NU_VHELIX_ALI

This function returns the natural-convection Nusselt number for a vertical helical coil using the Ali correlation. It is intended for coil-in-tank applications where convection occurs in the surrounding fluid.

The model uses Prandtl and Grashof numbers to estimate heat-transfer enhancement relative to conduction based on an empirical power-law fit.

\mathrm{Nu}_L = 0.555\,\mathrm{Gr}_L^{0.301}\,\mathrm{Pr}^{0.314}

Excel Usage

=NU_VHELIX_ALI(Pr, Gr)

Pr (float, required): Prandtl number of the surrounding fluid (-).
Gr (float, required): Grashof number of the surrounding fluid (-).

Returns (float): Nusselt number for a vertical helical coil, or error message if invalid.

Example 1: Ali correlation example

Inputs:

Pr	Gr
4.4	100000000000

Excel formula:

=NU_VHELIX_ALI(4.4, 100000000000)

Expected output:

1808.58

Example 2: Ali correlation at mid range

Inputs:

Pr	Gr
10	10000000000

Excel formula:

=NU_VHELIX_ALI(10, 10000000000)

Expected output:

1170.29

Example 3: Ali correlation with higher Prandtl number

Inputs:

Pr	Gr
100	50000000000

Excel formula:

=NU_VHELIX_ALI(100, 50000000000)

Expected output:

3914.56

Example 4: Ali correlation with lower Prandtl number

Inputs:

Pr	Gr
5	1000000000

Excel formula:

=NU_VHELIX_ALI(5, 1000000000)

Expected output:

470.727

Python Code

Show Code

from ht.conv_free_enclosed import Nu_vertical_helical_coil_Ali as ht_Nu_vertical_helical_coil_Ali

def Nu_VHelix_Ali(Pr, Gr):
    """
    Calculate the Nusselt number for natural convection around a vertical helical coil using the Ali correlation.

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

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

    Args:
        Pr (float): Prandtl number of the surrounding fluid (-).
        Gr (float): Grashof number of the surrounding fluid (-).

    Returns:
        float: Nusselt number for a vertical helical coil, or error message if invalid.
    """
    try:
        return ht_Nu_vertical_helical_coil_Ali(Pr=Pr, Gr=Gr)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Pr *

Prandtl number of the surrounding fluid (-).

Gr *

Grashof number of the surrounding fluid (-).