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eveS

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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).

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

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