MCEN90015 Assignmnet 3: Thermodynamics - Sem 1 2025

MCEN90015 PROBLEM 1 Convection Heat Transfer Analysis (15 pts) 

In the convection heat transfer workshop, the ambient air at 15??C and 1 atm flows in a pipe of 1 cm inner diameter and uniformly heated by induction heating. The air temperature and the inner wall temperature are measured at various locations along the pipe. Both laminar and turbulent conditions are measured.

MCEN90015 Convection in laminar flow

1. Determine the convection heat transfer coefficient, hm , using the air temperature and the wall temperature measured at 1 m and 1.5 m. Report Reynolds number using gas properties at the average flow temperature. Assume uniform wall heat flux over 1-1.5 m. (2 pts) 
2. Calculate the convection heat transfer coefficient, hc , using a suitable equation from the lecture. (1 pt) 
3. Comparehm and hc and discuss whether the theory of internal convection works at the laminar condition. (2 pts) Convection in turbulent flow 
4. Determine the convection heat transfer coefficient, hm , using the air temperature and the wall temperature measured at 1 m and 1.5 m. Report Reynolds number using gas properties at the average flow temperature. Assume uniform wall heat flux over 1-1.5 m. (2 pts) 
5. Calculate the convection heat transfer coefficient, hc , using a suitable equation from the lecture. (1 pt) 
6. Compare and hc and discuss whether the theory of internal convection works at the turbulent condition. (2 pts) Temperature distribution along the flow 
7. Plot the temperature of air and wall along the flow for the laminar condition with 15 L/min, and for the turbulent condition with 120 L/min. Discuss the temperature distribution of each case and compare the two cases. (3 pts)
8. Discuss whether the pipe is well insulated. (2 pts)

MCEN90015 PROBLEM 2 (15 pts)

The Thermodynamics Laboratory uses a 3-stage heat exchanger to cool hydrogen for cryogenic release experiment. The first stage and third stage use liquid nitrogen and liquid helium, respectively, where hydrogen coil is immersed in the liquid baths at 77 K and 4 K. The second stage is a thin-wall, counter-flow heat exchanger where hydrogen in the tube is cooled by boil-off helium in the annulus. Hydrogen is supplied at 25??C. The temperature after Stage 1, 2, and 3 is 80 K, 40 K, and 27 K, respectively. The cooled hydrogen is sent to a nozzle through a transfer hose, during which the gas is warmed to 30 K.

The hydrogen flow is at 0.43 g/s and 3 bar. The diameter of the hydrogen tube is 1.1 cm throughout the three stages. The gas properties at different temperature ranges are shown below. Ignore the thickness of all the walls involved.

1. Determine the consumption rate of liquid nitrogen and liquid helium. The enthalpy of vaporization is 200 kJ/kg for LN2 at 77 K and 23.3 kJ/kg for LHe at 4 K. (2 pts)
2. The second stage is 6 m long with a convection coefficient in the annulus as 20 W/(m2-K). Conduct heat exchanger analysis and determine the inlet and outlet temperature of the boil-off helium. (7 pts)
3. The transfer hose is a vacuum-jacketed double tube of 2.5 m length. Hydrogen flows in the inner tube which has a diameter of 5 cm and is wrapped with multi-layer insultation (MLI) material to reduce radiation heat transfer. Consider the exit plane of the transfer hose is well insulated. Estimate the emissivity of the MLI. Assume 1) the outer wall of the transfer hose is at a uniform temperature of 298 K, 2) the hydrogen flow is fully developed across the transfer hose length, and 3) the MLI surface is gray. (6 pts)