NU_ACHENBACH

This function computes the packed-bed Nusselt number using the Achenbach correlation for convective heat transfer around particles in a bed. It combines two Reynolds-number-dependent terms and is useful for estimating heat transfer when Reynolds number, Prandtl number, and bed void fraction are known.

The correlation is:

Nu = \left[(1.18Re^{0.58})^4 + \left(0.23\left(\frac{Re}{1-\epsilon}\right)^{0.75}\right)^4\right]^{0.25}

where Re is the particle Reynolds number, Pr is the Prandtl number, and \epsilon is the bed voidage.

Excel Usage

=NU_ACHENBACH(Re, Pr, voidage)
  • Re (float, required): Reynolds number using particle diameter as length scale (-).
  • Pr (float, required): Prandtl number of the fluid (-).
  • voidage (float, required): Void fraction of bed packing (-).

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

Example 1: Example Reynolds and Prandtl values

Inputs:

Re Pr voidage
2000 0.7 0.4

Excel formula:

=NU_ACHENBACH(2000, 0.7, 0.4)

Expected output:

117.703

Example 2: Lower Reynolds number case

Inputs:

Re Pr voidage
500 1.2 0.35

Excel formula:

=NU_ACHENBACH(500, 1.2, 0.35)

Expected output:

46.8431

Example 3: Mid range Reynolds number

Inputs:

Re Pr voidage
10000 0.9 0.38

Excel formula:

=NU_ACHENBACH(10000, 0.9, 0.38)

Expected output:

352.48

Example 4: Higher void fraction case

Inputs:

Re Pr voidage
1500 0.8 0.45

Excel formula:

=NU_ACHENBACH(1500, 0.8, 0.45)

Expected output:

100.512

Python Code

Show Code 
from ht.conv_packed_bed import Nu_Achenbach as ht_Nu_Achenbach

def Nu_Achenbach(Re, Pr, voidage):
    """
    Calculate Nusselt number for a packed bed using the Achenbach 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 (-).
        voidage (float): Void fraction of bed packing (-).

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

Online Calculator

Reynolds number using particle diameter as length scale (-).
Prandtl number of the fluid (-).
Void fraction of bed packing (-).