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

Table 8

Reduction: Case  2.2.

Algebra	Reduction	𝑧	𝑣
[𝑋1,𝑋2]=−2𝑋2	𝑘(𝑣)𝑣𝑧𝑧+𝑘𝑣𝑣^2𝑧−𝑁^2𝑐𝑣=0	𝑦	𝑢
[𝑋1,𝑋3]=0	𝑧^2𝑘(𝑣)𝑣𝑧𝑧+𝑧^2𝑘𝑣𝑣^2𝑧+𝑧𝑘(𝑣)𝑣𝑧+12𝑧^3𝑣𝑧−𝑁^2𝑐𝑣=0	𝑥𝑡^−1/2	𝑢
[𝑋2,𝑋3]=0	𝑧^2𝑘(𝑣)𝑣𝑧𝑧+𝑧^2𝑘𝑣𝑣^2𝑧+𝑧𝑘(𝑣)𝑣𝑧−𝑁^2𝑐𝑣=0	𝑥	𝑢