NU_PLATE_MARTIN

This function calculates the Nusselt number for single-phase flow in chevron-style plate heat exchangers using the Martin correlation. It combines Reynolds and Prandtl effects with a friction-factor-based term and supports either the 1999 or VDI friction variant.

The Martin heat transfer form is:

Nu = 0.122\,Pr^{1/3}\left(f_d Re^2\sin(2\phi)\right)^{0.374}

where f_d is the Darcy friction factor from the selected variant and \phi is the chevron angle. This is used for compact exchanger thermal performance estimation.

Excel Usage

=NU_PLATE_MARTIN(Re, Pr, chevron_angle, martin_variant)
  • Re (float, required): Reynolds number with respect to hydraulic diameter of the channels (-).
  • Pr (float, required): Prandtl number calculated with bulk fluid properties (-).
  • chevron_angle (float, required): Plate chevron angle relative to flow direction (degrees).
  • martin_variant (str, optional, default: “1999”): Friction factor correlation variant (-).

Returns (float): Nusselt number with respect to hydraulic diameter, or error message if invalid.

Example 1: Example with default variant

Inputs:

Re Pr chevron_angle
2000 0.7 45

Excel formula:

=NU_PLATE_MARTIN(2000, 0.7, 45)

Expected output:

30.4276

Example 2: VDI variant selection

Inputs:

Re Pr chevron_angle martin_variant
2000 0.7 45 VDI

Excel formula:

=NU_PLATE_MARTIN(2000, 0.7, 45, "VDI")

Expected output:

30.4187

Example 3: Lower Reynolds number case

Inputs:

Re Pr chevron_angle
500 2.5 30

Excel formula:

=NU_PLATE_MARTIN(500, 2.5, 30)

Expected output:

13.1012

Example 4: Higher Reynolds number with VDI variant

Inputs:

Re Pr chevron_angle martin_variant
8000 0.7 60 VDI

Excel formula:

=NU_PLATE_MARTIN(8000, 0.7, 60, "VDI")

Expected output:

105.462

Python Code

Show Code 
from ht.conv_plate import Nu_plate_Martin as ht_Nu_plate_Martin

def Nu_plate_Martin(Re, Pr, chevron_angle, martin_variant='1999'):
    """
    Calculate Nusselt number for chevron plate exchangers using the Martin correlation.

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

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

    Args:
        Re (float): Reynolds number with respect to hydraulic diameter of the channels (-).
        Pr (float): Prandtl number calculated with bulk fluid properties (-).
        chevron_angle (float): Plate chevron angle relative to flow direction (degrees).
        martin_variant (str, optional): Friction factor correlation variant (-). Valid options: Martin 1999, VDI. Default is '1999'.

    Returns:
        float: Nusselt number with respect to hydraulic diameter, or error message if invalid.
    """
    try:
        result = ht_Nu_plate_Martin(
            Re=Re,
            Pr=Pr,
            chevron_angle=chevron_angle,
            variant=martin_variant,
        )
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number with respect to hydraulic diameter of the channels (-).
Prandtl number calculated with bulk fluid properties (-).
Plate chevron angle relative to flow direction (degrees).
Friction factor correlation variant (-).