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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) = q, 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.

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) = q, 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.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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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) = q, sin(πx/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. Coolant Tmi, m, Cp. Fuel rod, D å = å sin (лx/L) ►x L (a) Obtain expressions for the local heat flux q"(x) and the total rate of 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. (c) Obtain an expression for the variation of the rod surface temperature T,(x) with distance x along the tube. Develop an expression for the x-location at which this temperature is maximized.
Transcribed Image Text: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) = q, sin(πx/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. Coolant Tmi, m, Cp. Fuel rod, D å = å sin (лx/L) ►x L (a) Obtain expressions for the local heat flux q"(x) and the total rate of 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. (c) Obtain an expression for the variation of the rod surface temperature T,(x) with distance x along the tube. Develop an expression for the x-location at which this temperature is maximized.
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