FIN_EFF_KERN_KRAUS

This function computes circular-fin efficiency for a constant-thickness fin attached to a tube, using the Kern-Kraus formulation with modified Bessel functions. It quantifies how effectively the fin transfers heat relative to an ideal isothermal fin.

\eta_f = \frac{2r_o}{m(r_e^2-r_o^2)}\left[\frac{I_1(mr_e)K_1(mr_o)-K_1(mr_e)I_1(mr_o)}{I_0(mr_o)K_1(mr_e)+I_1(mr_e)K_0(mr_o)}\right],\quad m=\sqrt{\frac{2h}{k_{\text{fin}}t_{\text{fin}}}}

Efficiency decreases as convection strength increases relative to fin conduction capability.

Excel Usage

=FIN_EFF_KERN_KRAUS(Do, D_fin, t_fin, k_fin, h)

• Do (float, required): Bare tube outer diameter (m).
• D_fin (float, required): Fin outer diameter (m).
• t_fin (float, required): Fin thickness (m).
• k_fin (float, required): Fin thermal conductivity (W/m/K).
• h (float, required): Heat transfer coefficient (W/m^2/K).

Returns (float): Fin efficiency, or an error message if invalid.

Example 1: Baseline fin geometry

Inputs:

Do	D_fin	t_fin	k_fin	h
0.0254	0.05715	0.00038	200	58

Excel formula:

=FIN_EFF_KERN_KRAUS(0.0254, 0.05715, 0.00038, 200, 58)

Expected output:

0.841259

Example 2: Thicker fin with higher conductivity

Inputs:

Do	D_fin	t_fin	k_fin	h
0.03	0.07	0.0006	230	65

Excel formula:

=FIN_EFF_KERN_KRAUS(0.03, 0.07, 0.0006, 230, 65)

Expected output:

0.841518

Example 3: Smaller fin diameter

Inputs:

Do	D_fin	t_fin	k_fin	h
0.02	0.045	0.0004	180	50

Excel formula:

=FIN_EFF_KERN_KRAUS(0.02, 0.045, 0.0004, 180, 50)

Expected output:

0.902913

Example 4: Higher heat transfer coefficient

Inputs:

Do	D_fin	t_fin	k_fin	h
0.025	0.06	0.00035	205	90

Excel formula:

=FIN_EFF_KERN_KRAUS(0.025, 0.06, 0.00035, 205, 90)

Expected output:

0.724212

Python Code

Show Code

from ht.air_cooler import fin_efficiency_Kern_Kraus as ht_fin_efficiency_Kern_Kraus

def fin_eff_kern_kraus(Do, D_fin, t_fin, k_fin, h):
    """
    Compute circular fin efficiency for constant-thickness fins.

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

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

    Args:
        Do (float): Bare tube outer diameter (m).
        D_fin (float): Fin outer diameter (m).
        t_fin (float): Fin thickness (m).
        k_fin (float): Fin thermal conductivity (W/m/K).
        h (float): Heat transfer coefficient (W/m^2/K).

    Returns:
        float: Fin efficiency, or an error message if invalid.
    """
    try:
        return ht_fin_efficiency_Kern_Kraus(
            Do=Do,
            D_fin=D_fin,
            t_fin=t_fin,
            k_fin=k_fin,
            h=h,
        )
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Do *

Bare tube outer diameter (m).

D_fin *

Fin outer diameter (m).

t_fin *

Fin thickness (m).

k_fin *

Fin thermal conductivity (W/m/K).

h *

Heat transfer coefficient (W/m^2/K).