Question

Water flows in a horizontal chlorinated polyvinyl chloride (CPVC) pipe with an inner and outer diameter of \(15 \mathrm{~mm}\) and \(20 \mathrm{~mm}\), respectively. The thermal conductivity of the CPVC pipe is $0.136 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}$. The convection heat transfer coefficient at the inner surface of the pipe with the water flow is $50 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}$. A section of the pipe is exposed to hot, quiescent air at \(107^{\circ} \mathrm{C}\), and the length of the pipe section in the hot air is \(1 \mathrm{~m}\). The recommended maximum temperature for CPVC pipe by the ASME Code for Process Piping is \(93^{\circ} \mathrm{C}\) (ASME B31.3-2014, Table B-1). Determine the maximum temperature that the water flowing inside the pipe can be without causing the temperature of the CPVC pipe to go above \(93^{\circ} \mathrm{C}\).

Short answer

After calculating the values, we get: \(Q_{air \to pipe} = 50 \mathrm{~W/m^2\cdot K} \cdot \pi \cdot (20\cdot10^{-3} \mathrm{~m}) \cdot 1\mathrm{~m} \cdot (14^{\circ} \mathrm{C})\) \(Q_{air \to pipe} \approx 43.98 \mathrm{~W}\)

Step-by-step solution

Calculate the heat transfer rate across the pipe wall

First, let's determine the heat transfer rate from the hot air to the outer surface of the pipe using the convection heat transfer formula: \(Q_{air \to pipe} = h_{a} \cdot A_{a} \cdot (T_{a} - T_{pipe})\) Where, \(Q_{air \to pipe}\) = heat transfer from hot air to pipe (W), \(h_{a}\) = convection heat transfer coefficient between hot air and outer surface of the pipe (W/m²K), \(A_{a}\) = outer surface area of the pipe (m²), \(T_{a}\) = hot air temperature (\(107^{\circ}C\)), \(T_{pipe}\) = pipe outer surface temperature (\(93^{\circ}C\)). We have: \(A_{a} = \pi \cdot (20\cdot10^{-3} \mathrm{~m}) \cdot 1\mathrm{~m}\) Plugging in the values, we get: \(Q_{air \to pipe} = 50 \mathrm{~W/m^2\cdot K} \cdot \pi \cdot (20\cdot10^{-3} \mathrm{~m}) \cdot 1\mathrm{~m} \cdot (107^{\circ} \mathrm{C} - 93^{\circ} \mathrm{C})\) Calculate the value of \(Q_{air \to pipe}\).