CHEN_BENNETT

This function estimates the two-phase flow boiling heat transfer coefficient using the Chen-Bennett correlation for saturated flow in tubes. It combines a convective contribution with a nucleate-boiling contribution through suppression and enhancement factors.

The combined form is:

h_{tp} = S h_{nb} + F h_{sp,l}

where h_{sp,l} is commonly modeled with a Dittus-Boelter style relation and h_{nb} with a Forster-Zuber style relation. The approach is widely used for engineering estimation of boiling heat transfer in internal flows.

Excel Usage

=CHEN_BENNETT(m, x, D, rhol, rhog, mul, mug, kl, Cpl, Hvap, sigma, dPsat, 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).
mug (float, required): Gas viscosity (Pa*s).
kl (float, required): Liquid thermal conductivity (W/m/K).
Cpl (float, required): Liquid heat capacity (J/kg/K).
Hvap (float, required): Heat of vaporization (J/kg).
sigma (float, required): Surface tension (N/m).
dPsat (float, required): Saturation pressure difference (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	mul	mug	kl	Cpl	Hvap	sigma	dPsat	Te
0.106	0.2	0.0212	567	18.09	0.000156	0.00000711	0.086	2730	200000	0.02	100000	3

Excel formula:

=CHEN_BENNETT(0.106, 0.2, 0.0212, 567, 18.09, 0.000156, 0.00000711, 0.086, 2730, 200000, 0.02, 100000, 3)

Expected output:

4938.28

Example 2: Higher quality with larger diameter

Inputs:

m	x	D	rhol	rhog	mul	mug	kl	Cpl	Hvap	sigma	dPsat	Te
0.2	0.4	0.03	900	15	0.0002	0.00001	0.12	3200	180000	0.025	80000	5

Excel formula:

=CHEN_BENNETT(0.2, 0.4, 0.03, 900, 15, 0.0002, 0.00001, 0.12, 3200, 180000, 0.025, 80000, 5)

Expected output:

7946.77

Example 3: Low quality at small diameter

Inputs:

m	x	D	rhol	rhog	mul	mug	kl	Cpl	Hvap	sigma	dPsat	Te
0.05	0.1	0.015	950	8	0.0003	0.000012	0.14	3500	220000	0.03	60000	2

Excel formula:

=CHEN_BENNETT(0.05, 0.1, 0.015, 950, 8, 0.0003, 0.000012, 0.14, 3500, 220000, 0.03, 60000, 2)

Expected output:

7020.18

Example 4: Mid-range inputs

Inputs:

m	x	D	rhol	rhog	mul	mug	kl	Cpl	Hvap	sigma	dPsat	Te
0.12	0.3	0.025	700	12	0.00018	0.000008	0.1	2600	190000	0.018	90000	4

Excel formula:

=CHEN_BENNETT(0.12, 0.3, 0.025, 700, 12, 0.00018, 0.000008, 0.1, 2600, 190000, 0.018, 90000, 4)

Expected output:

5751.45

Python Code

Show Code

from ht.boiling_flow import Chen_Bennett as ht_Chen_Bennett

def Chen_Bennett(m, x, D, rhol, rhog, mul, mug, kl, Cpl, Hvap, sigma, dPsat, Te):
    """
    Compute the Chen-Bennett 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).
        mug (float): Gas viscosity (Pa*s).
        kl (float): Liquid thermal conductivity (W/m/K).
        Cpl (float): Liquid heat capacity (J/kg/K).
        Hvap (float): Heat of vaporization (J/kg).
        sigma (float): Surface tension (N/m).
        dPsat (float): Saturation pressure difference (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_Chen_Bennett(m=m, x=x, D=D, rhol=rhol, rhog=rhog, mul=mul, mug=mug,
            kl=kl, Cpl=Cpl, Hvap=Hvap, sigma=sigma, dPsat=dPsat, 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).

mug *

Gas viscosity (Pa*s).

kl *

Liquid thermal conductivity (W/m/K).

Cpl *

Liquid heat capacity (J/kg/K).

Hvap *

Heat of vaporization (J/kg).

sigma *

Surface tension (N/m).

dPsat *

Saturation pressure difference (Pa).

Te *

Excess wall temperature (K).