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