According to our class notes if the length of a fin goes to

According to our class notes, if the length of a fin goes to infinity the temperature distribution will be e^-mx, where m= Squareroot hp/k A_c. Prove this case by using the temperature distribution in a case that we know the temperature at the end of the fin.

Solution

For infinitely long fin, we can say that the temperature at the end of the fin will be equal to the ambient temperature.

or T(inf) = Tamb

The given temperature distribution is (T - Tamb) / (Tbase - Tamb) = e^(-mx)

Putting x = infinity we get, right hand side = 0

So, T - Tamb = 0

or T = Tamb and this proves our case.