NU_WAKAO_KAGEI

This function estimates packed-bed convective heat transfer with the Wakao-Kagei correlation. The relationship depends on Reynolds and Prandtl numbers and provides a practical estimate when a simple, widely used packed-bed correlation is needed.

The correlation is:

Nu = 2 + 1.1Pr^{1/3}Re^{0.6}

where Re is the particle Reynolds number and Pr is the Prandtl number of the fluid.

Excel Usage

=NU_WAKAO_KAGEI(Re, Pr)

Re (float, required): Reynolds number using particle diameter as length scale (-).
Pr (float, required): Prandtl number of the fluid (-).

Returns (float): Nusselt number for heat transfer to the packed bed.

Example 1: Example Reynolds and Prandtl values

Inputs:

Re	Pr
2000	0.7

Excel formula:

=NU_WAKAO_KAGEI(2000, 0.7)

Expected output:

95.4064

Example 2: Lower Reynolds number case

Inputs:

Re	Pr
50	1.2

Excel formula:

=NU_WAKAO_KAGEI(50, 1.2)

Expected output:

14.2227

Example 3: Mid range Reynolds number

Inputs:

Re	Pr
12000	0.9

Excel formula:

=NU_WAKAO_KAGEI(12000, 0.9)

Expected output:

299.611

Example 4: Higher Prandtl number case

Inputs:

Re	Pr
1500	5

Excel formula:

=NU_WAKAO_KAGEI(1500, 5)

Expected output:

153.369

Python Code

Show Code

from ht.conv_packed_bed import Nu_Wakao_Kagei as ht_Nu_Wakao_Kagei

def Nu_Wakao_Kagei(Re, Pr):
    """
    Calculate Nusselt number for a packed bed using the Wakao-Kagei correlation.

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

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

    Args:
        Re (float): Reynolds number using particle diameter as length scale (-).
        Pr (float): Prandtl number of the fluid (-).

    Returns:
        float: Nusselt number for heat transfer to the packed bed.
    """
    try:
        Re = float(Re)
        Pr = float(Pr)
        return ht_Nu_Wakao_Kagei(Re=Re, Pr=Pr)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Re *

Reynolds number using particle diameter as length scale (-).

Pr *

Prandtl number of the fluid (-).