example 9.10

eq = λ T''[x] + H /. 
        H ->  H0 (1 - x/L)

ans1 = 
      ExpandAll[DSolve[eq == 0, T[x], x][[1]]]

tx = T[x] /. ans1
qx = -λ D[tx, x]

ans2 = Solve[{qx == α (Tb - tx) /. x ->  0, 
            qx == 0 /. x ->  L}, {C[1], 
            C[2]}][[1]]

Simplify[tx /. ans2]

para = {L ->  0.072, λ ->  0.25, 
        H0 ->  22 10^3, Tb ->  20}

txa = ExpandAll[tx /. ans2] /. para
ans3 = Solve[(txa /. x ->  L /. para) == 
            120, α][[1]]

txamm = txa /. x ->  0.001  mm

Plot[{txamm /. α ->  40, txamm /. ans3, 
        txamm /. α ->  20}, {mm, 0, 72}, 
      PlotRange -> {{0, 72},  {0, 140}}, GridLines ->  Automatic, 
      PlotStyle ->  {Hue[0.9], Hue[0.7], Hue[0.5]}]