The details of a double pipe heat exchanger are given as:

(a) cold fluid heat capacity rate \(C_{1}=1100 \mathrm{~W} /{ }^{\circ} \mathrm{C}\);

(b) Hot fluid heat capacity rate \(C_{2}=734 \mathrm{~W} /{ }^{\circ} \mathrm{C}\);

(c) overall heat transfer coefficient \(U=600 \mathrm{~W} / \mathrm{m}^{2 \circ} \mathrm{C}(d)\) heat exchanger area \(A=4 \mathrm{~m}^{2}\)

(e) cold fluid entry temperature \(T_{c i}=20^{\circ} \mathrm{C}(f)\) hot fluid entry temperature \(T_{h i}=80^{\circ} \mathrm{C}\). Set up the stiffness matrix and them solve for the outlet temperature and the effectiveness of the heat exchanger by using 1 element, 2 elements and 4 elements for the heat exchanger. Also determine the minimum number of elements required for converged solution (refer to Chapter 9).