Discuss how to improve fin's effectiveness and fin's efficiency, and give qualitative analysis of feasibility of different ways in engineering practice and relevant examples. Illustrate your answer using relevant equations and estimations Question 2 (25 marks) A 216 mm long, single rectangular copper fin of 118 mm width and 9 mm thickness, has one end maintained at 124 oC. The fin is exposed to the surrounding air at 14 oC with a convection heat transfer coefficient of 74 W/m2 oC. Neglect heat transfer from the fin's tip, and take the thermal conductivity of copper as 420 W/m oC. The working medium is air. Prandtl number is 0.7. Assume air to be an ideal gas and obtain the relevant properties from the appropriate expressions. (i) State the assumptions and draw a clear sketch showing the geometry and boundary conditions (10 marks) (ii) Calculate the fin's heat transfer rate. (5 marks) (iii) Determine the fin's effectiveness. (5 marks) (iv) Calculate the fin's efficiency. (5 marks) All equations should be briefly discussed, and all symbols should be clearly explained. Question 3 (20 marks) A carbon dioxide (CO2) cartridge is used to propel a small rocket cart as shown in Figure Question 3. The compressed CO2, stored at stagnation conditions of 45 MPa and 25 ºC, is expanded through a converging nozzle with a throat area of 0.15 cm2. The cartridge is assumed to be well insulated and the pressure surrounding it is 101 kPa. Take CO2 an ideal gas with R=189 J/(kg K) and = 1.30. (a) Calculate the pressure at the nozzle throat for choked flow. (3 marks) Question 3 continued… 3 Continuation of Question 3. (b) Find the mass flow rate of carbon dioxide through the nozzle for choked flow. (4 marks) (c) Calculate the force, F, required to hold the cart stationary for choked flow. Hint: formula for Thrust in Example of nozzle application (notes Studyspace 1_Slides1_compressible flow) (4 marks) (d) For what range of cartridge pressures will the flow through the nozzle be choked? Will the mass flow rate from the cartridge remain constant for this range of cartridge pressures? Provide explanations for your answer. (4 marks) (e) Write down the equations describing how the pressure within the tank varies with time while the flow is choked. (5 marks) Figure Question 3. Question 4 (30 marks) You are asked to propose a concept design and analyse a simple supersonic wind tunnel using your knowledge in compressible flows. The design is based on a simple open loop wind tunnel using atmospheric air at the inlet/intake. You should specify your chosen air conditions at the inlet/intake to the tunnel (air pressure, temperature, velocity etc…) and other appropriate data. In the test section of the tunnel, the air flow should be supersonic (you should chose a single value of Mach number in the range 1.2 to 3). The length of the test section is 1m. To simplify the analysis, you can assume the air flow to be isentropic. The tasks involve: (1) very brief literature research on open loop wind tunnels, (2) justification and selection of the components/parts of your proposed wind tunnel (3) specify and justify the selected dimensions of components/parts, (4) finding the test section cross-sectional area, (5) specify the pressure and temperature at several locations of the wind tunnel, with analysis (6) specify the mass flow rate of air (7) simple sketch of wind tunnel with components (8) any relevant analysis/discussion.