Analysis of Radiative Radial Fin with Temperature-Dependent Thermal Conductivity Using Nonlinear Differential Transformation Methods

Table 1

The fundamental operations of differential transform method.

Original function	Transformed function
𝑥(𝑡)=𝛼𝑓(𝑡)±𝛽𝑔(𝑡)	𝑋𝑗=𝛼𝐹𝑗±𝛽𝐺𝑗
𝑥(𝑡)=𝑑𝑓(𝑡)𝑑𝑡	𝑋𝑗=𝑗+1𝐹𝑗+1
𝑑𝑥(𝑡)=^2𝑓(𝑡)𝑑𝑡^2	𝑋𝑗=𝑗+1𝑗+2𝐹𝑗+2
𝑥(𝑡)=𝑡^𝑚	𝑋𝑗=𝛿𝑗−𝑚=1𝑗=𝑚0𝑗≠𝑚
𝑥(𝑡)=exp(𝜆𝑡)	𝑋𝑗=𝜆^𝑗𝑗!
𝑥(𝑡)=𝑓(𝑡)𝑔(𝑡)	𝑋𝑗=∑^𝑗𝑙=0𝐹(𝑙)𝐺𝑗−𝑙