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ChE 350 Problem Set 3 Due Thursday February 4, 2016

Question # 00202498
Subject: Engineering
Due on: 03/22/2016
Posted On: 02/21/2016 05:20 AM

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ChE 350 Problem Set 3
Due Thursday February 4, 2016

1. The fuel element in a nuclear reactor consists of a cylindrical thorium (k = 60 Wm-1K-1) fuel rod of 25 mm
diameter that is wrapped in a 2 mm-thick aluminum (k = 205 Wm-1K-1) cladding. The fuel rod may be
considered to be in perfect contact with the cladding material so that contact resistances may be neglected.
Energy generation occurs uniformly in the fuel rod, and the cladding is cooled with 95˚C water and a
convective heat transfer coefficient of h = 7000 Wm-2K-1. The melting points of thorium and aluminum are
2023K and 933K, respectively.
a. Steady-state operation of the fuel rod with a volumetric energy generation rate of 700 MWm-3 is proposed.
Is the proposed stead-state operation feasible?
b. In the event of a loss of coolant, the heat transfer coefficient h would decrease drastically. Explore the
effects of energy generation rate and heat transfer coefficient on the temperatures at the center of the fuel
rod and at the fuel rod-cladding interface. Plot these temperatures as functions of volumetric energy
generation rate in the fuel rod (over the range 100-1000 MWm-3) for different values of h (over the range
1-10 MWm-2K-1) in order to suggest an envelope of acceptable operating conditions.
2. Consider an electric space heater made of coiled Nichrome wire of 1 mm diameter, with cross flow of 50˚C air
over the wire to establish a convective heat transfer coefficient of 250 Wm-2K-1. The housing that encloses the
coiled wire is at Tsur = 50˚C. The Nichrome wire has electrical resistivity of ρe = 10


Ωm, thermal

conductivity of k = 25 Wm-1K-1, and surface emissivity of ε = 0.20.
a. Assuming negligible temperature variations within the wire, estimate the maximum allowable electric
current to avoid wire temperatures greater than 1200˚C.
b. Assess the validity of the assumption of uniform wire temperature in part (a) by computing the centerline
temperature corresponding to the maximum rate of heat generation.
c. (Extra credit) What is the corresponding length of wire that may be used in the heater for a maximum
available voltage of 110V? What is the power rating of the heater?
3. Plate glass at 600˚C is cooled during its manufacture by passing cooled air over its surfaces with a convective
heat transfer coefficient of 5 Wm-2K-1. To prevent cracking, the temperature gradient must not be allowed to
exceed 15 K/mm at any point in the glass during the cooling process. Plate glass has a thermal conductivity of
k = 1.4 Wm-1K-1 and a surface emissivity of ε = 0.80. Assuming the air temperature to be the same as that of
the surrounding walls, what is the lowest air temperature that can initially be used for the cooling process?

Tags 0 february thursday problem wire fuel coefficient transfer temperature heat rate wm1k1 wm2k1 cladding generation cooled temperatures plate surface heater nichrome used volumetric corresponding maximum mwm3 emiivity auming energy 50730c operation contact thorium aluminum

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ChE 350 Problem Set 3 Due Thursday February 4, 2016

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Tutorial Preview …the xxxx transfer xxxxxxxxxxx h would xxxxxxxx drastically Explore xxxxxxxxxx of xxxxxx xxxxxxxxxx rate xxx heat transfer xxxxxxxxxxx on the xxxxxxxxxxxx at xxx xxxxxx of xxx fuelrod and xx the fuel xxxxxxxxxxxx interface xxxx xxxxx temperatures xx functions of xxxxxxxxxx energygeneration rate xx the xxxx xxx (over xxx range 100-1000 xxxxxx for different xxxxxx of x xxxxx the xxxxxxxxx MWm-2K-1) in xxxxx to suggest xx envelope xx xxxxxxxxxx operating xxxxxxxxxx 2 Consider xx electric space xxxxxx made xx xxxxxx Nichrome xxxx of 1 xx diameter, with xxxxx…
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