Use the alternative conduction analysis of Section 3.2 to derive an expression relating the radial heat rate, \(q_{r}\), to the wall temperatures \(T_{s, 1}\) and \(T_{s, 2}\), for the hollow cylinder of Figure 3.7. Use your expression to calculate the heat transfer rate associated with a \(L=2 \mathrm{~m}\) long cylinder of inner and outer radii of \(r_{1}=50 \mathrm{~mm}\) and \(r_{2}=75 \mathrm{~mm}\), respectively. The thermal conductivity of the cylindrical wall is \(k=2.5 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\), and the inner and outer surface temperatures are \(T_{s, 1}=100^{\circ} \mathrm{C}\) and \(T_{s, 2}=67^{\circ} \mathrm{C}\), respectively.

Figure 3.7:-

Data From Section 3.2:-

Data From Section 3.1:-

Figure 3.1a:-

Transcribed Image Text:

Cold fluid Tz, h 111 Hot fluid Th 9r Tx1 T 12 T1 Tx1 T2 In(2/1) 2xkl FIGURE 3.7 Hollow cylinder with convective surface conditions.