Unless otherwise stated in the Question the following values may be assumed: - Air behaves as an ideal gas with constant specific heat capacities: cp 1005 J/(kgK) and cv 718J/(kgK) R 287J/(kgK) - Density of liquid water 1000kg/m3 - Gravitational field strength g 9.805 N/kg - The Stefan-Boltzmann constant = 5.67 10-8 W/m2 K4
Q1(a) A plane surface is provided with an array of straight rectangular fins of length and thickness 25 mm and 1.5 mm respectively. The fins are spaced on a 3.5 mm pitch. The fins are made of a material with a thermal conductivity of 100 W/m K, and the heat transfer coefficient at all exposed surfaces is 300 W/m2K. The fin base temperature is 95oC and the ambient fluid is at 25oC.
(i) Find the correct range for the overall surface efficiency of the array
(a) 30%-40% (b) 50%-60% (c) 80%-90% (d) None of the above (4 marks)
(ii) Find the correct range for the heat transferred to the fluid per square metre of primary surface.
(a) 10-15 kW/m2 (b) 17-22 kW/m2 (c) 5-7 kW/m2 (d) None of the above (2 marks)
Q1(b) (i) Is a proposed heat pump for domestic space heating possible: - using an ambient heat source at 10C, - with a pump motor power input of W = 200W, and - delivering Qd = 1kW at a space temperature of 20C? Please identify the correct statement.
(a) Clausius inequality gives a value in the range of (0.5 to 0.60) W/K and it is possible. (b) Clausius inequality gives a value in the range of (-0.6 to -0.50) W/K and it is possible. [MEC2003]
5 (c) Clausius inequality gives a value in the range of (-0.2 to -0.40) W/K and it is possible. (d) Clausius inequality gives a value in the range of (0.5 to 0.60) W/K and it is not possible. (4 marks)
(ii) With the same ambient source and extraction rate, and with the same motor, it is proposed to split the 1kW delivered heat equally between space heating at the same temperature of 20C and water heating at 40C. Identify the correct statement.
(a) Clausius inequality gives a value in the range of (-0.6 to -0.55) W/K and it is possible. (b) Clausius inequality gives a value in the range of (-0.6 to -0.55) W/K and it is not possible. (c) Clausius inequality gives a value in the range of (-0.5 to -0.40) W/K and it is possible. (d) Clausius inequality gives a value in the range of (0.4 to 0.50) W/K and it is not possible.
(3 marks)
Q1(c) Modifications to a chemical process will require 120,000 kg/h of toluene to be heated from 15oC to a temperature of at least 55oC. A steam-heated shell-and-tube exchanger is available. It has 100 steel tubes arranged in a single pass. The tube dimensions are: outside diameter 17 mm, inside diameter 15 mm, length 5.5 m. Saturated steam at 3 bar is used on the shell side. Take the shell side heat transfer coefficient ho = 8000 W/m2 K. Take the fouling factor to be 0.001 m2.K /W on both sides of the tube. Physical properties of toluene at the mean temperature of (15 + 55)/2 = 35oC are: density = 870 kg/m3, specific heat [MEC2003] 6 = 1.8 kJ/kg K, viscosity = 280 × 10−6 N.s/m2, thermal conductivity = 0.15 W/m.K.
Take the thermal conductivity of steel as 50 W/m.K.
(i) Estimate the correct range within which the mean velocity within the tube lies:
(a) 2.0 m/s – 3.0 m/s (b) 3.5 m/s – 4.0 m/s (c) 1.0 m/s – 1.5 m/s (d) None of the above (2 marks)
(ii) Estimate the correct range of the Reynolds number for the tube flow and nature of the flow:
(3 marks) (v) Is the heat exchanger suitable for duty?
(a) Yes (b) No (2 marks)
Q2. A cylindrical vessel of diameter 2.0 m contains molten metal whose surface temperature is 1600 K; the height of the vessel above the level of the liquid metal is 1.0 m and the vessel is in large surroundings at a mean temperature of 300 K. The cylindrical sides of the vessel are insulated. The emissivity of the liquid metal surface is 0.3. Assume steady state conditions.
Fig. Q2
Let us consider the molten metal surface as surface 1. The opening is taken to be surface 2. The curved cylindrical surface is taken to be surface 3.
[MEC2003] 8
(i) Identify the correct set of view factors (identify the choice that is the closest to your answer)
