COOPER

This function computes a nucleate pool-boiling heat transfer coefficient using the Cooper correlation. The method requires either excess wall temperature or heat flux and incorporates reduced pressure, molecular weight, and a roughness term.

In common form, the relation scales as:

h \propto q^{0.67}\left(\frac{P}{P_c}\right)^{a}\left[-\log_{10}\left(\frac{P}{P_c}\right)\right]^{-0.55}MW^{-0.5}

where the exponent a depends on the roughness parameter. This is a standard empirical approach for nucleate boiling estimation.

Excel Usage

=COOPER(P, Pc, MW, Te, q, Rp)
  • P (float, required): Saturation pressure (Pa).
  • Pc (float, required): Critical pressure (Pa).
  • MW (float, required): Molecular weight (g/mol).
  • Te (float, optional, default: null): Excess wall temperature (K).
  • q (float, optional, default: null): Heat flux (W/m^2).
  • Rp (float, optional, default: 0.000001): Surface roughness parameter (m).

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

Example 1: Example with excess temperature

Inputs:

P Pc MW Te
101325 22048321 18.02 4.3

Excel formula:

=COOPER(101325, 22048321, 18.02, 4.3)

Expected output:

1558.14

Example 2: Using heat flux input

Inputs:

P Pc MW q
101325 22048321 18.02 100000

Excel formula:

=COOPER(101325, 22048321, 18.02, 100000)

Expected output:

9530.96

Example 3: Rough surface with higher pressure

Inputs:

P Pc MW Te Rp
500000 4000000 44 10 0.000002

Excel formula:

=COOPER(500000, 4000000, 44, 10, 0.000002)

Expected output:

52990.3

Example 4: Alternate fluid with heat flux

Inputs:

P Pc MW q Rp
200000 5000000 30 50000 0.000005

Excel formula:

=COOPER(200000, 5000000, 30, 50000, 0.000005)

Expected output:

12524.6

Python Code

Show Code 
from ht.boiling_flow import Cooper as ht_Cooper

def Cooper(P, Pc, MW, Te=None, q=None, Rp=1e-06):
    """
    Compute the Cooper 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:
        P (float): Saturation pressure (Pa).
        Pc (float): Critical pressure (Pa).
        MW (float): Molecular weight (g/mol).
        Te (float, optional): Excess wall temperature (K). Default is None.
        q (float, optional): Heat flux (W/m^2). Default is None.
        Rp (float, optional): Surface roughness parameter (m). Default is 1e-06.

    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_Cooper(P=P, Pc=Pc, MW=MW, Te=Te, q=q, Rp=Rp)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Saturation pressure (Pa).
Critical pressure (Pa).
Molecular weight (g/mol).
Excess wall temperature (K).
Heat flux (W/m^2).
Surface roughness parameter (m).