NU_VCYL_ALARABI

This function evaluates the Al-Arabi and Khamis free-convection correlation for a vertical isothermal cylinder using the ht implementation. It requires Prandtl number, Grashof number, and cylinder geometry.

The piecewise formulation is based on Rayleigh scaling and geometric correction:

Ra = Gr\,Pr

and returns a dimensionless Nusselt number based on cylinder height.

Excel Usage

=NU_VCYL_ALARABI(Pr, Gr, L, D, turbulent)

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

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

Example 1: Al-Arabi Khamis example

Inputs:

Pr	Gr	L	D
0.71	20000000000	10	1

Excel formula:

=NU_VCYL_ALARABI(0.71, 20000000000, 10, 1)

Expected output:

280.398

Example 2: Al-Arabi Khamis forced laminar

Inputs:

Pr	Gr	L	D	turbulent
0.71	800000000	8	0.8	false

Excel formula:

=NU_VCYL_ALARABI(0.71, 800000000, 8, 0.8, FALSE)

Expected output:

144.232

Example 3: Al-Arabi Khamis forced turbulent

Inputs:

Pr	Gr	L	D	turbulent
0.71	3000000000	12	1.2	true

Excel formula:

=NU_VCYL_ALARABI(0.71, 3000000000, 12, 1.2, TRUE)

Expected output:

174.501

Example 4: Al-Arabi Khamis mid range

Inputs:

Pr	Gr	L	D
1.2	1200000000	6	0.6

Excel formula:

=NU_VCYL_ALARABI(1.2, 1200000000, 6, 0.6)

Expected output:

175.95

Python Code

Show Code

from ht.conv_free_immersed import Nu_vertical_cylinder_Al_Arabi_Khamis as ht_Nu_vertical_cylinder_Al_Arabi_Khamis

def Nu_vcyl_AlArabi(Pr, Gr, L, D, turbulent=None):
    """
    Calculate the Nusselt number for a vertical cylinder using Al-Arabi and Khamis.

    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).
        L (float): Cylinder length (m).
        D (float): Cylinder diameter (m).
        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_Al_Arabi_Khamis(Pr, Gr, L, D, 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).

L *

Cylinder length (m).

D *

Cylinder diameter (m).

turbulent

Whether to force turbulent or laminar regime (dimensionless).