Derive the steady-state finite differencing equation for node 3 of the fin shown

Question

Derive the steady-state finite differencing equation for node 3 of the fin shown. Your numerical solution tells you that the temperature distribution in the fin is [50.00, 46.47, 43.23, 40.24, 37.45, 34.82, 32.33] where T1 = 50.00 degree C, T2 = 46.47 degree C, ... T7=32.33 degree C. If k=15W/m/K, T infinity=25 degree C, w = 1.0cm, and there is 1.0cm between nodes, what must the convection coefficient be? For the steady-state temperature distribution given, what is the rate of heat transfer from the wall provided by the fin?

Explanation / Answer

U'll need help of FEM to answer this question.. :/

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