Central Rod in Two-group Model

The primary purpose of the present section is to exhibit the various interface conditions that have been proposed for use in control-rod calculations. It is of interest to mention that the accuracy of the entire computation is very much dependent on the proper choice of the interface condition for the fast flux. In the analyses which follow we consider a number of such choices and show how the appropriate criticality relation is derived for each case for both a solid and a hollow control rod. This section is concluded with a numerical example which compares the effectiveness of these two types of rods when fully inserted in the center of a bare cylindrical reactor. 

We begin the analysis with a summary of the general solutions derived for the two-group model. The appropriate differential equations for the fast flux ( i) and the thermal flux in the multiplying region of the reactor are given by (8.147). In the present problem it is convenient to write the solutions for these functions in the form [cf. Eqs. (8.164)] 

These must satisfy the boundary condition on the outer surface of the reactor  

If these relations are used in Eqs. (8.174), it is readily shown that for the bare cylindrical reactor the indicated functions are given by the expressions (refer to Fig. ll.l) 

The coefficients a, 9TI, and 9fl are evaluated by the application of the rod-reactor interface condition. 

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