# Thermodynamics and Heat Transfer

National Diploma in Mechanical Engineering Section A: COMPULSORY Answer ALL questions 1-12 1. A resistance temperature device has a resistance R0 = 100 ? at 0o C. If the resistance RT = 197. 7 ? in an oil bath, what is the temperature of the oil in the bath, given that RT = R0(1+? T)? Take R0 = 100 ? R0 = resistance at 0o C ? = 3. 9083 x 10-3 /o C (2 marks) NDE Thermodynamics and Heat Transfer Exam 2008 Name: _______________________________________
Read all the instructions before starting Do not open this paper until instructed Time allowed: 2 hours (plus 5 minutes reading time) Attempt ALL question in Section A (questions 1 – 12) Attempt any TWO from Section B (questions 13-15) Answer the questions in the spaces provided on the question paper. Use the back of the previous page if required. If you attempted all three questions in section B, then cross out the question you don’t want marked. The marker will mark the first 2 questions not crossed out. Show all relevant working.
Marks will be awarded for method as well as correct answers Add your name to the top of this page 3. A steel shaft has a diameter of 25. 0 mm at 20°C. A brass retaining collar has an internal diameter 24. 95 mm at the same temperature. If the shaft is cooled to 0°C, find the temperature to which the retaining collar must be heated if is to have a clearance of 0. 10 mm when it is fitted to the shaft. Take ? Steel = 12 x 10-6 /oCand ? Brass = 19 x 10-6 /oC. (4 marks) 2. A steel casting (C = 460 J/kgK) of mass 2. 4 kg is cooled from 350°C by placing in a container of 12 kg of water (C = 4200 J/kgK) at 18°C.

Assuming no heat is transferred to the container, calculate the final temperature. (4 marks) Instructions: Attachments: Marking: Formulae, saturated water tables Individual marks are shown on each question. There are a total of 70 marks representing 50% of your final mark in this subject. A minimum of 40% in this exam is a requirement for course completion Thermo exam November 2008 final. doc Version 23-Sep-08 ?Mechanical Consortium Printed 11/04/08 Page 2 National Diploma in Mechanical Engineering National Diploma in Mechanical Engineering 4.
Heat was added to 10 kg of saturated liquid water at a pressure of 2 bar at the rate of 20 kW for 10 minutes. Given the following information from the saturated water table, and assuming perfect insulation: hf = 505 kJ/kg, hfg = 2202 kJ/kg, hg = 2707 kJ/kg, Ts = 120. 2°C a. Find the dryness fraction of the steam after the initial 10 minutes. (4 marks) 5. For the complete combustion of acetylene, C2H2: a. Write down the balanced combustion equation (2 marks) b. Determine the stoichiometric air to fuel mass ratio (5 marks) Atomic weights: H = 1, C = 12, O = 16, N = 14 Air composition: 23% oxygen, 77% nitrogen (by mass) . Calculate the time (in minutes and seconds) for which the steam must be heated at the same rate in order to become fully dry. (3 marks) 6. Prepare a labelled sketch of a manometer inclined at 5o to a horizontal datum. If the manometer contains oil with a density of 800 kg / m3, and a change in the pressure applied to it is 50 Pa, find the oil deflection in mm. (4 marks) O f il de lect ion 5o Thermo exam November 2008 final. doc Version 23-Sep-08 ?Mechanical Consortium Printed 11/04/08 Page 3 Thermo exam November 2008 final. doc Version 23-Sep-08 ?Mechanical Consortium Printed 11/04/08
Page 4 National Diploma in Mechanical Engineering National Diploma in Mechanical Engineering 7. Explain for the Seebeck effect and how it may be applied to temperature measurement. (3 marks) 10. Find the total heat transfer, per m2, through the wall shown below. Neglect radiation. Air temperature –5°C h = 10 W/m2K Brick 70 mm thick k = 2. 3 W/mK Air Gap R = 1. 5 m2K/W (5 marks) Surface temperature 25°C Gib 9 mm k = 0. 1 W/mK 8. The non-flow energy equation is given as Q – W= ? U. State the equation as it applies to: a. Isothermal b. Polytropic, and c. Adiabatic processes . (3 marks) 9. 50 litres of oxygen at 200C has a pressure of 850 kPa (abs). Find the pressure if its volume is reduced to 100 litres at: a. constant temperature Batts R = 2. 2 b. 850C 11. A chilly bin is 400 mm long, 200 mm high, 200 mm deep and is made from material 2 cm thick with a coefficient of thermal conductivity of 0. 028. The chilly bin contains ice – how much ice will melt in eight hours if the ambient air temperature is 300C? Take enthalpy of fusion for water as 335 kJ/kg. (5 marks) (5 marks) Thermo exam November 2008 final. doc Version 23-Sep-08 ?Mechanical Consortium Printed 11/04/08 Page 5
Thermo exam November 2008 final. doc Version 23-Sep-08 ?Mechanical Consortium Printed 11/04/08 Page 6 National Diploma in Mechanical Engineering National Diploma in Mechanical Engineering 12. Air is compressed from 99 kPaABS, 20°C and 1. 5 litres to a volume of 0. 2 litres (5 marks) according to the law PV1. 25 = C. Find the following; a. Determine the mass of the gas Section B Answer any TWO questions from questions 13-15 13. A steam pipe is 75 mm external diameter and is 80 m long. It conveys steam at a rate of 1000 kg/h at a pressure of 2 Mpa. The steam enters the pipe with a dryness fraction of 0. 8 and is to leave the pipe with a dryness of not less than 0. 96. The pipe must be insulated – the material to be used has a thermal coefficient of conductivity of 0. 08 W/mK. If the temperature drop across the pipe is negligible, find the minimum thickness of insulation required to meet the conditions. The temperature at the outer surface of the insulation is 27 0C. (10 marks) b. Determine the final pressure c. Determine the final temperature End of Compulsory section. Answer only TWO of the remaining questions. Thermo exam November 2008 final. doc Version 23-Sep-08 ?Mechanical Consortium Printed 11/04/08
Page 7 Thermo exam November 2008 final. doc Version 23-Sep-08 ?Mechanical Consortium Printed 11/04/08 Page 8 National Diploma in Mechanical Engineering National Diploma in Mechanical Engineering Answer question 13 here 14. A one-shell-pass, eight-tube-passes heat exchanger is used to heat glycerine from 25oC to 60oC at mass flow rate of 3000 kg /h. The heating liquid is water which enters the thin-walled, 12 mm diameter tubes at 90oC with a mass flow rate of 26 kg / min. On the shell side the convective heat transfer coefficient is 2000 W / m2 K and on the water side the corresponding value is 2400 W / m2K.
After some time in operation a fouling factor of 0. 0004 m2 K / W develops on the outer tube surfaces. Take cGLYCERINE = 2. 43 kJ / kg K and cWATER = 4. 2 kJ / kg K. Calculate: Glycerine in Water Glycerine out a. The rate of heat transfer in the device before fouling occurs. (1 mark) b. Outlet temperature of water. (2 marks) c. Log mean temperature difference (LMTD). (2 marks) d. Coefficient of heat transfer after fouling has developed. (2 marks) e. Total length of tube required, using “dirty” coefficient of heat transfer (3 marks) Thermo exam November 2008 final. doc Version 23-Sep-08 Mechanical Consortium Printed 11/04/08 Page 9 Thermo exam November 2008 final. doc Version 23-Sep-08 ?Mechanical Consortium Printed 11/04/08 Page 10 National Diploma in Mechanical Engineering National Diploma in Mechanical Engineering Answer question 14 here Thermo exam November 2008 final. doc Version 23-Sep-08 ?Mechanical Consortium Printed 11/04/08 Page 11 Thermo exam November 2008 final. doc Version 23-Sep-08 ?Mechanical Consortium Printed 11/04/08 Page 12 National Diploma in Mechanical Engineering National Diploma in Mechanical Engineering Answer question 15 here 15.
Argon gas flows steadily through a turbine. The flow is entirely adiabatic. Entry conditions are 900 kPaABS at 450o C with a velocity of 80 m/s through an inlet measuring 75 mm x 80 mm. Argon leaves the turbine at 150 kPaABS at a velocity of 150 m/s. Work output from the turbine is 250 kW. Given the following ideal gas properties for argon R = 208. 1 J /kg K and cp = 520. 3 J /kg K, find: a. Mass flow of argon Inlet 75 mm x 80 mm p = 900 kPaABS T = 450oC V = 80 m/s 250 kW p = 150 kPaABS V = 150 m/s (3 marks) b. Outlet temperature of the gas. Assume change of height negligible. 7 marks) Thermo exam November 2008 final. doc Version 23-Sep-08 ?Mechanical Consortium Printed 11/04/08 Page 13 Thermo exam November 2008 final. doc Version 23-Sep-08 ?Mechanical Consortium Printed 11/04/08 Page 14 National Diploma in Mechanical Engineering National Diploma in Mechanical Engineering Extra page for working if required Saturated water properties Thermo exam November 2008 final. doc Version 23-Sep-08 ?Mechanical Consortium Printed 11/04/08 Page 15 Thermo exam November 2008 final. doc Version 23-Sep-08 ?Mechanical Consortium Printed 11/04/08 Page 16
National Diploma in Mechanical Engineering National Diploma in Mechanical Engineering Thermodynamics and Heat Transfer Formulary PV = mRT Q kA’t x P1V 1 = P2 V 2 T1 T2 Saturated water properties P V1n 1 P 2 V2 n n 1 Q hA’t A’t R T1 T2 §P· ? 1? ?P ? © 2? n 1 n § V2 · ? ? ? V ? © 1? Q R CP CV Q UA’t 1 1 J W cp cv PV1 P2V2 1 n 1 ¦ 1 ¦ W §V · ? ? PV ln ? 2 ? © V1 ? Q ‘ l = loD’T Q = m ‘h Q = m c ‘T ‘U P= Q 2? l’t ? § ro · ? « ln ? ? » ? r ? ¦ « ©k i ? » « » « » « » ¬ ? 2S rlk ‘t x mcv ‘T F A for all processes Q Q H V AT 4 hA’T 5. 67 x10 8 P Ugh ‘U W OUTPUT 100 INPUT Q V W m2 K 4 K= Q UA’t Mean t Mean ? 1 ? 2 §? · ln ? 1 ? ?? ? © 2? 2 § V2 V12 m? h2 h1 ? 2 © T1 m h2 h1 S. T. P. = 0°C and 101. 3 kPa N. T. P. = 15°C and 101. 3 kPa Cwater = 4200 J/kgK For Air Cp = 1005 J/kgK Cv = 718 J/kgK R = 287 J/kgK ? =1. 4 Q W mc p T2 g z2 · z1 ? ? ? Thermo exam November 2008 final. doc Version 23-Sep-08 ?Mechanical Consortium Printed 11/04/08 Page 17 Thermo exam November 2008 final. doc Version 23-Sep-08 ?Mechanical Consortium Printed 11/04/08 Page 18 National Diploma in Mechanical Engineering Thermo exam November 2008 final. doc Version 23-Sep-08 ?Mechanical Consortium Printed 11/04/08 Page 19

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