BIER

This function estimates nucleate boiling heat transfer coefficient with the Bier correlation using saturation and critical pressure plus either excess wall temperature or heat flux.

In general form, the model scales with reduced pressure and boiling driving force:

h = f\left(P, P_c, \Delta T_e\right) \; \text{or} \; h = f\left(P, P_c, q\right)

It is used for pool-boiling coefficient estimation when limited fluid inputs are available.

Excel Usage

=BIER(P, Pc, Te, q)

P (float, required): Saturation pressure of fluid (Pa).
Pc (float, required): Critical pressure of fluid (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: Water boiling with excess temperature

Inputs:

P	Pc	Te
101325	22048321	4.3

Excel formula:

=BIER(101325, 22048321, 4.3)

Expected output:

1290.53

Example 2: Water boiling with specified heat flux

Inputs:

P	Pc	q
101325	22048321	20000

Excel formula:

=BIER(101325, 22048321, 20000)

Expected output:

3166.1

Example 3: Elevated pressure with excess temperature

Inputs:

P	Pc	Te
300000	22048321	8

Excel formula:

=BIER(300000, 22048321, 8)

Expected output:

8045.32

Example 4: Elevated pressure with heat flux

Inputs:

P	Pc	q
300000	22048321	35000

Excel formula:

=BIER(300000, 22048321, 35000)

Expected output:

5252.28

Python Code

Show Code

from ht.boiling_nucleic import Bier as ht_Bier

def Bier(P, Pc, Te=None, q=None):
    """
    Compute nucleate boiling heat transfer coefficient using the Bier correlation.

    See: https://ht.readthedocs.io/en/latest/ht.boiling_nucleic.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        P (float): Saturation pressure of fluid (Pa).
        Pc (float): Critical pressure of fluid (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:
        return ht_Bier(P=P, Pc=Pc, Te=Te, q=q)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

P *

Saturation pressure of fluid (Pa).

Pc *

Critical pressure of fluid (Pa).

Excess wall temperature (K).

Heat flux (W/m^2).