LI_WU

This function estimates saturated flow-boiling heat transfer using the Li-Wu correlation, developed for mini and microchannel applications. It requires either heat flux or excess wall temperature.

A common representation is:

h_{tp} = 334\,Bg^{0.3}(Bo\,Re_l^{0.36})^{0.4}\frac{k_l}{D}

where Re_l is based on the liquid-phase flow, and Bg and Bo capture boiling intensity effects.

Excel Usage

=LI_WU(m, x, D, rhol, rhog, mul, kl, Hvap, sigma, q, Te)

m (float, required): Mass flow rate (kg/s).
x (float, required): Quality at the tube interval (dimensionless).
D (float, required): Tube diameter (m).
rhol (float, required): Liquid density (kg/m^3).
rhog (float, required): Gas density (kg/m^3).
mul (float, required): Liquid viscosity (Pa*s).
kl (float, required): Liquid thermal conductivity (W/m/K).
Hvap (float, required): Heat of vaporization (J/kg).
sigma (float, required): Surface tension (N/m).
q (float, optional, default: null): Heat flux (W/m^2).
Te (float, optional, default: null): Excess wall temperature (K).

Returns (float): Heat transfer coefficient (W/m^2/K), or an error message if invalid.

Example 1: Example with heat flux

Inputs:

m	x	D	rhol	rhog	kl	mul	sigma	Hvap	q
1	0.2	0.3	567	18.09	0.086	0.000156	0.02	900000	100000

Excel formula:

=LI_WU(1, 0.2, 0.3, 567, 18.09, 0.086, 0.000156, 0.02, 900000, 100000)

Expected output:

5345.41

Example 2: Using excess wall temperature

Inputs:

m	x	D	rhol	rhog	kl	mul	sigma	Hvap	Te
0.8	0.3	0.02	850	10	0.12	0.0002	0.025	180000	6

Excel formula:

=LI_WU(0.8, 0.3, 0.02, 850, 10, 0.12, 0.0002, 0.025, 180000, 6)

Expected output:

4267.15

Example 3: Small diameter with moderate quality

Inputs:

m	x	D	rhol	rhog	kl	mul	sigma	Hvap	q
0.5	0.4	0.01	900	12	0.1	0.00018	0.03	200000	60000

Excel formula:

=LI_WU(0.5, 0.4, 0.01, 900, 12, 0.1, 0.00018, 0.03, 200000, 60000)

Expected output:

3783.53

Example 4: Mid-range properties with Te

Inputs:

m	x	D	rhol	rhog	kl	mul	sigma	Hvap	Te
1.2	0.25	0.05	700	15	0.09	0.00022	0.018	160000	5

Excel formula:

=LI_WU(1.2, 0.25, 0.05, 700, 15, 0.09, 0.00022, 0.018, 160000, 5)

Expected output:

3753.9

Python Code

Show Code

from ht.boiling_flow import Li_Wu as ht_Li_Wu

def Li_Wu(m, x, D, rhol, rhog, mul, kl, Hvap, sigma, q=None, Te=None):
    """
    Compute the Li-Wu boiling heat transfer coefficient.

    See: https://ht.readthedocs.io/en/latest/ht.boiling_flow.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 (dimensionless).
        D (float): Tube diameter (m).
        rhol (float): Liquid density (kg/m^3).
        rhog (float): Gas density (kg/m^3).
        mul (float): Liquid viscosity (Pa*s).
        kl (float): Liquid thermal conductivity (W/m/K).
        Hvap (float): Heat of vaporization (J/kg).
        sigma (float): Surface tension (N/m).
        q (float, optional): Heat flux (W/m^2). Default is None.
        Te (float, optional): Excess wall temperature (K). Default is None.

    Returns:
        float: Heat transfer coefficient (W/m^2/K), or an error message if invalid.
    """
    try:
        if Te is None and q is None:
            return "Error: Te or q must be provided"
        return ht_Li_Wu(m=m, x=x, D=D, rhol=rhol, rhog=rhog, mul=mul, kl=kl,
            Hvap=Hvap, sigma=sigma, q=q, Te=Te)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

m *

Mass flow rate (kg/s).

x *

Quality at the tube interval (dimensionless).

D *

Tube diameter (m).

rhol *

Liquid density (kg/m^3).

rhog *

Gas density (kg/m^3).

mul *

Liquid viscosity (Pa*s).

kl *

Liquid thermal conductivity (W/m/K).

Hvap *

Heat of vaporization (J/kg).

sigma *

Surface tension (N/m).

Heat flux (W/m^2).

Excess wall temperature (K).