Chapter 8, Problem 8.65P

Consider a thin-walled, metallic tube of length $L=\text{ 1 m}$ and inside diameter $D_i=3 \text{mm}$ . Water enters the tube at $m=0.015\text{kg}/\text{s}$ and $T_{m,i} =\text{ 97}°\text{C}$ .

(a) What is the outlet temperature of the water if the tube surface temperature is maintained at 27°C?

(b) 1f a 0.5-mm-thick layer of insulation of $\text{k }=0.0\text{5 W}/\text{m}\cdot \text{K}$ is applied to the tube and its outer surface is maintained at $\text{27}°\text{C}$ , what is the outlet temperature of the water?

(c) If the outer surface of the insulation is no longer maintained al $\text{27}°\text{C}$ hut is allowed to exchange heat by free convection with ambient air at $\text{27}°\text{C}$ . what is the outlet temperature of the water? The free convection heat transfer coefficient is $5{\text{W/m}}^2\cdot \text{K}$ .