example 9.8    p.223

eq =  T''[x]
ans1 = 
      ExpandAll[DSolve[eq == 0, T[x], x][[1]]]

tx = T[x] /. ans1
qx = -λ D[T[x] /. ans1, x]

ans2 = Solve[{tx == T1 /. x ->  0, 
            tx == T2 /. x ->  L}, {C[1], 
            C[2]}][[1]]

ttans = ExpandAll[tx /. ans2]
qtans = ExpandAll[qx /. ans2]

parameter survey

para = {T1 -> 45, T2 ->  5, λ ->  1.1, 
        L -> 0.2}

tta = ttans /. para /. 
        x ->  0.001 mm
Plot[tta, {mm, 0, 200}, PlotRange -> {{0, 200},  {0, 50}}, 
      GridLines ->  Automatic]

qta = qtans /. para