A \(50 \mathrm{~mm}\) diameter, thin-walled tin tube is shown in the figure below. The tube is covered with a \(20 \mathrm{~mm}\) thick layer of insulation \(\left(k_{i}=0.05 \mathrm{~W} / \mathrm{m} \mathrm{K}\right)\) as shown in Figure P13.23. The tube is carrying a saturated liquid that is at atmospheric pressure and \(10^{\circ} \mathrm{C}\). The flow rate of the stream is \(50 \mathrm{~kg} / \mathrm{hr}\). Along the tube, the surface is heated and maintained at a constant temperature of \(T_{s}=150^{\circ} \mathrm{C}\) and provides an outside heat transfer coefficient of \(h_{o}=15\) \(\mathrm{W} / \mathrm{m}^{2} \mathrm{~K}\). At what point of the tube will the mean temperature of the liquid reach \(100^{\circ} \mathrm{C}\) ?

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h = 15 W/mK T=150C k = 0.05 W/mK D = 0.02 m T = 10C D = 0.05 m P = 1 atm m = 50 kg/hr FIGURE P13.23