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Equation (8.38), which is non-linear in the temperature, is linearized by application of the Kirchoff transformation (67)
                         ,T(r)

               T(T)   1g(T')dT'                    (8.39)
                        90T
                           0

where T denotes some reference temperature for which
       0

g(To) = go. From (8.39),


                    g0VT = g(T)VT                  (8.40)

Using this expression for g(T)VT, equation (8.38) becomes


                    V2T +   3   S = 0              (8.41)
                          16ag0

Since (8.41) has the same form as (8.10), the method used to solve (8.10) for T(r) can be used to obtain an expression similar to (8.35) for T(r). Substituting this expression for T(r) into (8.39) gives

                ~T(r)
                   g(T)dT'  = g0T(r)               (8.42)
               IT


When the integral can be evaluated analytically, the temperature distribution, T(r), is obtained by solving the equation


G(T) - g0T(r) = 0


(8.43)