September 2013
Intermediate to advanced
320 pages
11h 25m
English
Content preview from Finite Element Techniques for Fluid Flow
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DISPERSION PROBLEMS 265
After substitution into (8.27) we obtain for each element
(5θ
η
'
Γ
{ΚΘ
Μ
+ ΑΘ" + Mé" - Q} = 0 (8.29)
where
JM*
7
dS
Α
'ίί
ι
"
,
{"·*(^ϊ
+ ,
'*[^Ι
Τ
}
ΛΛ
(830)
M
=
Γ
Γ/*ρφφ
τ
dA
Q
= II hpf* dA- I
h(q„*
-
γθΑ) dS
+ Σ
ß
w
ζΐ,φ
For all the elements we obtain
jre +
s#e
+ JÎÙ = &
(8.3i)
where the
Θ
terms satisfy the θ =
Θ
conditions.
8.3 DIFFUSION PROBLEMS
Let us consider here the case of having a diffusion-only problem for
which the convective terms in (8.31) will be neglected, i.e.
jre + Jte = & (8.32)
This is the case when there is no flow of the material
(e.g.
temperature
diffusion in solid, concentration changes in still waters, etc.) ...
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