Posted: January 9th, 2022

(a) A fin with a length of L has a uniform cross-sectional area A and thermal conductivity k, as shown in Figure 12.23. A linearly distributed heat supply is applied on the fin. The temperature at the left end is fixed at T_{0}, and the heat flux at the right

end is q_{0}. The governing equation for the fin is given by

Develop the finite element equation for a two-node element.

(b) If L = 8 m, A = 1 m^{2}, k = 5 J/◦C ms, Q = 100 J/sm, T_{0} = 0 and q_{0} = 15 J/m^{2}s, determine the temperatures at the nodes by using two linear elements.

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