Models for heat and moisture transport in a microwave oven

Andrew Hill & Prof. C.J. BuddUniversity of Bath, UK

Greg HooperCCFRA, 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

Pa: Power absorbed

L

Solving Maxwell’s equations for electric field predicts that the power absorbed oscillates and decays.

dxa e

d

QP /

Starchy food

Lambert Law approximates this by

x

Maxwell v Lambert lawField 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

)),0(()),0(( 44aacy TtTTtThkT

))()()()(( /)(//)(/02 dyhdydxLdxt exdexceybeya

d

QTkH

10cm

2cm

FOOD

x

y

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+cos2(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.