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Mathematical Models for Heat and Moisture Transport in Microwave Ovens

This study aims to enhance understanding of heat and moisture transport in microwave ovens through mathematical models predicting temperature and moisture changes in food during heating. The models guide product development for uniform heating and optimal microwave performance.

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Mathematical Models for Heat and Moisture Transport in Microwave Ovens

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  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.

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