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

Table 6

Reduction: Case  1.1.

Algebra	Reduction	𝑧	𝑣
[𝑋1,𝑋2]=0	𝑣𝑧+𝑁^2𝑐𝑣=0	𝑡	𝑢
[𝑋1,𝑋3]=0	𝑣𝑧𝑧−1𝑣𝑣^2𝑧+𝑁^2𝑐𝛽𝛾𝑣=0	𝑥cos𝑦	𝛽−𝑢exp(−𝑁^2𝑐𝑡)
[𝑋1,𝑋4]=0	𝛾𝑣𝛽−𝑣^𝑧𝑧+𝛾(𝛽−𝑣)^2𝑣^2𝑧−𝑁^2𝑐𝑣=0	𝑥cos𝑦	𝑢
[𝑋2,𝑋3]=0	𝑣𝑧𝑧−1𝑣𝑣^2𝑧+𝑁^2𝑐𝛽𝛾𝑣=0	𝑥sin𝑦	𝛽−𝑢exp(−𝑁^2𝑐𝑡)
[𝑋2,𝑋4]=0	𝛾𝑣𝛽−𝑣^𝑧𝑧+𝛾(𝛽−𝑣)^2𝑣^2𝑧−𝑁^2𝑐𝑣=0	𝑥sin𝑦	𝑢
[𝑋3,𝑋5]=0	𝑧^2𝑣𝑧𝑧−𝑧^2𝑣𝑣^2𝑧+𝑧𝑣𝑧+𝑁^2𝑐𝛽𝛾𝑧^2𝑣=0	𝑥	𝛽−𝑢exp(𝑁^2𝑐𝑡)
[𝑋4,𝑋5]=0	𝛾𝑧𝛽−𝑣^2𝑣𝑧𝑧+𝛾(𝛽−𝑣)^2𝑧^2𝑣^2𝑧+𝛾𝛽−𝑣𝑧𝑣𝑧−𝑁^2𝑐𝑣𝑧^2=0	𝑥	𝑢