Consider the water pipe treated in Example 7.7.4. Suppose

Chapter , Problem 7.51

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Consider the water pipe treated in Example 7.7.4. Suppose now that the water is not flowing. The water is initially at \(120^{\circ} \mathrm{F}\). The copper pipe is 6 ft long, with inner and outer radii of 1/4 in. and 3/8 in. The temperature of the surrounding air is constant at \(70^{\circ} \mathrm{F}\). Neglect heat loss from the ends of the pipe, and use the following values. For copper, \(k=50 \ \mathrm{lb} / \mathrm{sec}-{ }^{\circ} \mathrm{F}\). The convection coefficient at the inner surface between the water and the copper is now different because the water is standing. Use \(h_{i}=6 \ \mathrm{lb} / \mathrm{sec}-\mathrm{ft}-{ }^{\circ} \mathrm{F}\). The convection coefficient at the outer surface between the air and the copper is \(h_{o}=1.1 \ \mathrm{lb} / \mathrm{sec}-\mathrm{ft}^{\circ} \mathrm{F}\). Develop and solve a dynamic model of the water temperature T (t) as a function of time.