NU_YAMAGATA

This function computes the Nusselt number for turbulent supercritical pipe flow using the Yamagata correlation. It uses Reynolds and Prandtl numbers and can apply pseudocritical-property corrections based on Prandtl number at the pseudocritical state, heat-capacity ratio, and the bulk/wall temperature window.

Nu = C\,Re^{m}Pr^{n}\,F(Pr_{pc},Cp_{avg}/Cp_b,T_b,T_w,T_{pc})

Excel Usage

=NU_YAMAGATA(Re, Pr, Pr_pc, Cp_avg, Cp_b, T_b, T_w, T_pc)

Re (float, required): Reynolds number with bulk fluid properties (-).
Pr (float, required): Prandtl number with bulk fluid properties (-).
Pr_pc (float, optional, default: null): Prandtl number at the pseudocritical temperature (-).
Cp_avg (float, optional, default: null): Average heat capacity between wall and bulk temperatures (J/kg/K).
Cp_b (float, optional, default: null): Heat capacity at bulk temperature (J/kg/K).
T_b (float, optional, default: null): Bulk temperature (K).
T_w (float, optional, default: null): Wall temperature (K).
T_pc (float, optional, default: null): Pseudocritical temperature at pressure (K).

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

Example 1: Yamagata correlation example

Inputs:

Re	Pr	Pr_pc	Cp_avg	Cp_b	T_b	T_w	T_pc
100000	1.2	1.5	2080.845	2048.621	650	700	600

Excel formula:

=NU_YAMAGATA(100000, 1.2, 1.5, 2080.845, 2048.621, 650, 700, 600)

Expected output:

292.347

Example 2: Yamagata correlation bulk properties only

Inputs:

Re	Pr
80000	1

Excel formula:

=NU_YAMAGATA(80000, 1)

Expected output:

203.004

Example 3: Yamagata correlation mid Reynolds number

Inputs:

Re	Pr	Pr_pc	Cp_avg	Cp_b	T_b	T_w	T_pc
200000	0.9	1.2	2200	2100	620	680	640

Excel formula:

=NU_YAMAGATA(200000, 0.9, 1.2, 2200, 2100, 620, 680, 640)

Expected output:

270.924

Example 4: Yamagata correlation higher Reynolds number

Inputs:

Re	Pr	Pr_pc	Cp_avg	Cp_b	T_b	T_w	T_pc
450000	1.4	1.3	2400	2200	700	760	680

Excel formula:

=NU_YAMAGATA(450000, 1.4, 1.3, 2400, 2200, 700, 760, 680)

Expected output:

1374.86

Python Code

Show Code

from ht.conv_supercritical import Nu_Yamagata as ht_Nu_Yamagata

def Nu_Yamagata(Re, Pr, Pr_pc=None, Cp_avg=None, Cp_b=None, T_b=None, T_w=None, T_pc=None):
    """
    Calculate Nusselt number for supercritical flow using the Yamagata 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 fluid properties (-).
        Pr_pc (float, optional): Prandtl number at the pseudocritical temperature (-). Default is None.
        Cp_avg (float, optional): Average heat capacity between wall and bulk temperatures (J/kg/K). Default is None.
        Cp_b (float, optional): Heat capacity at bulk temperature (J/kg/K). Default is None.
        T_b (float, optional): Bulk temperature (K). Default is None.
        T_w (float, optional): Wall temperature (K). Default is None.
        T_pc (float, optional): Pseudocritical temperature at pressure (K). Default is None.

    Returns:
        float: Nusselt number with bulk fluid properties (-).
    """
    try:
        return ht_Nu_Yamagata(
            Re=Re,
            Pr=Pr,
            Pr_pc=Pr_pc,
            Cp_avg=Cp_avg,
            Cp_b=Cp_b,
            T_b=T_b,
            T_w=T_w,
            T_pc=T_pc,
        )
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Re *

Reynolds number with bulk fluid properties (-).

Pr *

Prandtl number with bulk fluid properties (-).

Pr_pc

Prandtl number at the pseudocritical temperature (-).

Cp_avg

Average heat capacity between wall and bulk temperatures (J/kg/K).

Cp_b

Heat capacity at bulk temperature (J/kg/K).

T_b

Bulk temperature (K).

T_w

Wall temperature (K).

T_pc

Pseudocritical temperature at pressure (K).