Heat Transfer

Problem 3: A solid spherical nuclear fuel pellet of diameter D and thermal conductivity k has a uniform volumetric generation à throughout its volume. It is being steadily cooled by water flowing over its outside surface with a convection coefficient h and free stream temperature To.

(a) Starting with the heat diffusion equation in spherical coordinates (see Eq. 2.29 in the course text, or Exam 1 Equation Sheet in Lecture 15 in Canvas), derive an equation that describes the temperature distribution T(r) through the nuclear fuel pellet, in the radial direction. Represent your answer in terms of the information given in the problem; that is, your equation should have h and T, in it.

(b) Determine an equation for the maximum temperature within the nuclear fuel pellet. Where is the maximum temperature located?



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