A uniform bar is modeled by two identical two-node elements, as shown. Node 1
is maintained at temperature \(T_{1}=0^{\circ} \mathrm{C}\). The bar is
surrounded by fluid of temperature \(T_{\mathrm{f} \mathrm{f}}=200^{\circ}
\mathrm{C}\), which transfers heat across its cylindrical surface of area S. In
units listed in Section 12.1, data are: \(A=300\left(10^{-6}\right), h=600,
k=200\), and the surface area of the entire bar is \(S=0.020\).
(a) Formulate element matrices.
(b) Assemble element matrices, impose \(T_{1}=0^{\circ} \mathrm{C}\), and solve
for \(T_{2}\) and \(T_{3}\).
(c) Repeat part (b), but alter the FE model so that the left element is half
as long as the right element. The overall length remains \(0.300 \mathrm{~m}\).
(d) What conclusion might be drawn by comparing the results of parts (b) and
(c)?
