2. Consider a cylindrical nuclear fuel rod of length L and diameter D that is encased in a concentric tube. Pressur- ized water flows through the annular region between the rod and the tube at a rate m, and the outer surface of the tube is well insulated. Heat generation occurs within the fuel rod, and the volumetric generation rate is known to vary sinusoidally with distance along the rod. That is, q(x)=sin(x/L), where q.(W/m³) is a constant. A uniform convection coefficient h may be assumed to exist between the surface of the rod and the water. x Coolant Tmi, m, Cp Fuel rod, D q=q, sin (лx/L) (a) Obtain expressions for the local heat flux q"(x) and the total heat transfer q from the fuel rod to the water. (b) Obtain an expression for the variation of the mean temperature T(x) of the water with distance x along the tube. hint: This problem is to test your understanding of the physical process, and the analytical skills for a problem. You need a control volume, a volume that is small enough so that the physical parameters inside the volume can be considered as a single value. For this cylindrical geometry with change alone the z-axis, the control volume is a thin slice or a thin disk.
2. Consider a cylindrical nuclear fuel rod of length L and diameter D that is encased in a concentric tube. Pressur- ized water flows through the annular region between the rod and the tube at a rate m, and the outer surface of the tube is well insulated. Heat generation occurs within the fuel rod, and the volumetric generation rate is known to vary sinusoidally with distance along the rod. That is, q(x)=sin(x/L), where q.(W/m³) is a constant. A uniform convection coefficient h may be assumed to exist between the surface of the rod and the water. x Coolant Tmi, m, Cp Fuel rod, D q=q, sin (лx/L) (a) Obtain expressions for the local heat flux q"(x) and the total heat transfer q from the fuel rod to the water. (b) Obtain an expression for the variation of the mean temperature T(x) of the water with distance x along the tube. hint: This problem is to test your understanding of the physical process, and the analytical skills for a problem. You need a control volume, a volume that is small enough so that the physical parameters inside the volume can be considered as a single value. For this cylindrical geometry with change alone the z-axis, the control volume is a thin slice or a thin disk.
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Transcribed Image Text:2.
Consider a cylindrical nuclear fuel rod of length L and
diameter D that is encased in a concentric tube. Pressur-
ized water flows through the annular region between the
rod and the tube at a rate m, and the outer surface of
the tube is well insulated. Heat generation occurs within
the fuel rod, and the volumetric generation rate is known
to vary sinusoidally with distance along the rod. That
is, q(x)=sin(x/L), where q.(W/m³) is a constant. A
uniform convection coefficient h may be assumed to
exist between the surface of the rod and the water.
x
Coolant
Tmi, m,
Cp
Fuel rod, D
q=q, sin (лx/L)
(a) Obtain expressions for the local heat flux q"(x) and
the total heat transfer q from the fuel rod to the water.
(b) Obtain an expression for the variation of the mean
temperature T(x) of the water with distance x
along the tube.
hint: This problem is to test your understanding
of the physical process, and the analytical skills
for a problem. You need a control volume, a
volume that is small enough so that the physical
parameters inside the volume can be considered
as a single value. For this cylindrical geometry
with change alone the z-axis, the control volume
is a thin slice or a thin disk.
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