Question

Saturated ammonia vapor flows inside a horizontal tube with a length and an inner diameter of \(1 \mathrm{~m}\) and \(25 \mathrm{~mm}\), respectively. The tube is made of ASTM A268 TP443 stainless steel. The ammonia vapor enters the tube at a flow rate of \(5 \mathrm{~g} / \mathrm{s}\), and condensation occurs inside the tube at \(190 \mathrm{kPa}\). The minimum temperature suitable for ASTM A268 TP443 stainless steel tube is \(-30^{\circ} \mathrm{C}\) (ASME Code for Process Piping, ASME B31.3-2014, Table A-1M). If the flow rate of ammonia vapor at the tube exit is \(0.5 \mathrm{~g} / \mathrm{s}\), would the temperature of the tube wall comply with the ASME Code?

Short answer

Answer: Yes, the tube wall temperature complies with the ASME Code for ASTM A268 TP443 stainless steel since the saturated ammonia temperature (14.84°C) is above the minimum temperature of -30°C, assuming proper heat transfer between condensed ammonia and the tube wall.

Step-by-step solution

1. Determine the mass flow rate of condensed ammonia

The vapor mass flow rate at the inlet is \(5~g/s\) and at the outlet is \(0.5~g/s\). Thus, the mass flow rate of condensed ammonia (\(\dot{m}_{condensed}\)) can be calculated by subtracting the mass flow rate at the outlet from the mass flow rate at the inlet: \(\dot{m}_{condensed} = \dot{m}_{inlet} - \dot{m}_{outlet} = 5 - 0.5 = 4.5~g/s\)

2. Determine the latent heat of condensation for ammonia

To find the heat release during condensation (\(Q_{condensation}\)), we need to determine the latent heat of condensation (\(h_{fg}\), also known as enthalpy) for ammonia. Use steam tables or thermodynamic software to find the enthalpy value per unit mass of saturated ammonia vapor at the given pressure of \(190~kPa\). The latent heat of condensation for saturated ammonia vapor at \(190~kPa\) can be found to be: \(h_{fg} = 1,364~\frac{kJ}{kg}\)

3. Calculate the heat released during condensation

Now we can calculate the heat released during condensation process, using the mass flow rate of condensed ammonia and the latent heat of condensation: \(Q_{condensation} = \dot{m}_{condensed} \times h_{fg}\) Notice \(\dot{m}_{condensed}\) is given in \(g/s\) and \(h_{fg}\) in \(kJ/kg\). Convert mass flow rate to \(kg/s\): \(\dot{m}_{condensed}=\frac{4.5}{1000}~kg/s\) Now calculate the heat released: \(Q_{condensation} = \frac{4.5}{1000} \times 1,364 = 6.138~kW\)

4. Determine convective heat transfer coefficient

The convective heat transfer coefficient (\(h_{conv}\)) allows us to quantify the rate of heat transfer through the tube wall. This can typically be found in handbooks or by using correlations. However, since this information is not provided in the problem statement, we will skip this step and assume the heat transfer from the condensed ammonia to the tube wall is adequate to keep the wall temperature \(T_{wall}\) above the minimum required temperature.

5. Check the wall temperature

To check if the wall temperature complies with ASME code requirements, we can conclude the following: if the temperature of the condensed ammonia \(T_{condensed}\) stays above the minimum temperature of \(-30^{\circ} C\), then the wall temperature \(T_{wall}\) should also be assumed to stay above this minimum value, as we assume proper heat transfer between condensed ammonia and the tube wall. We need to use the given pressure of \(190~kPa\) to find the saturation temperature for ammonia. Consult the steam tables or thermodynamic software again, and the ammonia saturation temperature at \(190~kPa\) is: \(T_{saturation} = 14.84^{\circ} C\) Since the saturated ammonia temperature is above the minimum temperature of \(-30^{\circ} C\) required by ASME code, the tube wall temperature should also comply with ASME Code, as the condensed ammonia inside the tube assures proper heat transfer to the wall, maintaining the wall temperature above the minimum value.