Calculation of Fin Temperature for Adiabatic Tip and Infinite Fins
The following CDF tool calculates the normalized fin temperature ($$\theta(x)/\theta_{base}$$) for two cases:
- Case 1: Adiabatic fin tip
- Case 2: Infinitely long fin
In both cases, the cross sectional area of the fin is assumed to be constant.
We use the conventional definition of the fin eigenvalue $$m$$:
$$m = \sqrt{\frac{hP}{kA_c}}$$
where:
- h is the convective heat transfer coefficient
- P is the fin perimeter
- k is the fin’s thermal conductivity
- $$A_c$$ is the fin’s cross-sectional area
Graphical CDF Tool
The CDF tool follows. Note that the distance from the fin base is normalized by the fin length (i.e., x in the formulas below represents the dimensional distance from the base divided by the fin length L).
