I am analyzing the lengthwise temperature distribution in a cooling fin (length: 30mm, width: 10mm, the tip is assumed to be adiabatic, Biot number is smaller than 0.1).(adsbygoogle = window.adsbygoogle || []).push({});

When I try to calculate the dimensionless temperature distribution (see calculation below), I obtain a curve which has a minimum at about 2/3 of the fin length and increases again after that (see attachment).

I don't understand why the temperature should increase again towards the tip of the fin. Using Ansys to model the fin I obtained the other curve in the graph, which shows decreasing temperatures towards the tip of the fin (and makes more sense to me).

I don't know whether I am making a mistake in my calculations, or whether there is a simple explanation.

Any advice would be appreciated!

calculation:

distribution "theta" (x) = cosh(m*(1-x/L)) / cosh(m) ,

where m= sqrt [ ( P*L*h) / (A*k) ]

L=length

P=perimeter

A=area

h=heat transfer coefficient

k=thermal conductivity

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Temperature distrubution in a cooling fin (result interpretation)

**Physics Forums | Science Articles, Homework Help, Discussion**