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        The temperature distribution is obtained by using numerical methods to solve equation (8.49). This equation is first written in the form K                                   _1      R K
  d2T   F -      idT          R   3 dKR 11dT R    (8.51)
  dr2             dr    KRR dT    'drJ     l6(T5

The temperature gradient is evaluated over the interval [0, RI as follows:

                 (ITr               dT            (.2
               (r) =     F(r')dr' + d(            (.52)

                       0

The temperature distribution over [0, R] is then given by jrdl-rr)                         d                8.3

               T(r) =        (T   dr' + T(0)      (8.53)


                                dT
using the values from (8.52) for d-i(r'). In order to

                 dT
obtain values for jr using (8.52), F(r) must be initially evaluated at r = 0. From (8.51), the first term of F(0) appears to be undefined since limI rda) =    an inder+0

terminate form. To eliminate this computational difficulty, r is replaced by r + s0 when r&[0,s&0], where s0 is an arbitrarily small positive constant. This allows the numerical integration to begin at r = 0 since the first term of F(0) becomes