Details

The axial temperature distributions for a fin of uniform cross section for an adiabatic tip and a tip with convection are:

,

,

,

for a rectangular fin:

,

,

for a pin fin:

,

,

where and are the base and ambient air temperatures, is fin length (m), is position down the fin (m), is the convection heat transfer coefficient, is the thermal conductivity of the material (W/(m K)), is a simplification term, is fin perimeter (m), is the fin cross-sectional area (), and are the width and height of the rectangular fin (m) and is the pin fin diameter (m).

The fin heat transfer rates for each tip condition are:

,

,

,

where is in W, and is a simplification term.

The thermal conductivities for the fin materials are:

,

,

.

Reference

[1] T. L. Bergman, A. S. Lavine, F. P. Incropera and D. P. DeWitt, Introduction to Heat Transfer, 6th ed., Hoboken: John Wiley and Sons, 2011 p. 161.