	1000	2.5	2300	0.6	0.001	0.0012	4

Excel formula:

=KNOTT(1, 0.9, 0.3, 1000, 2.5, 2300, 0.6, 0.001, 0.0012, 4)

Expected output:

4225.54

Example 2: Using a provided liquid coefficient

Inputs:

m	x	D	rhol	rhog	hl
0.7	0.4	0.05	980	2	500

Excel formula:

=KNOTT(0.7, 0.4, 0.05, 980, 2, 500)

Expected output:

3447.05

Example 3: Without wall viscosity correction

Inputs:

m	x	D	rhol	rhog	Cpl	kl	mu_b	L
0.6	0.3	0.04	990	1.8	4180	0.6	0.001	2

Excel formula:

=KNOTT(0.6, 0.3, 0.04, 990, 1.8, 4180, 0.6, 0.001, 2)

Expected output:

13136.3

Example 4: Higher quality flow

Inputs:

m	x	D	rhol	rhog	Cpl	kl	mu_b	mu_w	L
1.4	0.8	0.06	950	2.8	3600	0.52	0.0014	0.0016	3

Excel formula:

=KNOTT(1.4, 0.8, 0.06, 950, 2.8, 3600, 0.52, 0.0014, 0.0016, 3)

Expected output:

18181.3

Python Code

Show Code

from ht.conv_two_phase import Knott as ht_Knott

def Knott(m, x, D, rhol, rhog, Cpl=None, kl=None, mu_b=None, mu_w=None, L=None, hl=None):
    """
    Calculate two-phase heat transfer coefficient using the Knott 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, optional): Liquid heat capacity at constant pressure (J/kg/K). Default is None.
        kl (float, optional): Liquid thermal conductivity (W/m/K). Default is None.
        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.
        L (float, optional): Tube length (m). Default is None.
        hl (float, optional): Liquid-only heat transfer coefficient (W/m^2/K). Default is None.

    Returns:
        float: Heat transfer coefficient (W/m^2/K).
    """
    try:
        return ht_Knott(
            m=m,
            x=x,
            D=D,
            rhol=rhol,
            rhog=rhog,
            Cpl=Cpl,
            kl=kl,
            mu_b=mu_b,
            mu_w=mu_w,
            L=L,
            hl=hl,
        )
    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).

Liquid thermal conductivity (W/m/K).

mu_b

Liquid viscosity at bulk conditions (Pa*s).

mu_w

Liquid viscosity at wall temperature (Pa*s).

Tube length (m).

Liquid-only heat transfer coefficient (W/m^2/K).