Eccentric Control Rod in Two-group Model

Substitution into the differential equations yields the eigenfunctions 

The substitution of these results, along with (11.63), into (11.18) yields for the fluxes in the core  

The coefficients dn, n, 3Tln, and 3t are arbitrary constants to be deter-mined from the boundary conditions at the outer surface of the reactor and at the rod-reactor interface. The application of these requirements will also yield a criticality condition for the reactor with inserted rod, as in the analyses of the preceding section. 

On the basis of the assumptions and postulates set forth above, we select the following pair of functions to describe the rapid variation in the flux distribution in the vicinity of the control rod  

But these functions are symmetric about the center of the rod therefore, they cannot satisfy the boundary condition (11,19) at p = 5 in the 

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