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University of Toronto Faculty of Applied Science and Engineering

M1E313H1S - Heat and Mass Transfer Instructor: Prof. A. Bazylak

Final Exam April 26, 2017

Closed Book Exam

Name:

Student #:

UTOR email address:

Time allotted: . 2.5 hours

Aids allowed: . Calculator

Instructions: Provide all work in the pages provided.

State all of your assumptions. Express your solution in terms of parameters before substituting values for the calculation.

Show all the steps in your calculations to receive full credit.

Include units with all your final numerical answers to 5 significant figures.

Other notes: All coats, bags, cell phones, smart watches, and any other objects not included under the list of

allowable aids must be left at the front of the classroom. Possessing an unauthorized aid such as

a cell-phone or smart-watch during the test is an academic offence.

The point values for each question are provided.

Total points: 120

Good Luck!

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Question 1(5 points): Circle the best answer for each of the following multiple choice questions.

a) Which of the following is not a form of degradation in a CAINDU fuel channel? Hydrogen Ingress causing increased fracture toughness. Flaws formed from debris in the primary heat transport system Pressure tube to calandria tube contact resulting in hydride blister formation Radiation resulting in geometrical changes in the pressure tube.

b) The main function of the is to ensure a gap between the pressure tube and calandria tube? End fitting Fuel bundle bearing Annulus spacer Polymer spring

c) The main function(s) of the pressure tube is to: House the nuclear fuel Provide leak detection in case of rupture Act as a pressure boundary for the coolant All of the above A and C

d) Probabilistic assessments provide a risk-informed solution. True False

e) Which of the following is not a typical phenomenon occurring in the polymer electrolyte membrane fuel cell?

Thermal conduction through the gas diffusion layer solid space Electricity flow through fuel cell membrane Oxygen diffusion through the gas diffusion layer pore space Water formation in the cathode side of the fuel cell

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L . Question 2 (14 points): Consider a container of liquid water in a room, where the room temperature and pressure are 20°C and

100kPa, respectively. The relative humidity of the room is 75%, and the liquid water is at a temperature

of 20°C.

State all assumptions. Determine the mole fraction of water vapour in the room air.

Determine the mole fraction of the water vapour in the air adjacent to the liquid water surface.

Determine the mole fraction of air in the liquid water near the surface.

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Question 3 (15 points): A spherical tank has an outer diameter of im. The outer surface of the spherical tank is at 200°C, and the

ambient air temperature is at 25°C. An engineer is considering whether to insulate the outer surface with

urethane foam. Urethane foam has a thermal conductivity of k = 0.026 W/mK. The combined

convection, and radiation heat transfer coefficient for the outside surface is h = 20 W/m2 K.

State all assumptions. What is the rate of heat loss, in kW, from the tank without insulation?

Determine the thickness, in mm, of urethane foam required to achieve a temperature of 40°C on the

exterior surface of the urethane, assuming the convection coefficient does not change.

What is the rate of heat loss, in kW, from the insulated tank when the insulation is added?

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Question 4 (16 points): Consider a pipe that is 17-rn long and has an inner radius of ri = 15 cm, outer radius of r2 = 20 cm, and

thermal conductivity of k = 14 W/mK. Electricity is flowing through the pipe, causing heat to be

generated in the material uniformly at a rate of 25 M. The temperature of the inner surface of the pipe

at ri is Ti = 60°C, and the outer surface of the pipe at r2 is at 12 = 80°C.

State all assumptions. Obtain the simplified relation for the temperature distribution inside the pipe, T(r), under steady state

conditions.

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IE ..;. Question 5 (18 points): Consider the following square channel. The inner surface of the channel is at a uniform temperature of

600K, and the outer surface is exposed to convection with a fluid at 300K and a convection coefficient

of 50W/m2 K. Assume steady state conditions. Taking advantage of symmetry in the channel, heat

transfer is to be modeled using the 2-dimensional grid shown in the figure below. Some nodal

temperatures have been measured and are given in the figure. /

/

2 4

/ ty

6 7 / I

7 / /

9/ x= y=0.01m .,

T1 = 430K T6 = 492K

T3 =394K T8 =T9 -600K

State all assumptions. Derive the finite-difference equations for nodes 2, 4, and 7. Determine the temperatures: T2, T4, and T7, in K. Calculate the heat loss per unit length from the channel.

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Question 6 (24 points): Consider a square pan (15 in x 15 in) filled with liquid water. Air at 80°F, 1 atm, and 30% relative humidity is blown over the surface of this pan with a free stream velocity of lOfi/s. The liquid water is maintained at a uniform temperature of 80°F.

State all assumptions. Determine the rate of evaporation of water, in ibm/s. Determine the amount of heat that needs to be supplied to the liquid water to maintain the constant

temperature, in Btu/s.

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Question 7 (28 points): On a hot summer day, someone coming out of a swimming pool experiences the cooling effects of being

coated with liquid water in windy weather. Consider someone that is 180-cm tall, and the perimeter of

their waist spans 90cm. The skin is at a temperature of 30°C and has an emissivity of 0.95. The

temperatures of the ambient air and surroundings are at 20°C. The ambient air is at latm and 30%

relative humidity. The wind speed is 25km1h. Hint: Approximate the body as a cylinder.

Some additional properties

Pvapour,surf ace 0.0304 kg/m3

Pvapour,co 0.005 1893 kg/m3

The Nusselt number for forced convection over a circular cylinder in cross-flow is:

Nu = 0.027Re0805Pr113

State all assumptions. Determine the total rate of heat loss, in W, from the body of a dry person standing in these conditions.

Determine the total rate of heat loss, in W. from a person who has just come out of a swimming pool.

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