Question

The fuel element of a nuclear reactor is in the shape of a plane wall of thickness L = 20 mm. It is being maintained at a constant temperature of 250ºC on both of its surfaces. At normal operating power, heat is generated uniformly within the element at a volumetric rate of q = 107 W/m3. A departure from the steady-state conditions associated with normal operation will occur if there is a change in the generation rate. Consider a sudden change in the heat generation rate to 2 x 107 W/m3. Your goal is to use the explicit finite volume method to determine the temperature distribution in the element as a function of time after the step-change in heat generation rate: The fuel element thermal properties are: K (thermal conductivity) = 30 W/m-K ? = 5 x 10-6 m2/s.

1. First derive an analytical expression for the steady-state temperature distribution under a constant heat generation rate of: q = 107 W/m3 (10 pts)

2. Clearly write down and show the discretized form of your linear equation with its associated coefficients (aP, aE, aW, etc…) and their numerical values. The coefficients for your boundary and interior cells may be different and you need to show this.

3. Use the coefficients computed in the previous question in a spreadsheet to determine the temperature distribution in the element as a function of time (20 pts)

4. How long does it take for the fuel element to attain a new steady-state? How would you assess the accuracy of your estimate? (10 pts)

Answer 1