Modeling the Effect of Headspace Steam on Microwave Heating Performance of Mashed Potato J. Chen, K. Pitchai, D. Jones, J. Subbiah University of Nebraska Lincoln October 9 th, 2014 Session : Electromagnetic Heating 1
Microwave Heating Convenient but Non-uniform 2
Microwave Heating Models Computer model use science based approach for : product formulation design product layout design package develop cooking instructions 3
Novel Food Product Development Café steamer 4
Objectives Develop a comprehensive multiphysics model that includes: Electromagnetic heating Heat and mass transfer Phase change of water evaporation Laminar flow and heat transfer in headspace Evaluate the headspace steam on microwave heating performance 5
Model Development 6
Problem Description in Food Sample Vapor convection Liquid pumping Microwave heating Internal heating Internal water vaporization Food sample Microwave heating J. Chen, K. Pitchai, S. Birla, M. Negahban, D. Jones, J. Subbiah. 2014. Heat and mass transport during microwave heating of mashed potato in domestic oven model development, validation, and sensitivity analysis. Journal of Food Science. DOI: 10.1111/1750-3841.12636. 7
Problem Description in Headspace Outlet flow Vapor inlet Vapor inlet Vapor inlet 8
Geometric Model Coaxial feed Oven cavity Waveguide Lid with slit Turntable Mashed potato 9
Assumptions Frequency 2.45 GHz Moisture condensation in headspace was ignored. The radiation from the hot steam to the food product was ignored. EM field and heat source was calculated using room temperature dielectric properties. 10
Governing Equations Electromagnetics Maxwell s Equations µ r 1 EE 2πf c 2 ε r iε EE = 0 QQ = πfε 0 ε EE 2 f Microwave frequency c Speed of light ε r Dielectric constant ε Dielectric loss factor µ r Permeability Q Power dissipation density Food sample 11
Governing Equations Phase Change (Water Vaporization / Condensation) I= K Mw (p v,eq p v ) R T K p v p v,eq R T Mw Evaporation rate constant Vapor pressure Equilibrium water vapor pressure Ideal gas constant Temperature Molecular weight of vapor/water Food sample 12
Governing Equations Momentum Conservation Darcy s Law u i = k in,i k r,i μ i P u i Darcy s velocity, k in,i Intrinsic permeability k r,i Relative permeability µ ii Dynamic viscosity P Total pressure Food sample 13
Governing Equations Mass Conservation c i + D i c i + uu c i = ± I/Mw Diffusion Convection Phase change c D I u Concentration of the species Diffusion coefficient Evaporation rate Darcy s velocity Food sample 14
Governing Equations Energy Conservation ρc p eff + ρc puu = k eff λii + Q Food sample ρ C p u (ρc p ) eff k eff λ I Q fluid density fluid heat capacity fluid velocity field effective heat capacity effective thermal conductivity latent heat of evaporation evaporation rate heat source 15
Governing Equations Laminar flow of vapor Navier-Stokes Equation ρ u t + (ρu) = 0 + ρ u u= [ pi +μμ u + u T 2 3 μ u I] + F p Pressure μ Viscosity 16
Governing Equations Heat transfer of fluid ρcp T t + ρc pu T= k T ρ C p u K T Fluid density Fluid heat capacity Fluid velocity field Thermal conductivity Temperature 17
Meshing Tetrahedral and prime elements 246247 658784 104399 18
Simulation Strategy EM field at 12 locations Averaged heat source Heat from 4 C for 90 s Laminar flow of vapor Heat transfer in fluid of vapor Heat and mass transfer Phase change of water evaporation Darcy s velocity Fully coupled 19
Results and Discussion 20
Velocity in Headspace Animation 21
Spatial Temperature on Top Surface The headspace steam increased the temperature on the top surface Time, s 30 60 90 C C C Without headspace C C C With headspace 22
Total Moisture Evaporation The headspace steam increased the total moisture evaporation Total moisture evaporation, g 3 2.5 2 1.5 1 0.5 0 Without headspace steam With headspace steam 0 30 60 90 Time, s 23
Heating Nonuniformity The headspace steam increased the heating uniformity on the top surface by 8%, but not for the whole food product. Heating nonuniformity, % 100 90 80 70 60 50 40 30 20 10 0 Without headspace steam With headspace steam 0 30 60 90 Time, s Whole food product Heating nonuniformity, % Standard deviation / average temperature 80 70 60 50 40 30 20 Without headspace steam 10 With headspace steam 0 0 30 60 90 Time, s Top surface 24
Conclusions A comprehensive model of microwave heating coupled with heat and mass transfer in food product and headspace was developed. The headspace steam increased the temperature on the top surface and the total moisture evaporation. The headspace steam increased the heating uniformity on the top surface by 8%, but not for the whole food product. The model needs to be further refined and validated before it can be used by the food industry to assist food development. 25
Thank you very much! Jiajia Chen chenjj0422@huskers.unl.edu 26