Analytical Solution for Different Profiles of Fin with Temperature-Dependent Thermal Conductivity

Table 1

The fundamental operations of differential transform method.

Original function	Transformed function
𝑓(𝑥)=𝛼𝑔(𝑥)±𝛽ℎ(𝑥)	𝐹(𝑘)=𝛼𝐺(𝑘)±𝛽𝐻(𝑘)
𝑓(𝑥)=𝑔(𝑥)ℎ(𝑥)	𝐹(𝑘)=∑^𝑘𝑖=0𝐺(𝑖)𝐻(𝑘−𝑖)
𝑓(𝑥)=𝑔(𝑥)^(𝑛)	𝐹(𝑘)=(𝑘+1)(𝑘+2)⋯(𝑘+𝑛)𝐺(𝑘+𝑛)
𝑓(𝑥)=𝑥^𝑛	𝐹(𝑘)=𝛿(𝑘−𝑛)=^1𝑘=𝑛0𝑘≠𝑛
𝑓(𝑥)=exp(𝛼𝑥)	𝐹(𝑘)=𝛼^𝑘/𝑘!
𝑓(𝑥)=(1+𝑥)^𝑛	𝐹(𝑘)=𝑘(𝑘−1)⋯(𝑘−𝑚−1)/𝑘!