example 9.9  insulation window with  3 layers  p.225

para = {Lg ->  0.005, λg -> 1, λa ->  
          0.026, αi ->  10, αo ->  20, 
        A ->  10, Ti -> 20, To ->  5}

rr1 = 
      1/αi + Lg/λg + 1/αo
rr2 = 
      1/αi + Lg/λg + La/λa + Lg/λg + 
        1/αo

Plot[{rr1 /. para, rr2 /. para}, {La, 0, 0.01}, 
      GridLines ->  Automatic, PlotRange ->  {0, 0.8}]

ans = Solve[rr2 == 3 rr1 /. para, La][[1]]

temparature distribution

eq1 = {qq1 == αi A (Ti - T1), 
          qq1 == λg/Lg A (T1 - T2), 
          qq1 == αo A (T2 - To)};
ans1 = Chop[
          Simplify[Solve[eq1 /. para, {qq1, T1, T2}]]][[1]]

eq2 = {qq2 == αi A (Ti - T1), 
          qq2 == λg/Lg A (T1 - T2), 
          qq2 == λa/La A (T2 - T3), 
          qq2 == λg/Lg A (T3 - T4), 
          qq2 == αo A (T4 - To)};
ans2 = Chop[
          Simplify[
            Solve[eq2 /. para /. ans, {qq2, T1, T2, T3, 
                T4}]]][[1]]

temparature plot

tabx = {-10,   0,     0,    5, 5, 5 + x, 10 + x, 10 + x, 
          10 + x + 10} /. ans

tab1 = {Ti, Ti, T1, 
            T2,    To,       To,     To,     To, To} /. 
          ans1 /. para
tab2 = {Ti, Ti, T1, T2, 
            T2,    T3,       T4,      To,     To} /. 
          ans2 /. para
ne = Length[tabx]

list1 = 
      Table[{tabx[[i]], tab1[[i]]}, {i, ne}] /. 
        x ->  0
list2 = Table[{tabx[[i]], tab2[[i]]}, {i, ne}] /. 
          x ->  1000 La /. 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, 
      PlotRange ->  {0, 20}]