microwave cooking modeling heat and moisture transport andriy rychahivskyy
Post on 18-Jan-2018
223 Views
Preview:
DESCRIPTION
TRANSCRIPT
Microwave Cooking Microwave Cooking ModelingModelingHeat and moisture transport
Andriy Andriy RychahivskyyRychahivskyy
OutlineOutline
• What is a microwave?
• Nature of microwave heating
• Goals of the project
• Model description
• Results
• Conclusions and recommendations
Scheme of a microwave ovenScheme of a microwave oven
HH
── electric fieldelectric field ─ ─ magnetic fieldmagnetic field
── wavelength (12.2 cm for 2.45 GHz)wavelength (12.2 cm for 2.45 GHz)
HH
What is a microwave?What is a microwave?
Microwave cooking principleMicrowave cooking principle
• Microwaves act on 1) salt ionssalt ions to accelerate them;2) water moleculeswater molecules to rapidly change their polar direction
+
+
Microwave cooking principleMicrowave cooking principle
• Microwaves act on 1) salt ionssalt ions to accelerate them;2) water moleculeswater molecules to rapidly change their polar direction
• Food’s water content heats the food due to molecular “friction”
Goal of the projectGoal of the project
• Design a model of microwave cooking predicting temperature and moisture distribution within the food product
Phenomena to modelPhenomena to model
• Electromagnetic wave distribution
• Heat transport within the product
• Mass (water and vapor) transport
Governing equations and lawsGoverning equations and laws
• Maxwell’s equations
• Energy balance equation
• Water and vapor balance equations
• Ideal gas law
• Darcy’s law for a flow in a porous medium
Porous mediumPorous medium
watewaterr
vapovaporr
solid solid particleparticle
Porous mediumPorous medium
watewaterr
vapovaporr
solid solid particleparticle
VVfluid
fluidVVS w
w
Geometrical modelGeometrical model
M
C
y
z
O−
+
+G
C MW cavityMW cavity
M food food productproduct
G waveguidewaveguide
toptop
bottobottomm
Heat sourceHeat source
– electromagnetic properties:electromagnetic properties: εε, , σσ (control how a material heats up) εε = = εε* + * + i i εε****
– radial frequency:radial frequency: ωω = 2 = 2**2.45 GHz2.45 GHz
Heat sourceHeat source
Electric field intensity
Heat sourceHeat source
Electric field intensity
Heat sourceHeat source
Electric field intensity Heat source
-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04
1
2
3
4
5
6
x 106
length coordinate x [m]
heat
sou
rce
Q [W
/m3 ]
Convection-diffusion equationConvection-diffusion equation
M
C
y
z
O−
+
Λ
ΣO
Γ
Σ
Σ
+G
heat capacityheat capacity:: (how much heat the food holds)
thermal conductivity:thermal conductivity: (how fast heat moves)
latent heat:latent heat: (absorbed due to evaporation)interface mass transfer interface mass transfer rate:rate:
QIlTCCT
TSCSCtTC
vw
vwvvwwww
2
1
eff
eff
uu
C
l
Mx
Ι
Boundary and initial conditionsBoundary and initial conditions
M
C
y
z
O−
+
Λ
ΣO
Γ
Σ
Σ
+G
thermal conductivity:thermal conductivity: (how fast heat moves)
heat transfer coef.:heat transfer coef.: (thermal resistance)latent heat:latent heat: (absorbed due to evaporation)
wwwSlTThT unn eff0 vw ppp
x
0t1,4 wST
h
l
One-dimensional modelOne-dimensional model
:,,, txTTtxSSw
xxt
/,2
2
vvEvvDv TS ,v
),()( 21 vv bxSb
xT
0),( TSp
with
1,4 ST
Lx
at
at
0t
Numerical results /without mass Numerical results /without mass transport/transport/
-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04
20
40
60
80
100
length coordinate x [m]
tem
pera
ture
T [0 C
]
10 20 30 40 50 600
20
40
60
80
100
time t [s]
tem
pera
ture
T [0 C
]
x = 1x = 3/4x = 0
Numerical results /without mass Numerical results /without mass transport/transport/
10 20 30 40 50 600
20
40
60
80
100
time t [s]
tem
pera
ture
T [0 C
]
x = 1x = 3/4x = 0
4),(eff
* tCQtxT
Numerical results /general 1D Numerical results /general 1D model/model/
-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04
20
40
60
80
100
110
length coordinate x [m]
tem
pera
ture
T [0 C
]
-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.040.3
0.4
0.5
0.6
0.7
0.8
0.9
1
length coordinate x [m]
moi
stur
e S
Interpretation of resultsInterpretation of results
ConclusionsConclusions
• Electromagnetic source is constant
• Heating-up of the product until 100oC develops linear in time
• T at the boundary >> T in the kernel
• Moisture loss occurs only in a boundary layer
RecommendationsRecommendations
• Validate the results
• Extend our implementation
• Perform a parameter study
top related