NU_KTA

This function evaluates the KTA packed-bed heat transfer correlation to estimate the Nusselt number from Reynolds number, Prandtl number, and bed void fraction. It is commonly used for pebble-bed and related packed-bed thermal calculations within the recommended validity ranges.

The KTA expression is:

Nu = 1.27\frac{Pr^{1/3}}{\epsilon^{1.18}}Re^{0.36} + 0.033\frac{Pr^{0.5}}{\epsilon^{1.07}}Re^{0.86}

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

Excel Usage

=NU_KTA(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_KTA(2000, 0.7, 0.4)

Expected output:

102.085

Example 2: Lower Reynolds number case

Inputs:

Re	Pr	voidage
400	1.1	0.36

Excel formula:

=NU_KTA(400, 1.1, 0.36)

Expected output:

55.6902

Example 3: Mid range Reynolds number

Inputs:

Re	Pr	voidage
12000	0.9	0.38

Excel formula:

=NU_KTA(12000, 0.9, 0.38)

Expected output:

396.986

Example 4: Higher void fraction case

Inputs:

Re	Pr	voidage
1500	0.8	0.42

Excel formula:

=NU_KTA(1500, 0.8, 0.42)

Expected output:

85.8885

Python Code

Show Code

from ht.conv_packed_bed import Nu_KTA as ht_Nu_KTA

def Nu_KTA(Re, Pr, voidage):
    """
    Calculate Nusselt number for a packed bed using the KTA 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_KTA(Re=Re, Pr=Pr, voidage=voidage)
    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 (-).

voidage *

Void fraction of bed packing (-).