MORIMOTO_HOTTA

This function computes the internal-flow Nusselt number for spiral heat exchangers using the Morimoto–Hotta correlation. It relates convection performance to Reynolds and Prandtl numbers and the ratio of hydraulic diameter to spiral radius.

Excel Usage

=MORIMOTO_HOTTA(Re, Pr, Dh, Rm)

Re (float, required): Reynolds number (-).
Pr (float, required): Prandtl number (-).
Dh (float, required): Average hydraulic diameter (m).
Rm (float, required): Average spiral radius (m).

Returns (float): Nusselt number with respect to hydraulic diameter (-).

Example 1: Spiral exchanger example

Inputs:

Re	Pr	Dh	Rm
100000	5.7	0.05	0.5

Excel formula:

=MORIMOTO_HOTTA(100000, 5.7, 0.05, 0.5)

Expected output:

634.488

Example 2: Moderate Reynolds number

Inputs:

Re	Pr	Dh	Rm
50000	2	0.03	0.4

Excel formula:

=MORIMOTO_HOTTA(50000, 2, 0.03, 0.4)

Expected output:

249.663

Example 3: Higher Reynolds number case

Inputs:

Re	Pr	Dh	Rm
200000	1.1	0.08	0.6

Excel formula:

=MORIMOTO_HOTTA(200000, 1.1, 0.08, 0.6)

Expected output:

798.615

Example 4: Compact spiral geometry

Inputs:

Re	Pr	Dh	Rm
80000	0.8	0.04	0.35

Excel formula:

=MORIMOTO_HOTTA(80000, 0.8, 0.04, 0.35)

Expected output:

329.11

Python Code

Show Code

from ht.conv_internal import Morimoto_Hotta as ht_Morimoto_Hotta

def morimoto_hotta(Re, Pr, Dh, Rm):
    """
    Calculate the Nusselt number for flow in a spiral heat exchanger.

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

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).
        Dh (float): Average hydraulic diameter (m).
        Rm (float): Average spiral radius (m).

    Returns:
        float: Nusselt number with respect to hydraulic diameter (-).
    """
    try:
        return ht_Morimoto_Hotta(Re=Re, Pr=Pr, Dh=Dh, Rm=Rm)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Re *

Reynolds number (-).

Pr *

Prandtl number (-).

Dh *

Average hydraulic diameter (m).

Rm *

Average spiral radius (m).