LIU_WINTERTON

This function computes the Liu-Winterton flow-boiling heat transfer coefficient for saturated boiling in tubes. The method combines a convective liquid term and a nucleate-boiling term into a single composite prediction.

The combined form is:

h_{tp} = \sqrt{(F h_l)^2 + (S h_{nb})^2}

where F and S are empirical factors and h_{nb} is typically linked to Cooper-type nucleate boiling behavior.

Excel Usage

=LIU_WINTERTON(m, x, D, rhol, rhog, mul, kl, Cpl, MW, P, Pc, 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).
Cpl (float, required): Liquid heat capacity (J/kg/K).
MW (float, required): Molecular weight (g/mol).
P (float, required): Pressure (Pa).
Pc (float, required): Critical pressure (Pa).
Te (float, required): Excess wall temperature (K).

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

Example 1: Example from reference

Inputs:

m	x	D	rhol	rhog	kl	mul	Cpl	P	Pc	MW	Te
1	0.4	0.3	567	18.09	0.086	0.000156	2300	1000000	22000000	44.02	7

Excel formula:

=LIU_WINTERTON(1, 0.4, 0.3, 567, 18.09, 0.086, 0.000156, 2300, 1000000, 22000000, 44.02, 7)

Expected output:

4747.75

Example 2: Lower quality with higher pressure

Inputs:

m	x	D	rhol	rhog	kl	mul	Cpl	P	Pc	MW	Te
0.6	0.2	0.02	820	10	0.12	0.0002	3000	1500000	4000000	30	5

Excel formula:

=LIU_WINTERTON(0.6, 0.2, 0.02, 820, 10, 0.12, 0.0002, 3000, 1500000, 4000000, 30, 5)

Expected output:

60702.1

Example 3: Higher quality in small tube

Inputs:

m	x	D	rhol	rhog	kl	mul	Cpl	P	Pc	MW	Te
0.8	0.6	0.015	900	12	0.1	0.00018	2800	800000	3000000	18	6

Excel formula:

=LIU_WINTERTON(0.8, 0.6, 0.015, 900, 12, 0.1, 0.00018, 2800, 800000, 3000000, 18, 6)

Expected output:

107814

Example 4: Mid-range properties

Inputs:

m	x	D	rhol	rhog	kl	mul	Cpl	P	Pc	MW	Te
1.2	0.35	0.05	700	15	0.09	0.00022	2600	1200000	6000000	40	8

Excel formula:

=LIU_WINTERTON(1.2, 0.35, 0.05, 700, 15, 0.09, 0.00022, 2600, 1200000, 6000000, 40, 8)

Expected output:

34338.6

Python Code

Show Code

from ht.boiling_flow import Liu_Winterton as ht_Liu_Winterton

def Liu_Winterton(m, x, D, rhol, rhog, mul, kl, Cpl, MW, P, Pc, Te):
    """
    Compute the Liu-Winterton 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).
        Cpl (float): Liquid heat capacity (J/kg/K).
        MW (float): Molecular weight (g/mol).
        P (float): Pressure (Pa).
        Pc (float): Critical pressure (Pa).
        Te (float): Excess wall temperature (K).

    Returns:
        float: Heat transfer coefficient (W/m^2/K), or an error message if invalid.
    """
    try:
        return ht_Liu_Winterton(m=m, x=x, D=D, rhol=rhol, rhog=rhog, mul=mul,
            kl=kl, Cpl=Cpl, MW=MW, P=P, Pc=Pc, 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).

Cpl *

Liquid heat capacity (J/kg/K).

MW *

Molecular weight (g/mol).

P *

Pressure (Pa).

Pc *

Critical pressure (Pa).

Te *

Excess wall temperature (K).