A Moisture Transfer Model for Drying of Grain
Transcript of A Moisture Transfer Model for Drying of Grain
A Moisture Transfer Model for Drying of Grainby
Kurt O. Lund
Kurt Lund Consulting
135 Sixth Street, Del Mar, CA 92014. [email protected]
Presented at the COMSOL Conference 2009 Boston
∂
∂∂∂
=∂
∂r
MDrrrt
M kk
k 22
1 ( )R
kkeqRkm r
MDMMh∂
∂−=−
∂∂
∂∂
=∂∂
ξξ
ξξτmm 2
21
m = (M – Meq)/(M0 – Meq)
02
11 ≈
∂∂
−=ξm
Bim
m
ξ = r/R τ = t/tk tk = dk2/Dk
Bim = hmdk/Dk ≈ 107
Single-Kernel Moisture Transfer
Dk = Akexp(-Bk/Ta)
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1-.05
0
.05
.1
.15
.2
.25
.3
.35
rh
Meq
Meq = Eeq – Feqln[-(T [C]+Ceq)ln(rh)]Chung-Henderson Correlation:
Equilibrium Moisture Content (Meq= EMC)
T = 25 C50 C75 C
scaled time, τ0.0 0.1 0.2 0.3 0.4 0.5
m avg
0.0
0.2
0.4
0.6
0.8
1.0
0011.011.012
++
=τ
τβ
)(11 eqkkkkk MMShdtMdV −=− ρρ
hk = βdk/6tk= 2/3 β Dk/dk
mdmd βτ
=−
Single-Kernel Moisture Transfer Correlation
One-Dimensional Mass Transport Equations
)(6)1( eqk
kk
T
mVm MM
dh
VQq −−== ρε
Vmsk qx
MUt
M−=
∂∂
+∂
∂− ρε )1(
Vmaa qx
Ut
=
∂∂
+∂∂ ωωερ
Volumetric Moisture Transfer
Solid-Phase Moisture Transport
Air Humidity Transport
One-Dimensional Heat Transport Equations
Volumetric Heat Transfer
Solid-Phase Heat Transport
Air Heat Transport
)(6)1( sak
a
TV TT
dh
VQq −−== ε
tMhquq
xTCU
tTC
fgsVmmVss
sss
s ∂∂
−−−=
∂∂
+∂
∂− ρερε )1()1(
''
VmmVaa
aaa
a quqxTCU
tTC
+−=
∂∂
+∂
∂ ''ερ
C’a = Ca + ωCm um - um0 = Cm(Ts – Tm0)
C’s = Cs + CmM