1. Models for heat and moisture transport in a microwave oven Andrew Hill & Prof. C.J. Budd University of Bath, UK Greg Hooper CCFRA, UK Faraday CASE award

2. Microwave oven

3. Thermal image of surface of food after 5 minutes heating

4. Aims • To increase understanding of the field, heat and moisture transport in a microwave oven. • To produce relatively simple mathematical models able to predict temperature and moisture changes in food during heating and implement these in an easy to use package. • To guide the development of products that heat evenly and give good microwave performance.

5. Maxwell and Lambert Law L Starchy food L: Domain length: 2-14cm d: Penetration depth: 8mm Pa: Power absorbed Solving Maxwell’s equations for electric field predicts that the power absorbed oscillates and decays. Lambert Law approximates this by

6. Maxwell v Lambert lawField calculations for 1-D domain

7. Decay of amplitude of oscillations as length increases

8. Higher Dimensional Model • Model includes end correction to approximate 3-D geometry from a basic 2-D solution • Probe 4 • Probe 3 • Probe 2 • Probe 1

9. 2-D model with constant dielectric properties FOOD 2cm 10cm

10. We can measure • Point temperatures continuously during heating using fibre optic thermal probes. • Surface temperatures after heating using thermal imaging cameras. • Moisture loss by weight of samples before and after heating. • Average power absorbed by measuring temperature rise of a water load in the oven.

11. 650W Oven, Mode stirrer, Averaged: a=b=c=d=1

12. 650W Point Temperatures

13. 650W Moisture Loss

14. 1000W Oven, Mode stirrer, Averaged: a=b=c=d=1

15. Thermal image of cross section after 3 minutes heating

16. 1000W Point Temperatures

17. 1000W Moisture Loss

18. Turntable oven, thermal image taken after 5 minutes heating

19. 750W turntable oven,a=b=1, c=d=0.5*(1+cos2(ωx))

20. Moisture loss

21. Model Summary • 2-D model and 3-D end corrections implemented using Lambert Law with constant dielectric properties assumed radiation field pattern at surface. • Mode stirrers average out field effects • Rotation requires variable field model • Inputs: dielectric properties, physical characteristics of food, power absorbed by load. • Outputs: Point temperatures, cross sectional temperature profile, moisture loss. • Experimental validation • Computation time: minutes on a PC

22. Conclusion • Through the use of analysis, modelling and efficient numerical methods the model can predict quickly the temperature and moisture content of food loads heated in a variety of microwave ovens • Mode stirred ovens produce a more even heating pattern than turntable ovens. • Work is continuing on improving the model to incorporate more complicated field patterns.