The fuel assembly shown in the left figure consists of periodic arrays of annular bare fuel rods,…

The fuel assembly shown in the left figure consists of
periodic arrays of annular bare fuel rods, which are cooled by passing water
through the center of the rods as well as over the outer surface. We want to
analyze the thermal performance of the fuel rods by dividing the assembly into
a number of unit cells (control volumes) and evaluating the performance of a
cell, as shown in the right figure.

a) Find the ratio of the average coolant velocities in the
inner and outer channels at the axial level z. At this level, the
pressure drop per unit length is the same in both channels and the
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The fuel assembly shown in the left figure consists of
periodic arrays of annular bare fuel rods, which are cooled by passing water
through the center of the rods as well as over the outer surface. We want to
analyze the thermal performance of the fuel rods by dividing the assembly into
a number of unit cells (control volumes) and evaluating the performance of a
cell, as shown in the right figure.

a) Find the ratio of the average coolant velocities in the
inner and outer channels at the axial level z. At this level, the
pressure drop per unit length is the same in both channels and the bulk coolant
temperature is 293 C. Assume that the flow is turbulent and fully developed in
both channels.

b) Find the maximum temperature in the rod, and the radius
at which the maximum temperature occurs, for a particular axial location where
the inner and outer surface temperatures of the rod are 371 C. At that level
the volumetric heat generation rate may be assumed to be uniform and equal to
0.1 MW/m3. Assume constant fuel conductivity for the fuel.

c) Find the mean temperature of the coolant at the core exit
(i.e., the mixture of the coolant passing through the inner channel and that
passing through the outer channel). The fuel rod is 4.3 m long and the axial
power profile along the channel is give by:

where z is in m and ___o =
.0 52 MW/m3 . Other pertinent data: Inlet water temperature = 293 C,
water pressure at the outlet = 14 MPa, water flow rate per unit cell = 18.37
kg/s, unit cell side (L) = 6.35 cm, fuel inner radius (r1)
= 1.27 cm, and fuel outer radius (r2) = 2.54 cm.

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