- 145 -


Performing those integration in (8.29) which can be evaluated analytically, the temperature distribution becomes


T(r) = TR +  2- 1(2 + A,/A23 (R2 - r2) - 4I(r     (
           R LK

where
               R         -r 2/22
        I(r) =    r' nr'e   /2b  dr'
                r


8.30)


8.31)


From (8.30) and (8.31), the second boundary condition of (8.11), T(R) = TR' is seen to be satisfied. The first boundary condition of (8.11) gives

                  A 2F
        To    R + T    ( 2 + AI/A2)R2 - 41(o      (8.32)


The ratio Al/A2 is evaluated using (8.32) and (7.3).


A1   alC' T2   2 f!


  NU (R) - NU (0)

      -R'/2bN U (o)e  U2b - N u (R)


(8.33)


From (8.32), the constant A2 is


A2 =


   4KR (To - TR)

(2 + A,/A,)R2 - 41(o)


(8.34)


The temperature given by (8.30) becomes T(r) = TR +       0o  R          K2 + A,/A,)(R2-r2)-4I(r
            (2 + Ai/Aa)R2 - 41(o)

                                                  (8.35)