Chapter 3, Problem 3.146P

Consider the fuel element of Example 5.11, which operates at a uniform volumetric generation rate of ${\stackrel{\dot{}}{q}}_1={10}^{7}W/m^3$ until the generation rate suddenly changes to ${\stackrel{\dot{}}{q}}_2=2\times {10}^{7}W/m^3$. Use the finite-element software FEHT to obtain the following solutions.

(a) Calculate the temperature distribution 1.5 s after the change in operating power and compare your results with those tabulated in the example. Hint: First determine the steady-state temperature distribution for ${\stackrel{\dot{}}{q}}_1$, which represents the initial condition for the transient temperature distribution after the step change in power to ${\stackrel{\dot{}}{q}}_2$. Next, in the Setup menu, click on Transient: in the Specify/Internal Generation box, change the value to ${\stackrel{\dot{}}{q}}_2$; and in the Run command, click on Continue (not Calculate). See the Run menu in the FEHT Help section for background information on the Continue option.

(b) Use your FEHT model to plot temperature histories at the midplane and surface for $0\le T\le 400s$. What are the steady-state temperatures, and approximately how long does it take to reach the new equilibrium condition after the step change in operating power?