FIN_EFFICIENCY_KK

This function computes the efficiency of a circular constant-thickness fin attached to a tube using the Kern-Kraus formulation. Fin efficiency represents the ratio of actual heat transfer from the fin to the ideal heat transfer if the entire fin were at base temperature.

The model is based on modified Bessel-function solutions for radial conduction in annular fins, with the key conduction-convection parameter:

m = \sqrt{\frac{2h}{k_{fin} t_{fin}}}

Efficiency decreases as convective resistance drops relative to conduction resistance, and increases with higher fin conductivity or thickness.

Excel Usage

=FIN_EFFICIENCY_KK(Do, D_fin, t_fin, k_fin, h)
  • Do (float, required): Outer diameter of the bare tube (m).
  • D_fin (float, required): Outer diameter of the fin (m).
  • t_fin (float, required): Fin thickness (m).
  • k_fin (float, required): Thermal conductivity of the fin (W/m/K).
  • h (float, required): Heat transfer coefficient at the fin surface (W/m^2/K).

Returns (float): Fin efficiency for a circular fin on a tube (-).

Example 1: Reference fin efficiency

Inputs:

Do D_fin t_fin k_fin h
0.0254 0.05715 0.00038 200 58

Excel formula:

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

Expected output:

0.841259

Example 2: Thinner fin increases conduction resistance

Inputs:

Do D_fin t_fin k_fin h
0.02 0.05 0.0002 180 45

Excel formula:

=FIN_EFFICIENCY_KK(0.02, 0.05, 0.0002, 180, 45)

Expected output:

0.776471

Example 3: Higher fin conductivity

Inputs:

Do D_fin t_fin k_fin h
0.03 0.07 0.0005 250 60

Excel formula:

=FIN_EFFICIENCY_KK(0.03, 0.07, 0.0005, 250, 60)

Expected output:

0.839039

Example 4: Higher heat transfer coefficient

Inputs:

Do D_fin t_fin k_fin h
0.03 0.07 0.0005 180 120

Excel formula:

=FIN_EFFICIENCY_KK(0.03, 0.07, 0.0005, 180, 120)

Expected output:

0.661053

Python Code

Show Code 
from ht.core import fin_efficiency_Kern_Kraus as ht_fin_efficiency_Kern_Kraus

def fin_efficiency_kk(Do, D_fin, t_fin, k_fin, h):
    """
    Compute circular fin efficiency using the Kern-Kraus correlation.

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

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

    Args:
        Do (float): Outer diameter of the bare tube (m).
        D_fin (float): Outer diameter of the fin (m).
        t_fin (float): Fin thickness (m).
        k_fin (float): Thermal conductivity of the fin (W/m/K).
        h (float): Heat transfer coefficient at the fin surface (W/m^2/K).

    Returns:
        float: Fin efficiency for a circular fin on a tube (-).
    """
    try:
        return ht_fin_efficiency_Kern_Kraus(Do, D_fin, t_fin, k_fin, h)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Outer diameter of the bare tube (m).
Outer diameter of the fin (m).
Fin thickness (m).
Thermal conductivity of the fin (W/m/K).
Heat transfer coefficient at the fin surface (W/m^2/K).