Derivation of Basic Transport Equation (A. Ertürk)
Derivation of Basic Transport Equation (A. Ertürk)
Derivation of Basic Transport Equation (A. Ertürk)
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Number <strong>of</strong> particles passing from I to II in Δt<br />
Q<br />
Δt<br />
= 0.5<br />
<strong>Equation</strong> 16<br />
⋅ Δx<br />
⋅<br />
A<br />
0.5 ⋅ Δx<br />
⋅ A ⋅<br />
=<br />
Δt<br />
( − )<br />
C 1 C 2<br />
Number <strong>of</strong> particles passing from I to<br />
II in unit time per unit area = FLUX<br />
⋅<br />
( C − C )<br />
Q 1 2<br />
<strong>Equation</strong> 17<br />
C = C1<br />
∂C<br />
∂x<br />
2 + ⋅<br />
<strong>Equation</strong> 18<br />
Q<br />
A ⋅ Δt<br />
=<br />
J<br />
<strong>Equation</strong> 22<br />
DISP<br />
=<br />
Δx<br />
− 0.5 ⋅ Δx<br />
⋅<br />
Δt<br />
∂C<br />
∂x<br />
⋅ Δx<br />
Divide<br />
by time<br />
Divide<br />
by<br />
Area<br />
Number <strong>of</strong> particles passing from I to<br />
II in unit time<br />
⎛ ⎛ ∂C<br />
⎞⎞<br />
0.5 ⋅ Δx<br />
⋅ A ⋅ ⎜C1<br />
− ⎜C1<br />
+ ⋅ Δx⎟⎟<br />
Q<br />
⎝ ⎝ ∂x<br />
⎠<br />
=<br />
⎠<br />
Δt<br />
Δt<br />
<strong>Equation</strong> 19<br />
Q<br />
Δt<br />
Q<br />
Δt<br />
⎛<br />
0.5 ⋅ Δx<br />
⋅ A ⋅ ⎜C1<br />
− C<br />
=<br />
⎝<br />
Δt<br />
<strong>Equation</strong> 20<br />
=<br />
<strong>Equation</strong> 21<br />
x<br />
I<br />
− 0.5 ⋅ Δx<br />
⋅ A<br />
Δt<br />
Δx<br />
∂C<br />
∂x<br />
Δx<br />
1<br />
⋅ Δx<br />
II<br />
∂C<br />
−<br />
∂x<br />
⎞<br />
⋅ Δx⎟<br />
⎠<br />
24<br />
Particle