NU_VCYL_EIGENSON

This function computes natural-convection Nusselt number for a vertical isothermal cylinder using the Eigenson-Morgan model in ht. It allows automatic or forced regime selection through the turbulent argument.

The implementation uses piecewise relations in Rayleigh number:

Ra = Gr\,Pr

and returns a dimensionless Nusselt number referenced to cylinder height.

Excel Usage

=NU_VCYL_EIGENSON(Pr, Gr, turbulent)

Pr (float, required): Prandtl number of the fluid (dimensionless).
Gr (float, required): Grashof number based on cylinder height (dimensionless).
turbulent (bool, optional, default: null): Whether to force turbulent or laminar regime (dimensionless).

Returns (float): Nusselt number based on cylinder height (dimensionless).

Example 1: Eigenson Morgan example

Inputs:

Pr	Gr
0.7	20000000000

Excel formula:

=NU_VCYL_EIGENSON(0.7, 20000000000)

Expected output:

230.559

Example 2: Eigenson Morgan forced laminar

Inputs:

Pr	Gr	turbulent
0.7	2000000000	false

Excel formula:

=NU_VCYL_EIGENSON(0.7, 2000000000, FALSE)

Expected output:

92.8481

Example 3: Eigenson Morgan forced turbulent

Inputs:

Pr	Gr	turbulent
0.7	50000000000	true

Excel formula:

=NU_VCYL_EIGENSON(0.7, 50000000000, TRUE)

Expected output:

356.518

Example 4: Eigenson Morgan mid range

Inputs:

Pr	Gr
1	8000000000

Excel formula:

=NU_VCYL_EIGENSON(1, 8000000000)

Expected output:

177.359

Python Code

Show Code

from ht.conv_free_immersed import Nu_vertical_cylinder_Eigenson_Morgan as ht_Nu_vertical_cylinder_Eigenson_Morgan

def Nu_vcyl_Eigenson(Pr, Gr, turbulent=None):
    """
    Calculate the Nusselt number for a vertical cylinder using Eigenson-Morgan.

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

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

    Args:
        Pr (float): Prandtl number of the fluid (dimensionless).
        Gr (float): Grashof number based on cylinder height (dimensionless).
        turbulent (bool, optional): Whether to force turbulent or laminar regime (dimensionless). Default is None.

    Returns:
        float: Nusselt number based on cylinder height (dimensionless).
    """
    try:
        result = ht_Nu_vertical_cylinder_Eigenson_Morgan(Pr, Gr, turbulent=turbulent)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Pr *

Prandtl number of the fluid (dimensionless).

Gr *

Grashof number based on cylinder height (dimensionless).

turbulent

Whether to force turbulent or laminar regime (dimensionless).