Model of Heat and Mass Transfer with Moving Boundary during Roasting of Meat in Convection-Oven

COMSOL Conference October 15, 2009, Milan, ITALY

Aberham Hailu Feyissa, PhD studentJens Adler-Nissen, Prof, dr. techn. Krist V. Gernaey, Assoc.Prof, Ph.D

Food Production Engineering

Presented at the COMSOL Conference 2009 Milan

liOutline

IntroductionTheoretical backgroundModelling

Governing model equationsBoundary and initial condition Model Solution Model Solution

Results Conclusion

2 Food Production Engineering, DTU Fødevareinstituttet, Danmarks Tekniske Universitet

Roasting process

Model Better quantitative knowledge Prediction of T, CQuality, safety Quality, safety Minimize loss

Mass and energy energy

UpscaleProcess control

Transport processes during oven‐convection

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Transport processes during oven convection roasting

Water transport Water transport

Pure diffusion (often assumed)( )But doesn’t capture pressure

ConvectiveT

DenaturationWHC

Pressure gradientWHC

Shrinkage (protein network) velocity

4 Food Production Engineering, DTU Fødevareinstituttet, Danmarks Tekniske Universitet

Change of microstructure g

Permeability(K)Elastic modulus (E) RElastic modulus (E) Raw

surface Case-1

Roasted

center

T- T- low

Pio

center

high

P

surfaceCase-2

Change of microstructure during roasting

center

T-high T- low

Pio

Case

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(cross-sectional view)R-low R -high

iAssumptions

Fat transport is negligible (lean meat)p g g ( )Evaporation takes place at the surfaceNo internal heat generation and no chemical

tireactionDissolved matter lost with water is smallReduction of water holding capacity and Reduction of water holding capacity and shrinkage are considered.

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i i f h d f

,

Governing equation of heat and mass transfer

Heat transfer( )

Water transport

0)( =∇+∇−∇+∂∂ TucTktTc wwpwmmpm ρρ ( )TfD =

( )Cfc pm =

( )Cfm =ρ

( )Tfw =µ

Water transport

CDCutC

w ∇∇=∇+∂∂ )(

( ) ( )( )mx

oTE

EE +=(

Velocity of watert∂ ( ) ( )( )Dn

oT ETE −−+ exp1(

( )CCKE∇

−K( ))(TCeqCEP −=

)))(20(301(345.075.0)(C Teq −=

( )eqw

w CCu −∇=µPKu

ww ∇

−=

µ

Da c ’s la

7 Food Production Engineering, DTU Fødevareinstituttet, Danmarks Tekniske Universitet

)))(25.0exp(301()(

σTTq

−−+Darcy’s law

h i k /i f l iShrinkage /interface velocity

Proportional to the volume of liquid water Proportional to the volume of liquid water removedFormation of air filled pores

lwVVV ,0 β−= β=1, no pore formation

β = 0, no shrinkage 1-β= fraction of Vw,l replaced by air

ZRVV

ZVV

R

VV

VV

lwlw

lw

.,

1,

1

,1

23/1

0

3/220

00

πββ

π

β

=⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎠

⎞⎜⎜⎝

⎛−=

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛−

−−

−=

−=

av

av

ww

dlw C

CC

CCVXXmV11

1,0

00000

ρρ

ρVV 00 ⎠

⎜⎝⎠

⎜⎝

( )lwlw

z Vdtd

VV

VZ

dtdZv ,

,1

3

3/2

00

0−

⎟⎟⎠

⎞⎜⎜⎝

⎛−−==ββ

⎠⎝

( )dt

dCC

CVdt

dV av

avw

lw2

000

111,

⎟⎟⎠

⎞⎜⎜⎝

⎛−

−−=

ρρ

( )lwlw

r Vdtd

VV

VR

dtdRv ,

,1

3

3/2

00

0−

⎟⎟⎠

⎞⎜⎜⎝

⎛−−==ββ

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dtVVdt 3 00 ⎠⎝

Boundary conditions and initial conditionBoundary conditions and initial condition

BC 1:

Axial symmetry vr=0 Axial symmetry, vr=0

BC (2, 3, and 4):

HT- heat flux

MT- mass flux

ALE- velocity

IC: ( )IC: ( ) 0at const , 0 === tTzrT

( ) 0at const , 0 === tCzrC

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l iSolution

COMSOL Multiphyics®version3.5 p y2D cylindrical

Radius of 20 mm and length of 54 mmChemical Engineering module

Transient heat transfer Transient mass transferTransient mass transfer

Moving mesh module (ALE)

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lResults

Temperature distribution Water content distribution

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t=500s

Temperature profile across Iso-concentration linesTemperature profile acrosscylindrical sample (Z = 0) C (kg/kg) at t = 500 s

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d l di i i h ( ) i h ( )Model prediction with (-) MB vs. with FB (--)

Temperature profile Water content profilep p

blue-center(0, 0)

green-surface (r = 0.02, z = 0)

Water content profile

blue(0, 0), red (0.017, 0)

green (0.019, 0), cyan (0.02, 0)

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Radial shrinkage

I II III

Relative radius of cylinder as function of time

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(R/R0)

ConclusionConclusionA 2D model of HMT with MB is developed and models equations were solved using COMSOL for convection roasting process.Effect of WHC and shrinkage are incorporated. B tt i i ht i bt i dBetter insight is obtained.

ACKNOWLEDGEMENTACKNOWLEDGEMENTDTU for a Ph.D. Grant (Globalization Fund).

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Thank you for your y yattention!

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