H_ESDU_HIGH_FIN

This function estimates air-side heat-transfer coefficient for high-fin tube banks using the ESDU formulation. The method computes a Nusselt correlation with Reynolds and Prandtl dependence plus correction factors for wall-property effects and tube-row count.

Nu = 0.242\,Re^{0.658}\left(\frac{\text{bare length}}{\text{fin height}}\right)^{0.297}\left(\frac{p_1}{p_2}\right)^{-0.091}Pr^{1/3}F_1F_2

The returned coefficient is converted to a bare-tube reference basis using fin efficiency and area-ratio terms.

Excel Usage

=H_ESDU_HIGH_FIN(m, A, A_min, A_increase, A_fin, A_tube_showing, tube_diameter, fin_diameter, fin_thickness, bare_length, pitch_parallel, pitch_normal, tube_rows, rho, Cp, mu, k, k_fin, Pr_wall)

• m (float, required): Mass flow rate across the tube bank (kg/s).
• A (float, required): Total exposed surface area (m^2).
• A_min (float, required): Minimum flow area (m^2).
• A_increase (float, required): Surface area ratio relative to bare tube (-).
• A_fin (float, required): Total fin surface area (m^2).
• A_tube_showing (float, required): Exposed bare tube area (m^2).
• tube_diameter (float, required): Bare tube diameter (m).
• fin_diameter (float, required): Finned tube outer diameter (m).
• fin_thickness (float, required): Fin thickness (m).
• bare_length (float, required): Bare tube length between fins (m).
• pitch_parallel (float, required): Tube pitch parallel to flow (m).
• pitch_normal (float, required): Tube pitch normal to flow (m).
• tube_rows (int, required): Number of tube rows (-).
• rho (float, required): Air density (kg/m^3).
• Cp (float, required): Air heat capacity (J/kg/K).
• mu (float, required): Air viscosity (Pa*s).
• k (float, required): Air thermal conductivity (W/m/K).
• k_fin (float, required): Fin thermal conductivity (W/m/K).
• Pr_wall (float, optional, default: null): Prandtl number at wall temperature (-).

Returns (float): Heat transfer coefficient on a bare-tube basis (W/m^2/K), or an error message if invalid.

Example 1: Baseline high-fin bundle

Inputs:

m	A	A_min	A_increase	A_fin	A_tube_showing	tube_diameter	fin_diameter	fin_thickness	bare_length	pitch_parallel	pitch_normal	tube_rows	rho	Cp	mu	k	k_fin
1.2	40	4	12	35	5	0.02	0.05	0.001	0.003	0.05	0.06	4	1.2	1005	0.000018	0.026	200

Excel formula:

=H_ESDU_HIGH_FIN(1.2, 40, 4, 12, 35, 5, 0.02, 0.05, 0.001, 0.003, 0.05, 0.06, 4, 1.2, 1005, 0.000018, 0.026, 200)

Expected output:

92.5103

Example 2: Higher flow rate and larger pitch

Inputs:

m	A	A_min	A_increase	A_fin	A_tube_showing	tube_diameter	fin_diameter	fin_thickness	bare_length	pitch_parallel	pitch_normal	tube_rows	rho	Cp	mu	k	k_fin
2	55	5	10	48	7	0.025	0.06	0.0012	0.0035	0.06	0.07	6	1.1	1010	0.000019	0.027	210

Excel formula:

=H_ESDU_HIGH_FIN(2, 55, 5, 10, 48, 7, 0.025, 0.06, 0.0012, 0.0035, 0.06, 0.07, 6, 1.1, 1010, 0.000019, 0.027, 210)

Expected output:

87.2028

Example 3: Compact geometry with lower flow

Inputs:

m	A	A_min	A_increase	A_fin	A_tube_showing	tube_diameter	fin_diameter	fin_thickness	bare_length	pitch_parallel	pitch_normal	tube_rows	rho	Cp	mu	k	k_fin
0.9	32	3.5	13	28	4	0.016	0.045	0.0009	0.0025	0.045	0.055	3	1.25	1000	0.000017	0.025	180

Excel formula:

=H_ESDU_HIGH_FIN(0.9, 32, 3.5, 13, 28, 4, 0.016, 0.045, 0.0009, 0.0025, 0.045, 0.055, 3, 1.25, 1000, 0.000017, 0.025, 180)

Expected output:

85.0774

Example 4: Wall Prandtl correction applied

Inputs:

m	A	A_min	A_increase	A_fin	A_tube_showing	tube_diameter	fin_diameter	fin_thickness	bare_length	pitch_parallel	pitch_normal	tube_rows	rho	Cp	mu	k	k_fin	Pr_wall
1.5	45	4.5	11	38	7	0.018	0.055	0.0011	0.0032	0.052	0.062	5	1.18	1008	0.0000185	0.0265	240	0.72

Excel formula:

=H_ESDU_HIGH_FIN(1.5, 45, 4.5, 11, 38, 7, 0.018, 0.055, 0.0011, 0.0032, 0.052, 0.062, 5, 1.18, 1008, 0.0000185, 0.0265, 240, 0.72)

Expected output:

89.9773

Python Code

Show Code

from ht.air_cooler import h_ESDU_high_fin as ht_h_ESDU_high_fin

def h_ESDU_high_fin(m, A, A_min, A_increase, A_fin, A_tube_showing, tube_diameter, fin_diameter, fin_thickness, bare_length, pitch_parallel, pitch_normal, tube_rows, rho, Cp, mu, k, k_fin, Pr_wall=None):
    """
    Compute air-side heat transfer coefficient for high-fin tube banks.

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

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

    Args:
        m (float): Mass flow rate across the tube bank (kg/s).
        A (float): Total exposed surface area (m^2).
        A_min (float): Minimum flow area (m^2).
        A_increase (float): Surface area ratio relative to bare tube (-).
        A_fin (float): Total fin surface area (m^2).
        A_tube_showing (float): Exposed bare tube area (m^2).
        tube_diameter (float): Bare tube diameter (m).
        fin_diameter (float): Finned tube outer diameter (m).
        fin_thickness (float): Fin thickness (m).
        bare_length (float): Bare tube length between fins (m).
        pitch_parallel (float): Tube pitch parallel to flow (m).
        pitch_normal (float): Tube pitch normal to flow (m).
        tube_rows (int): Number of tube rows (-).
        rho (float): Air density (kg/m^3).
        Cp (float): Air heat capacity (J/kg/K).
        mu (float): Air viscosity (Pa*s).
        k (float): Air thermal conductivity (W/m/K).
        k_fin (float): Fin thermal conductivity (W/m/K).
        Pr_wall (float, optional): Prandtl number at wall temperature (-). Default is None.

    Returns:
        float: Heat transfer coefficient on a bare-tube basis (W/m^2/K), or an error message if invalid.
    """
    try:
        return ht_h_ESDU_high_fin(
            m=m,
            A=A,
            A_min=A_min,
            A_increase=A_increase,
            A_fin=A_fin,
            A_tube_showing=A_tube_showing,
            tube_diameter=tube_diameter,
            fin_diameter=fin_diameter,
            fin_thickness=fin_thickness,
            bare_length=bare_length,
            pitch_parallel=pitch_parallel,
            pitch_normal=pitch_normal,
            tube_rows=tube_rows,
            rho=rho,
            Cp=Cp,
            mu=mu,
            k=k,
            k_fin=k_fin,
            Pr_wall=Pr_wall,
        )
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

m *

Mass flow rate across the tube bank (kg/s).

A *

Total exposed surface area (m^2).

A_min *

Minimum flow area (m^2).

A_increase *

Surface area ratio relative to bare tube (-).

A_fin *

Total fin surface area (m^2).

A_tube_showing *

Exposed bare tube area (m^2).

tube_diameter *

Bare tube diameter (m).

fin_diameter *

Finned tube outer diameter (m).

fin_thickness *

Fin thickness (m).

bare_length *

Bare tube length between fins (m).

pitch_parallel *

Tube pitch parallel to flow (m).

pitch_normal *

Tube pitch normal to flow (m).

tube_rows *

Number of tube rows (-).

rho *

Air density (kg/m^3).

Cp *

Air heat capacity (J/kg/K).

mu *

Air viscosity (Pa*s).

k *

Air thermal conductivity (W/m/K).

k_fin *

Fin thermal conductivity (W/m/K).

Pr_wall

Prandtl number at wall temperature (-).