example 9.9  taika-renga 3 layers

para = {L1 ->  0.05, L2 -> x, 
        L3 -> 0.1, λ1 ->  0.8, λ2 ->  
          0.4, λ3 ->  0.9, α1 ->  
          120, α2 ->  11, A ->  1}

rr = 
      1/α1 + L1/λ1 + L2/λ2 + L3/λ3 + 
        1/α2
rr = rr /. para

Plot[rr, {x, 0, 0.2}, GridLines ->  Automatic, 
      PlotRange ->  {0, 1}]

ans = Solve[rr == 2 (rr /. x ->  0), 
          x][[1]]

temparature distribution

para1 = {Tb1 ->  800, Tb2 ->  20}

eq0 = {qq == α1 A (Tb1 - T1), 
        qq == λ1/L1 A (T1 - T2), 
        qq == λ3/L3 A (T3 - T4), 
        qq == α2 A (T4 - Tb2)}

eq = Flatten[{eq0, T2 == T3}]

ans1 = Chop[
          Simplify[
            Solve[eq /. para, {qq, T1, T2, T3, 
                T4}]]][[1]]
ans1 /. para1

eq = 
      Flatten[{eq0, qq == λ2/L2 A (T2 - T3)}]

ans2 = Chop[
          Simplify[
            Solve[eq /. para /. ans, {qq, T1, T2, T3, 
                T4}]]][[1]]
ans2 /. para1

temparature plot

tabx = {-20, 0, 0, 50, 50 + x, 150 + x, 150 + x, 
        150 + x + 20}
tab1 = {Tb1, Tb1, T1, T2, T3, T4, Tb2, Tb2} /. ans1 /. 
        para1
tab2 = {Tb1, Tb1, T1, T2, T3, T4, Tb2, Tb2} /. ans2 /. 
        para1
ne = Length[tabx]

list1 = 
      Table[{tabx[[i]], tab1[[i]]}, {i, ne}] /. 
        x ->  0
list2 = Table[{tabx[[i]], tab2[[i]]}, {i, ne}] /. 
          x ->  1000 x /. ans

zu1 = 
      ListPlot[list1, PlotJoined ->  True, 
        PlotStyle ->  {PointSize[0.2], Hue[0.9]}]

zu2 = 
      ListPlot[list2, PlotJoined ->  True, 
        PlotStyle ->  {PointSize[0.2], Hue[0.7]}]

Show[zu1, zu2, GridLines -> Automatic]