Research Article

Steady Heat Transfer through a Two-Dimensional Rectangular Straight Fin

Table 1

Extra point symmetries admitted by (3.2).

𝑆 ( 𝜔 ) Symmetries

( 𝛼 1 + 𝛼 2 𝜔 ) 𝑚 ; 𝛼 1 , 𝛼 2 , 𝑚 0 , 1 𝑋 4 = ( 2 ( 𝛼 1 + 𝛼 2 𝜔 ) / 𝛼 2 ( 𝑚 1 ) ) ( 𝜕 / 𝜕 𝜔 ) + 𝑦 ( 𝜕 / 𝜕 𝑦 ) + 𝑥 ( 𝜕 / 𝜕 𝑥 )
𝜔 𝑚 , 𝑚 0 , 1 𝑋 4 = ( 2 𝜔 / ( 𝑚 1 ) ) ( 𝜕 / 𝜕 𝜔 ) + 𝑦 ( 𝜕 / 𝜕 𝑦 ) + 𝑥 ( 𝜕 / 𝜕 𝑥 )
𝜔 𝑋 4 = 𝜔 ( 𝜕 / 𝜕 𝜔 ) , 𝑋 5 = 𝑃 ( 𝑥 , 𝑦 ) ( 𝜕 / 𝜕 𝜔 )
where 𝐸 2 𝑃 𝑦 𝑦 + 𝑃 𝑥 𝑥 = 𝐸 2 𝑃