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It could be solved with finite differences

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2.26 A straight triangular fin made of alumi-
num is shown below. The thickness of the fin
increases linearly with x from zero . al X
=
2Y at
X
=
L. The fin thickness 27 at the base
x = L is small enough so that the temperature
may be assumed uniform in the y direction. The
heat transfer from the fin edges (one is shown

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cross hatched may be neglected in comparison
to that from the slammed faces of the fin. There is
no temperature variation in the : direction.

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la) From basic principles. derive the governing
ordinary differential equation describing the
steady-state temperature distribution along
the fin (i.e., in the x direction).
(b) Obtain an algebraic expression for the tem-
perature distribution.
(c) Obtain an algebraic expression for the heat
loss from the fin.
(d) Evaluate the tip temperature ("F) and the
energy leaving the fin (Bou/hr-ft) for the
following data:
h = 10 Btu/hr-ft -FF
k = 117 Btu/hr-At-F
L = 2 in.
1 = 0.125 in.
I, = 200 F
70 F

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