Presented at the COMSOL Conference 2008 Boston Coupled Electromagnetics- Multiphase Porous Media Model for Microwave Combination Heating Vineet Rakesh and Ashim Datta Biological & Environmental Engineering Cornell University 2008 COMSOL Conference
Contents Introduction and objectives Fully coupled electromagneticsmultiphase porous media model Governing Equations Implementation Results Conclusions Ongoing Work
Goals Convection- Radiant Heating Microwave Heating Combination Heating Used for cooking Slow Processing Variables Heating Modes Power levels Cycling Fast and convenient Non-uniform heating Mostly used for reheating Food Factors Physical properties Thermal Dielectric Size Fast and convenient Can be used for cooking Can provide custom cooking ability Desired Product Uniform heating Crust formation Appropriate texture
Modeling Methods Primary Variables: microwave energy deposition, temperature, moisture, pressure Microwave heating (Electromagnetics) Model: Exponential decay(empirical)- 1D, 2D Maxwell s equations- 3D Variables: energy deposition- not valid in general energy deposition Increasing complexity (physics + geometry) Model: Heat Transfer only Variables: temperature Transport Heat and mass transfer (no pressure driven flow) temperature and moisture Increasing complexity (physics) Heat and mass transfer with pressure driven flow temperature, moisture, pressure, phase change Present work Fully Coupled Electromagnetics- Heat and Mass Transfer with pressure driven flow (multiphase porous media model) : in 3D
Process Description Microwave, hot air, radiant heating Multiphase transport in sample treated as a porous medium 1,2,3 Water bulk flow/convection capillary flow phase change Heat transfer (for the mixture) Sample Gas (Vapor + Air) bulk flow binary diffusion phase change Solid Element 1 Whitaker S., Advanced Heat Transfer, 13, 119-203 (1997) 2 Ni H., Datta, A. K. and Torrance, K. E., International Journal of Heat and Mass Transfer, 42, 1501-12 (1999) 3 Halder A., Dhall A., and Datta A. K., Food & Bioproducts Processing, 85, 209-19 (2007)
Governing equations: Electromagnetics Maxwell s equations: E= jωµ H H = jωεε E ( εe) = H = 0 0 Relative permittivity: 0 E = Electric field intensity H = Magnetic field intensity ω = microwave angular frequency dielectric loss ε = ε jε dielectric constant Boundary condition (oven walls): E tangential, oven wall = 0 Power absorbed (by the sample): Qmic 1 = ωε0ε E 2 2
Governing Equations: Multiphase Porous Media Model Momentum balance Darcy s Law: kk i ri, v i = µ i for water and gas (vapor/ air) P
G.E.- Mass balance Liquid phase (water): c w + ( nw ) n w Gas phase (vapor and air): c g t t ( ρ ) g vg + = I = I kk kk kk p = ρ P p = ρ P+ ρ S ( ) cap r r r w cap w w w µ µ µ Sw D w kk p r cap = cw = ρϕ w Sw ϕµ Sw cw + ( ρwvw ) = ( Dw cw) I t bulk flow flux phase change bulk flow phase change capillary phase flow change
G.E.- Mass balance (contd..) Vapor: 2 c v ( ) C + ρω g vv = ϕsg MMD a v eff, g xv + I g t ρg bulk flow ω + ω = 1 v mass fractions a Phase change # (evaporation/ condensation): M ( ) v, eq v v I = K p p RT binary diffusion (vapor and air) # Halder A., Dhall A., and Datta A. K., Food & Bioproducts Processing, 85, 209-19 (2007)
G.E.- Energy balance For the mixture: ( ) cc ( ) ( ), T + c, T = k T λi+ Q t n i i= swva,,, i p i i= wva,, p i eff mic Fluxes: n n n v a w = ρωv g g v = ρωv a = ρ v D c w w w, cap w water flux due to liquid pressure, P p Average thermal conductivity: g g bulk flow ( 1 ϕ) ϕ ( ω ω ) cap conduction { } k = k+ Sk + S k+ k eff s w w g v v a a phase change microwave source
Boundary Conditions Vapor convection P = n = P amb n = ρ u, when S = 1 w w w w v hc T k = ht ( T ) T T n nc nc oven v pv w m pw v when S w = 1 Insulated Sample Liquid pumping Hot air & radiant heating Oven at temp, T oven
Computational Scheme Microwave combination oven geometry Solve Maxwell s equations of Electromagnetics Source term for microwave heating Update dielectric properties Solve multiphase porous media model in the sample
Implementation Equations coupled using scripting in COMSOL Problems 3D first time- EM (~2.4M DOFs) and Porous media (~200k DOFs): 42 hrs for 10 min heating: 16 Gb RAM Different mesh and solver (stationary, transient, iterative/ direct) needed for the two physics To make equations implementable in COMSOL additions terms were addedconvergence problems
Computed Results Radiant & hot air Microwave(10s/50 on), radiant & hot air Temperature Moisture
Temperatures & moisture distributions after 10 min of heating Radiant & hot air Microwave(10s/50 on), radiant & hot air Temperature Moisture
Microwave combination heating increases the speed of heating while maintaing the uniformity
Conclusions First study - complex coupling of Maxwell s equations with a multiphase porous media model Optimum combination of heating parameters can be developed that can speed up the process and maintain heating uniformity at the same time Results can be used to develop design recommendations for combination heating for different thermal processes
Ongoing Work Experimental validation using Magnetic Resonance Imaging (MRI): UC Davis Coupled multiphase porous mediasolid mechanics model to study processes with large volume change (e.g. microwave puffing)
Acknowledgements USDA Grant GE for the oven Research group members(bee, Cornell University) Amit Halder Ashish Dhall
Questions? Thank You!