Consider a cylindrical nuclear fuel rod of length

Chapter 8, Problem 8.14

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Consider a cylindrical nuclear fuel rod of length Landdiameter Dthat is encased in a concentric tube. Pressur-ized water flows through the annular region between therod and the tube at a rate , and the outer surface of the tube is well insulated. Heat generation occurs within the fuel rod, and the volumetric generation rate is knownto vary sinusoidally with distance along the rod. That is, sin(?x/L), where (W/m3) is a constant. Auniform convection coefficient hmay be assumed toexist between the surface of the rod and the water.(a) Obtain expressions for the local heat flux q(x) andthe total heat transfer qfrom the fuel rod to the water.(b) Obtain an expression for the variation of the meantemperature Tm(x) of the water with distance xalong the tube.(c) Obtain an expression for the variation of the rodsurface temperature Ts(x) with distance xalong thetube. Develop an expression for the x-location atwhich this temperature is maximized.