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

Microwave oven

Thermal image of surface of food after 5 minutes heating

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.

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

Maxwell v Lambert law Field calculations for 1-D domain

Decay of amplitude of oscillations as length increases

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

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

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.

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

650W Point Temperatures

650W Moisture Loss

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

Thermal image of cross section after 3 minutes heating

1000W Point Temperatures

1000W Moisture Loss

Turntable oven, thermal image taken after 5 minutes heating

750W turntable oven, a=b=1, c=d=0.5*(1+cos 2 (ωx))

Moisture loss

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

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.