MECH 3460 Heat Transfer (W20) A01 On-line Term Test #3
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University of Manitoba
Department of Mechanical Engineering
MECH 3460 Heat Transfer (W20)
Term Test #3
(Prof. S.J. Ormiston)
25 March 2020
Duration: see below
Total time of 150 minutes includes solving, scanning, and submission to UM Learn.
1. This test is to be completed individually with no consultation with anyone other
than the course instructor.
2. You are permitted to use the textbook for the course, summary information sheets, lecture
notes, your assignments, UM Learn reference materials, and a calculator.
3. Clear, systematic solutions are required. Show your work. Marks will not be assigned for
problems that require unreasonable effort for the marker to decipher.
4. Use linear interpolation in the property tables as necessary.
5. Keep 4 or 5 significant figures in intermediate calculations, and use 4 or 5 significant figures
in final answers. Final answers must have units.
6. The weights of the two problems are given. The test will be marked out of 100.
7. When you have completed solving the problems, produce a pdf file containing images of the
pages of your solution. Please make sure your name and student number are on the first page
and number all your pages sequentially. Upload the pdf file to UM Learn under
Assessments->Assignments in the Term Test 3 folder.
Please name the file using the following approach:
“your family name”-“your first initial”-TT3.pdf (e.g., Ormiston-S-TT3.pdf).
Values
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1. As a result of certain weather conditions, a hailstone (solid sphere made of ice) that is 11 [mm]
in diameter is formed in a high altitude cloud at −20 [◦ C]. Consider the hailstone as it falls
through warmer air at 5 [◦ C]. Assume that it has a constant falling velocity as soon as it
encounters the warmer air.
The properties of the hailstone (indicated with subscript h for “hailstone”) may be taken as:
ρh = 920 [kg/m3 ], kh = 1.89 [W/m · K], and Cp h = 2040 [J/kg · K].
For the purposes of this problem, take the air properties at 250 [K].
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9
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(a) Using an estimated constant hailstone drop velocity of 13 [m/s], after how much time (in
seconds) of falling will the outer
of the hailstone start to melt? For the purposes
µ surface
¶
µ
of this question, assume that
= 1.
µs
(b) Determine the temperature at the centre of the hailstone at the time calculated in
part (a). Sketch qualitatively the temperature of the centre and the surface of the
hailstone from the start of falling in warm air until the time calculated in part (a). Label
known temperature and time values on the sketch.
(c) Using the following function for the drag coefficient CD for a sphere (instead of Figure 7.9
of the text book):
CD = 0.1155 Re0.137
D
(1)
solve for the terminal velocity of the hailstone by balancing drag and gravitational forces.
Use g = 9.81 [m/s2 ].
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MECH 3460 Heat Transfer (W20) A01 On-line Term Test #3
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2. The outflow from a particular parabolic trough solar collector is fully developed flow of molten
salt with a bulk temperature of 400◦ C. The molten salt enters an AISI 316 stainless steel pipe
with Di = 62 [mm], Do = 70 [mm], and kss = 18.3 [W/m · K]. The pipe has a layer of glass
wool insulation with thickness tins =19 [mm] wrapped around its outer surface. The insulation
thermal conductivity may be taken as kins = 0.038 [W/m · K].
The volume flow rate of the molten salt is 8.00×10−4 [m3 /s] and the properties of the salt
may be taken as: ρs = 1850 [kg/m3 ], µs = 2.00×10−3 [N · s/m2 ], Cp s = 1508 [J/kg · K], and
ks = 0.515 [W/m · K].
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The outer surface of the insulation is exposed to outdoor air flow. Air at 1 [atm] and 25◦ C
with a speed of 9 [m/s] is in crossflow with the outside of the insulation layer. For the purposes
of this problem, take the air properties at 300 [K].
The pipe is to be used to transfer the molten salt from the solar collector to a building for use
in a power generation process.
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(a) Determine the maximum length of the tube if the bulk temperature of the salt must be
at least 375◦ C when it exits the tube and enters the other building.
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(b) Determine the pumping power required for the tube length determined in part (a) for a
pump efficiency of 95%.
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(c) Determine the temperature of the outer surface of the insulation at the end of the pipe.
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