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Improving Finâ€™s Efficiency and Effectiveness in Engineering Practice

## Justifying and Selecting Practical Ways of Improving Fin’s Efficiency

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, diagrams and estimations. The tasks of the assignment involve the followings:

(a) Justify and select the practical ways of improvement of the fin’s efficiency.

(b) Discuss practical examples of the use of the identified ways of improvements in engineering practice.

(c) Provide relevant equations, diagrams and estimations. All equations should be briefly discussed, and all symbols should be clearly explained.

An aluminium tube carrying a hot liquid at 117 oC has 14 integrally machined longitudinal fins on its outer surface. The tube’s inner and outer radii are 13 and 18 mm, and its total length is 270 mm, while the fins’ height is 22 mm and their thickness is 2 mm. Air at 23oC flows over the fin surface, providing an approximately uniform convection heat transfer coefficient of 29 W/m2 oC, and the heat transfer coefficient of the hot liquid inside the tube is 45 W/m2 oC. The thermal conductivity of aluminium is 202 W/m oC.

(a) State the assumptions and draw a clear sketch showing the geometry, boundary conditions and equivalent thermal circuit.

(b) Calculate the thermal resistance of the entire fin system.

(c) Calculate the fin’s heat transfer rate. All equations should be briefly discussed, and all symbols should be clearly explained. Continued…

(3.a) A gas with a molar mass of 40 kg/kmol and a specific heat ratio ?=1.67 flows isentropically through a venturi meter. At the inlet, the velocity is 135 m/s, the pressure 120 kPa and the temperature 20ºC. At the throat, the temperature is found to be -20ºC.

(i) Determine the Mach number at the inlet.

(ii) Find the Mach number, pressure and velocity at the throat.

(3.b) A carbon dioxide (CO2) cartridge is used to propel a small rocket cart as shown in Figure Question 3b. 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 cm 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.

(i) Calculate the pressure at the nozzle’s throat for choked flow.

(ii) Find the mass flow rate of carbon dioxide through the nozzle for choked flow.

(iii) Calculate the force, F, required to hold the cart stationary for choked flow.Hint: formula for Thrust in Example of nozzle application (in notes provided)

(iv) For what range of cartridge pressures will the flow through the nozzle bechoked? Will the mass flow rate from the cartridge remain constant for this range of cartridge pressures? Provide explanations for your answer.

(v) Write down the equations describing how the pressure within the tank varies

with time while the flow is choked.