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Mathematical Problems in Engineering
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Special Issues
Mathematical Problems in Engineering
/
2011
/
Article
/
Tab 1
/
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
∈
ℜ
,
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