L UNAM Université, ONIRIS, CNRS, GEPEA, UMR6144, Nantes, F-44322, France.

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1 ing Heating During Batch Processing of Liquid Sample in a Single Mode Cavity S. Curet 1, F. Bellincanta Begnini, O. Rouaud 1, L. Boillereau 1 1 L UNAM Université, ONIRIS, CNRS, GEPEA, UMR6144, Nantes, F-44322, France sebastien.curet@oniris-nantes.fr

2 P in = 5 W t = 16 s 2

3 Mesh generation in COMSOL tetrahedral elements ( elements for the water sample). water 3

4 Governing equations Heat transfer equation (HT module) C T div.( kt ) Q p t abs Thermophysical properties of pure water* absorbed power (W.m -3 ) Resolution of the Mawell s equations * From the COMSOL material library 4

5 Governing equations Electric field propagation (RF module) Mawell s equations for a TE 1 rectangular waveguide (sinusoidal time-varying fields with w = 2p f) 1 r js we 2 ' E k e r E with k w e Q abs : volumetric rate (W.m -3 ) s : Electrical conductivity (S/m) f : frequency of microwaves ( Hz) e : permittivity of free space (F.m -1 ) e r : relative dielectric loss factor E local : local electric field strength (V.m -1 ) Q abs 1 w. e. e r ''. E 2 local ² 5

6 Governing equations Fluid flow modeling (CFD module) Incompressible Navier-Stokes equations u v w ( continuity) y z du du U g P U ( momentum) with UU dt dt t u, v, w : velocity field components following, y and z directions : density of water (kg.m -3 ) P: static pressure (Pa) : dynamic viscosity of water (Pa.s) 6

7 7 Governing equations Initial & boundary conditions z b y y a at n n E E n j L z L z at n z at ab P Z with E a E E z y t at E r r sample air in TE in,. / 2, / 2, /, 4 cos, H H H w s e e p walls boundary eternal at T h T T k z y t at T T, interfaces - container liquid 22, the at U mm L with z y t at gl P and U HT RF CFD

8 Material properties = f (q C) Dielectric properties of pure water* (2.45 GHz) * Zhang, Q., T. H. Jackson and A. Ungan. Numerical modeling of microwave induced natural convection. International Journal of Heat and Mass Transfer 43: (2). 8

9 Temperature distribution at t =16 s q ( C) At the end of microwave processing, the surface of the water is close to 7 C while the eternal temperatures of the walls range from 55 to 6 C (PTFE is only heated by conduction) 9

10 Velocity fields and temperature variations = f (t) waves, P in = 5W, f=2.45ghz v (m/s) q ( C) water PTFE support plate z 1

11 Cross sections areas of velocity fields v (m/s) 11

12 Cross sections areas of velocity fields at t = 16 s v (m/s) At the end of processing, the gravitationally driven flow of water leads to ma velocity gradients around 6 mm/s 12

13 Cross sections areas of temperature and electric field shape at t = 8 s q ( C) E/ E The hot spots are depicted at the near bottom zone of the liquid-container interface 13

14 Eperimental validation of numerical T 1, T 2 and T 3 : 2 mm, 5 mm and 1 mm below the upper water surface - 2 mm - 5 mm - 1 mm Gr * 2 5 g L Q 2 k abs fairly good agreement between ep. vs. numerical model As Gr*, microwave induced natural convection as a function of processing time 14

15 Highlights «Modeling microwave of a liquid sample in a static configuration»: Non uniform inner temperature distribution within a small liquid sample (8.5 ml) Modeling enables to locate precisely the hot spots. The Navier-Stokes equations must be coupled to the heat transfer and the Mawell s equations in order to give realistic. High computational resources are needed for a strong coupling between the differential equations. 15

16 Future prospects Etension of this preliminary study to investigate the development of microwave applicators dedicated to liquid phase processing under continuous flows. Thank you for your attention, 16

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