NU_BISHOP

This function estimates the internal convective heat transfer Nusselt number for turbulent upward flow at supercritical pressure using the Bishop correlation. It uses Reynolds and Prandtl numbers, and can optionally apply density-ratio and thermal-entry corrections when wall and bulk densities and geometry inputs are provided.

Nu = C\,Re^{m}Pr^{n}\,\Phi_{\rho}\,\Phi_{entry}

Excel Usage

=NU_BISHOP(Re, Pr, rho_w, rho_b, D, x)

Re (float, required): Reynolds number with bulk fluid properties (-).
Pr (float, required): Prandtl number with bulk properties and averaged heat capacity (-).
rho_w (float, optional, default: null): Density at wall temperature (kg/m^3).
rho_b (float, optional, default: null): Density at bulk temperature (kg/m^3).
D (float, optional, default: null): Tube diameter (m).
x (float, optional, default: null): Axial distance along the tube (m).

Returns (float): Nusselt number with wall fluid properties (-).

Example 1: Bishop correlation example

Inputs:

Re	Pr	rho_w	rho_b	D	x
100000	1.2	330	290	0.01	1.2

Excel formula:

=NU_BISHOP(100000, 1.2, 330, 290, 0.01, 1.2)

Expected output:

265.362

Example 2: Bishop correlation bulk properties only

Inputs:

Re	Pr
80000	0.9

Excel formula:

=NU_BISHOP(80000, 0.9)

Expected output:

166.506

Example 3: Bishop correlation with density ratio

Inputs:

Re	Pr	rho_w	rho_b
150000	1.4	350	300

Excel formula:

=NU_BISHOP(150000, 1.4, 350, 300)

Expected output:

419.337

Example 4: Bishop correlation with entry correction

Inputs:

Re	Pr	rho_w	rho_b	D	x
250000	1.1	400	320	0.02	2

Excel formula:

=NU_BISHOP(250000, 1.1, 400, 320, 0.02, 2)

Expected output:

597.428

Python Code

Show Code

from ht.conv_supercritical import Nu_Bishop as ht_Nu_Bishop

def Nu_Bishop(Re, Pr, rho_w=None, rho_b=None, D=None, x=None):
    """
    Calculate Nusselt number for supercritical pipe flow using the Bishop correlation.

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

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

    Args:
        Re (float): Reynolds number with bulk fluid properties (-).
        Pr (float): Prandtl number with bulk properties and averaged heat capacity (-).
        rho_w (float, optional): Density at wall temperature (kg/m^3). Default is None.
        rho_b (float, optional): Density at bulk temperature (kg/m^3). Default is None.
        D (float, optional): Tube diameter (m). Default is None.
        x (float, optional): Axial distance along the tube (m). Default is None.

    Returns:
        float: Nusselt number with wall fluid properties (-).
    """
    try:
        return ht_Nu_Bishop(Re=Re, Pr=Pr, rho_w=rho_w, rho_b=rho_b, D=D, x=x)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Re *

Reynolds number with bulk fluid properties (-).

Pr *

Prandtl number with bulk properties and averaged heat capacity (-).

rho_w

Density at wall temperature (kg/m^3).

rho_b

Density at bulk temperature (kg/m^3).

Tube diameter (m).

Axial distance along the tube (m).