EML 6154
Homework Set 2
Due Friday, September 11
1)
Separation of variables leads to the following orthogonal function,
n
(
x
) = cos(
n
x
), with eigenvalues
n
= (2n+1)
/2L, for n = 0, 1, 2…..
over the interval x = 0 to L, noting that the weighting function is one.
i) Show that the integral
dx
x
x
m
L
x
n
)
(
)
(
0
0 for
n
m
.
ii) Evaluate the integral
dx
x
L
x
n
)
(
0
2
iii) Determine the general Fourier series expansion coefficients (a
n
) for the following:
)
cos(
2
0
2
x
a
x
n
n
n
.
Simplify integrals as much as possible
.
2)
Work problems 1.12 in text.
Note: Mathematical formulation requires statement of the simplified
governing equation and the appropriate boundary and/or initial conditions.
Do NOT solve
.
3)
Consider a solid copper sphere of diameter 10 cm, see figure below.
The sphere has
6
equally spaced
solid copper cylinders that extend from the sphere as shown in the figure.
Each cylinder is 1cm in
diameter, and 10 cm long.
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 Fall '08
 Staff
 Thermodynamics, Fourier Series, Heat, Heat Transfer, solid copper sphere, cylinder temperature distribution, following orthogonal function

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