Model of Heat and Mass Transfer with Moving Boundary during Roasting of Meat in Convection-Oven
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1 Presented at the COMSOL Conference 2009 Milan 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 student Jens Adler-Nissen, Prof, dr. techn. Krist V. Gernaey, Assoc.Prof, Ph.D Food Production Engineering
2 Outline Introduction Theoretical background Modelling Results Conclusion Governing model equations Boundary and initial condition Model Solution 2 Food Production Engineering, DTU Fødevareinstituttet, Danmarks Tekniske Universitet
3 Roasting process Model Better quantitative knowledge Prediction of T, C Quality, safety Minimize loss Upscale Mass and energy Process control Transport processes during oven convection roasting 3 Food Production Engineering, DTU Fødevareinstituttet, Danmarks Tekniske Universitet
4 Water transport Pure diffusion (often assumed) But doesn t capture pressure Convective T Denaturation WHC Shrinkage (protein network) Pressure gradient velocity 4 Food Production Engineering, DTU Fødevareinstituttet, Danmarks Tekniske Universitet
5 Change of microstructure Permeability(K) Elastic modulus (E) Raw surface o P i Case-1 center T- T- low high Roasted surface o T-high R-low P i Case-2 T- low R -high center Change of microstructure during roasting (cross-sectional view) 5 Food Production Engineering, DTU Fødevareinstituttet, Danmarks Tekniske Universitet
6 Assumptions Fat transport is negligible g (lean meat) Evaporation takes place at the surface No internal heat generation and no chemical reaction Dissolved matter lost with water is small Reduction of water holding capacity and shrinkage are considered. 6 Food Production Engineering, DTU Fødevareinstituttet, Danmarks Tekniske Universitet
7 , Governing equation of heat and mass transfer Heat transfer T ρ m cp m + ( km T) + ρwc p uw T = 0 t w Water transport ρ m = D = f c pm = C + Cu w = D C ( ) Emx t E ( T ) = E o + (1+ exp( E ( T E ) ) Velocity of water µ w = n f ( T ) f f ( C ) ( C ) ( T ) D u w = K µ w P P= EC ( Ceq(T) ) u w KE = C µ w ( C C ) eq Darcy s law C eq ( T ) = 0.75 (1 + 30exp( 0.25( T Tσ ))) 7 Food Production Engineering, DTU Fødevareinstituttet, Danmarks Tekniske Universitet
8 Shrinkage hi /interface velocity Proportional to the volume of liquid water removed Formation of air filled pores V = V 0 β V w, l β=1, no pore formation β = 0, no shrinkage 1-β= fraction of Vw,l replaced by air V = πr βv w, V0 1 V / 3 1/ 3 w, l βv w, l Z 0 1 V 0 V0 2/3 0β Vw, l d 1 ( Vw l ) V 0 V 0 dt βv 1 V l = m ( X X) ρ V ( 1 C ) dz Z β v z = =, dt 3 2/ 3 dr R0β βvw, l d v r = = 1, dt 3V 0 V 0 dt ( V ) w l = πr 2. Z V, = w l d 0 ρ w dvw, dt l = 0 0 ρ ρ0v 0 = ρ w 0 ( 1 C ) w 0 C 0 1 C C Cav 1 C av 2 av dc dt av 8 Food Production Engineering, DTU Fødevareinstituttet, Danmarks Tekniske Universitet
9 Boundary conditions and initial condition BC 1: Axial symmetry, vr=0 BC (2, 3, and 4): HT- heat flux MT- mass flux ALE- velocity IC: T C ( r, z ) = T 0 = const at t = 0 ( r, z ) = C 0 = const at t = 0 9 Food Production Engineering, DTU Fødevareinstituttet, Danmarks Tekniske Universitet
10 Solution COMSOL Multiphyics version3.5 2D cylindrical Radius of 20 mm and length of 54 mm Chemical Engineering module Transient heat transfer Transient mass transfer Moving mesh module (ALE) 10 Food Production Engineering, DTU Fødevareinstituttet, Danmarks Tekniske Universitet
11 Results Temperature distribution Water content distribution 11 Food Production Engineering, DTU Fødevareinstituttet, Danmarks Tekniske Universitet
12 t=500s Temperature profile across cylindrical sample (Z = 0) Iso-concentration lines C (kg/kg) at t = 500 s 12 Food Production Engineering, DTU Fødevareinstituttet, Danmarks Tekniske Universitet
13 Model prediction i with (-) MB vs. with FB (--) Temperature profile 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) 13 Food Production Engineering, DTU Fødevareinstituttet, Danmarks Tekniske Universitet
14 Radial shrinkage I II III Relative radius of cylinder as function of time (R/R0) 14 Food Production Engineering, DTU Fødevareinstituttet, Danmarks Tekniske Universitet
15 Conclusion A 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. Better insight i is obtained. ACKNOWLEDGEMENT DTU for a Ph.D. Grant (Globalization Fund). 15 Food Production Engineering, DTU Fødevareinstituttet, Danmarks Tekniske Universitet
16 Thank you for your attention! 16 Food Production Engineering, DTU Fødevareinstituttet, Danmarks Tekniske Universitet
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