Models for heat and moisture transport in a microwave oven Andrew Hill & Prof. C.J. Budd University...
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![Page 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.](https://reader034.fdocuments.us/reader034/viewer/2022051613/5515df4955034638038b4b42/html5/thumbnails/1.jpg)
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
![Page 2: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051613/5515df4955034638038b4b42/html5/thumbnails/2.jpg)
Microwave oven
![Page 3: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051613/5515df4955034638038b4b42/html5/thumbnails/3.jpg)
Thermal image of surface of food after 5 minutes heating
![Page 4: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051613/5515df4955034638038b4b42/html5/thumbnails/4.jpg)
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.
![Page 5: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051613/5515df4955034638038b4b42/html5/thumbnails/5.jpg)
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
![Page 6: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051613/5515df4955034638038b4b42/html5/thumbnails/6.jpg)
Maxwell v Lambert lawField calculations for 1-D domain
![Page 7: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051613/5515df4955034638038b4b42/html5/thumbnails/7.jpg)
Decay of amplitude of oscillations as length increases
![Page 8: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051613/5515df4955034638038b4b42/html5/thumbnails/8.jpg)
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
![Page 9: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051613/5515df4955034638038b4b42/html5/thumbnails/9.jpg)
2-D model with constant dielectric properties
)),0(()),0(( 44aacy TtTTtThkT
))()()()(( /)(//)(/02 dyhdydxLdxt exdexceybeya
d
QTkH
10cm
2cm
FOOD
x
y
![Page 10: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051613/5515df4955034638038b4b42/html5/thumbnails/10.jpg)
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.
![Page 11: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051613/5515df4955034638038b4b42/html5/thumbnails/11.jpg)
650W Oven, Mode stirrer, Averaged: a=b=c=d=1
![Page 12: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051613/5515df4955034638038b4b42/html5/thumbnails/12.jpg)
650W Point Temperatures
![Page 13: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051613/5515df4955034638038b4b42/html5/thumbnails/13.jpg)
650W Moisture Loss
![Page 14: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051613/5515df4955034638038b4b42/html5/thumbnails/14.jpg)
1000W Oven, Mode stirrer, Averaged: a=b=c=d=1
![Page 15: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051613/5515df4955034638038b4b42/html5/thumbnails/15.jpg)
Thermal image of cross section after 3 minutes heating
![Page 16: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051613/5515df4955034638038b4b42/html5/thumbnails/16.jpg)
1000W Point Temperatures
![Page 17: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051613/5515df4955034638038b4b42/html5/thumbnails/17.jpg)
1000W Moisture Loss
![Page 18: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051613/5515df4955034638038b4b42/html5/thumbnails/18.jpg)
Turntable oven, thermal image taken after 5 minutes heating
![Page 19: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051613/5515df4955034638038b4b42/html5/thumbnails/19.jpg)
750W turntable oven,a=b=1, c=d=0.5*(1+cos2(ωx))
![Page 20: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051613/5515df4955034638038b4b42/html5/thumbnails/20.jpg)
Moisture loss
![Page 21: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051613/5515df4955034638038b4b42/html5/thumbnails/21.jpg)
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
![Page 22: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051613/5515df4955034638038b4b42/html5/thumbnails/22.jpg)
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.