A Lie Symmetry Classification of a Nonlinear Fin Equation in Cylindrical Coordinates

Table 7

Reduction: Case  1.2.

Algebra	Reduction	𝑧	𝑣
[𝑋1,𝑋2]=0	𝑣𝑧+𝑁^2𝑐𝑣=0	𝑡	𝑢
[𝑋1,𝑋3]=𝑋1	𝑣𝑧−2𝛾𝛼^(1+𝛼)/𝛼(2𝛼+1)𝑣^(1/𝛼)+1+𝑁^2𝑐𝑣=0	𝑡	𝑥cos𝑦^2𝛼𝑢
[𝑋1,𝑋4]=0	𝑣𝑧𝑧+1𝛼1𝑣𝑣^2𝑧=0	𝑥cos𝑦	exp(𝑁^2𝑐𝑡)𝑢
[𝑋1,𝑋5]=0	𝛾(𝛼𝑣)^1/𝛼𝑣𝑧𝑧+𝛾(𝛼𝑣)^(1/𝛼)−1𝑣^2𝑧−𝑁^2𝑐𝑣=0	𝑥cos𝑦	𝑢
[𝑋2,𝑋3]=𝑋2	2𝛾𝛼^(1/𝛼)+1(2𝛼+1)𝑣^(1/𝛼)+1−𝑁^2𝑐𝑣−𝑣𝑧=0	𝑡	𝑥sin𝑦^−2𝛼𝑢
[𝑋2,𝑋4]=0	𝛾𝛼^1/𝛼𝑣^1/𝛼𝑣𝑧𝑧+𝛾𝛼^1/𝛼𝑣^(1/𝛼)−1𝑣^2𝑧=0	𝑥sin𝑦	exp(𝑁^2𝑐𝑡)𝑢
[𝑋3,𝑋4]=0	𝑣𝑧𝑧+1𝛼𝑣^2𝑧+4𝛼(𝛼+1)𝑣^(1/𝛼)+1=0	𝑦	𝑒^𝑁2𝑐𝑡𝑥^−2𝛼𝑢
[𝑋3,𝑋5]=0	𝛾𝛼^1/𝛼𝑣^1/𝛼𝑣𝑧𝑧+𝛾𝛼^(1/𝛼)−1𝑣^(1/𝛼)−1𝑣^2𝑧+4𝛾𝛼^(1/𝛼)+1(𝛼+1)𝑣^(1/𝛼)+1=0	𝑦	𝑥^−2𝛼𝑢
[𝑋3,𝑋6]=0	𝑣𝑧−4𝛾𝛼^(1/𝛼)+1𝑣^(1/𝛼)+1+𝑁^2𝑐𝑣=0	𝑡	𝑥^−2𝛼𝑢
[𝑋5,𝑋6]=0	𝛾𝑧^2(𝛼𝑣)^1/𝛼𝑣𝑧𝑧+𝛾𝑧^2(𝛼𝑣)^(1/𝛼)−1𝑣^2𝑧−𝑁^2𝑐𝑧^2𝑣=0	𝑥	𝑢