FORSTER_ZUBER

This function calculates nucleate boiling heat transfer using the Forster-Zuber correlation. It supports either excess wall temperature or heat flux as the driving input and uses thermophysical properties of the liquid-vapor system.

A representative expression is:

h \propto \left(\frac{k_l^{0.79} c_{p,l}^{0.45} \rho_l^{0.49}}{\sigma^{0.5} \mu_l^{0.29} H_{vap}^{0.24} \rho_g^{0.24}}\right) \Delta T_e^{0.24} \Delta P_{sat}^{0.75}

The correlation is frequently used as a nucleate-boiling component in broader flow-boiling models.

Excel Usage

=FORSTER_ZUBER(rhol, rhog, mul, kl, Cpl, Hvap, sigma, dPsat, Te, q)

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).
Hvap (float, required): Heat of vaporization (J/kg).
sigma (float, required): Surface tension (N/m).
dPsat (float, required): Saturation pressure difference (Pa).
Te (float, optional, default: null): Excess wall temperature (K).
q (float, optional, default: null): Heat flux (W/m^2).

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

Example 1: Example with excess temperature

Inputs:

Te	dPsat	Cpl	kl	mul	sigma	Hvap	rhol	rhog
4.3	16885.8	4180	0.688	0.000275	0.0588	2250000	958	0.597

Excel formula:

=FORSTER_ZUBER(4.3, 16885.8, 4180, 0.688, 0.000275, 0.0588, 2250000, 958, 0.597)

Expected output:

3534.06

Example 2: Using heat flux input

Inputs:

q	dPsat	Cpl	kl	mul	sigma	Hvap	rhol	rhog
120000	15000	3500	0.12	0.0003	0.025	200000	900	10

Excel formula:

=FORSTER_ZUBER(120000, 15000, 3500, 0.12, 0.0003, 0.025, 200000, 900, 10)

Expected output:

1890

Example 3: Alternate fluid properties with Te

Inputs:

Te	dPsat	Cpl	kl	mul	sigma	Hvap	rhol	rhog
6	20000	3000	0.1	0.00022	0.02	180000	850	12

Excel formula:

=FORSTER_ZUBER(6, 20000, 3000, 0.1, 0.00022, 0.02, 180000, 850, 12)

Expected output:

1255.8

Example 4: Higher heat flux case

Inputs:

q	dPsat	Cpl	kl	mul	sigma	Hvap	rhol	rhog
200000	25000	3800	0.15	0.00028	0.03	210000	920	8

Excel formula:

=FORSTER_ZUBER(200000, 25000, 3800, 0.15, 0.00028, 0.03, 210000, 920, 8)

Expected output:

3325

Python Code

Show Code

from ht.boiling_flow import Forster_Zuber as ht_Forster_Zuber

def Forster_Zuber(rhol, rhog, mul, kl, Cpl, Hvap, sigma, dPsat, Te=None, q=None):
    """
    Compute the Forster-Zuber nucleate 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:
        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).
        Hvap (float): Heat of vaporization (J/kg).
        sigma (float): Surface tension (N/m).
        dPsat (float): Saturation pressure difference (Pa).
        Te (float, optional): Excess wall temperature (K). Default is None.
        q (float, optional): Heat flux (W/m^2). 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_Forster_Zuber(rhol=rhol, rhog=rhog, mul=mul, kl=kl, Cpl=Cpl,
            Hvap=Hvap, sigma=sigma, dPsat=dPsat, Te=Te, q=q)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

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).

Hvap *

Heat of vaporization (J/kg).

sigma *

Surface tension (N/m).

dPsat *

Saturation pressure difference (Pa).

Excess wall temperature (K).

Heat flux (W/m^2).