Problem:
Consider the unsteadystate heat transfer in solid slabs with two different boundary
conditions, respectively:
(1) Semiinfinite boundary (see lecture note and Examples 12.11 in 2
nd
edition, or 11.11
in the 1
st
edition). At time t = 0, the surface at y = 0 is suddenly raised to temperature T
1
and maintained at that temperature for t > 0.
(2) Finite boundary (see lecture note and Examples 12.12 in 2
nd
edition, or 11.12 in the
1
st
edition). At time t = 0, the surfaces at y = ±b is suddenly raised to temperature T
1
and
maintained at that temperature for t > 0.
Compare the solutions corresponding to the boundary conditions for SHORT times. What
error is made by using the solution for the semiinfinite slab instead of that for the finite
slab, when
α
t/b
2
= 0.01 and for a position 0.9 of the way from the midplane to the slab
surface? Use the graphically presented solution for the finite boundary (Fig. 12.11, or
11.11 in the 1
st
edition) for making the comparison.
Answer:
Consider short times at which the heat flow does not reach the midplane of the solid
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 Fall '08
 Peters
 Heat, Heat Transfer, Boundary value problem, semiinfinite boundary condition

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