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Radioactive waste (kw = 20 Wm-1K-1) is to be stored in spherical stainless

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Subject: Engineering
Due on: 03/22/2016
Posted On: 02/21/2016 05:19 AM

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ChE 350 Problem Set 4
Due Thursday February 11, 2016
1. Radioactive waste (kw = 20 Wm-1K-1) is to be stored in spherical stainless steel (ks = 16 Wm-1K-1)
containers. Heat generation occurs uniformly within the radioactive waste at a volumetric rate of
100 kWm-3, while the outer surface of the container is cooled by 25˚C water with a convective heat
transfer coefficient of h = 1000 Wm-2K-1.
a. Safety considerations require that the maximum steady-state temperature of the system remain
below 475˚C. Will a spherical container with inner and outer diameters of 1.0 m and 1.2 m,
respectively, satisfy this requirement?
b. Determine the steady-state temperature at the outer surface of the container in part (a).
c. It is proposed to use a spherical container of 1.0 m inner diameter for storing radioactive waste
with the same thermal conductivity but twice the volumetric heat generation rate.

Safety

considerations require that the container wall thickness be no less than 4 cm. If the outside heat
transfer coefficient can be increased up to a maximum value of 5000 Wm-2K-1, determine if the
proposed design is feasible.

If so, recommend operating and design conditions for h and

container wall thickness, respectively.
2. A spherical reactor with diameter of 20 cm is filled with a reacting mixture undergoing an
exothermic reaction that generates heat uniformly at a temperature-dependent volumetric rate of
Qoexp(-A/T), where Qo = 5 kWm-3, A = 75 K and T is the mixture temperature in K. The reactor is
enclosed in an insulation layer (k = 0.05 Wm-1K-1, ε = 0.9) of 8-mm thickness. The exterior surface of
-2

the insulation layer is exposed to 25˚C air with convective heat transfer coefficient of h = 5 Wm K-1,
and also exchanges radiation with the surrounding surfaces that are at 35˚C. The thickness of the
reactor wall is negligibly small and the reactant mixture is well stirred so that the reactant mixture
and the reactor wall may be considered to be at the same temperature.
a.

What are the steady-state temperatures of the reacting mixture and the outer surface of the
insulation?

b. You are asked to maintain a steady-state reactor temperature of 95˚C. At the same time, to avoid
potential burn injuries to those who may come into contact with the exposed surface of the
insulation, we would like to keep the temperature at the outer surface of the insulation below
45˚C. Plot the outer surface temperature and the reactor temperature as a function of insulation
thickness (in the range of 0 to 10 mm). Is increasing the insulation thickness a practical solution?
c. (Extra credit) What other parameter could be varied to achieve the desired reactor operation?
Provide quantitative justification.

3. Aluminum cylindrical-spine fins (k = 205 Wm-1K-1) with diameters d = 2, 5, and 10 mm are to be
used in a convection environment with h = 40 Wm-2K-1. If all fins are of length L = 5 cm, use the
result obtained in class for an insulated-tip fin of constant cross-sectional area to answer the
following questions.
a. Compare the relative performance of the fins in terms of heat transfer rate.
b. Compare the relative performance of the fins in terms of heat transfer rate per unit mass.

Tags spherical stainle stored wm1k1 waste radioactive surface temperature outer reactor heat thickne container steadystate mixture insulation fins spherical wall volumetric rate wm1k1 radioactive transfer wm2k1 design require maximum reacting coefficient determine diameters inner diameter layer exposed

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Radioactive waste (kw = 20 Wm-1K-1) is to be stored in spherical stainless

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Tutorial Preview …reacting xxxxxxx undergoing xxxxxxxxxxxx reaction that xxxxxxxxx heat uniformly xx a xxxxxxxxxxxxxxxxxxxxx xxxxxxxxxx rate xxxxxxxxxxxxxx where Qo x 5 kWm-3, x = xx x and x is the xxxxxxx temperature in x The xxxxxxx xxxxxxxxxx in xx insulation layer xx = 0 xx Wm-1K-1, xxxxxx x 0 xx of 8-mm xxxxxxxxx The exterior xxxxxxx of-2the xxxxxxxxxx xxxxx is xxxxxxx to 25˚C xxx with convective xxxx transfer xxxxxxxxxxxxxxxxx xx h x 5 Wm xxxxxxx also exchanges xxxxxxxxx with xxx xxxxxxxxxxx surfaces xxxx are at xxxxxxxxx The thickness xx thereactor xxxx xx negligibly xxxxx and the xxxxxxxx mixture is xxxx stirred xx xxxx the…
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