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EML 6154
HW 3
Due Wednesday 9/23/09
A)
Work Problem
2.11
, but make the following change
.
Let the initial temperature T(t=0) = F(x,y,z),
where this initial condition function may NOT be expressed as a product of the separated 1D
functions.
Therefore solve the general 3D T=T(x,y,z,t) problem using separation of variables.
B)
A rectangular region of dimensions LxW has the following boundary conditions:
Constant heat
flux (q
o
”) into the solid from the bottom side (y=0), prescribed temperature T(x=0,y) = F(y) on the left
side (x=0), insulated on the top side (y=W), while the right side (x=L) is maintained at a constant
temperature of zero.
Solve for the steadystate temperature distribution T(x,y).
C)
A rectangular region of dimensions LxW has constant internal energy generation
g
(W/m
3
) and the
following boundary conditions:
Zero temperature on the bottom side (y=0) and left side (x=0),
insulated on the top side (y=W), while the right side (x=L) dissipates heat by convection with
convection coefficient h into a medium at zero temperature.
Solve the problem for T(x,y) at steady
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 Fall '08
 Staff
 Heat Transfer

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