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Maths Makes Crispier Cereals

Dr Mark McGuinness

Mathematicians in New Zealand and Australia have been tackling how to improve the cooking of cereal grains, for better taste and crispiness of breakfast cereals.

Uncle Tobys in Melbourne brought this problem to the 1996 Mathematics in Industry Study Group. Applied mathematicians at Victoria University have been working on the intriguing task.

Whole grains are cooked in huge rotating steam pressure cookers. They swell and burst, due to both heat and moisture penetration, and provide the raw material for drying, rolling, toasting and packaging into breakfast cereals. It is important that the whole grains are completely and accurately cooked. Over-cooking gives a cereal that quickly goes soggy in milk.

The problem is that the grains cook from the outside first, so that by the time the centre of a grain is cooked, the outer regions are over-cooked. The task of the mathematicians was to produce mathematical models of the way heat and moisture penetrate a single grain, under different heating conditions, for different grain types and sizes.

A key result that the mathematicians came up with was that heat penetrates the grain much more rapidly than moisture, so the pressure cooking process is bottle-necked by waiting for the moisture to get into the grain. In fact, the cooking of the whole grains is itself a bottleneck in the factory, which should be eased by soaking the grains before heating.

Not only will this reduce the time needed to heat the grains, but it will allow better control of the cooking process, since heat penetrates so quickly that cooking is practically uniform throughout the grain, provided enough moisture is present.

The mathematics involved is at several levels. Heat transport is governed by a relatively simple linear conduction equation, which is easily solved exactly for a variety of grain geometries.

Moisture transport, however, is modelled by a nonlinear conduction equation, with temperature-dependent conductivity. This may be further complicated by accounting for the effects of the swelling of the grain as it gets wetter. The equations that model moisture transport have been tackled in three ways: by using computers to solve them numerically; by using asymptotic methods to solve them analytically but approximately; and by using a tricky method called Mean Action Time to solve exactly.

The price paid in using Mean Action Time is that it does not reveal every detail about what is happening, just an averaged view of the wetting process. Results have led to a paper to be published in the IMA Journal of Mathematics Applied to Business and Industry. The study of this moisture transport problem is ongoing.

The outcome of all this, besides a bunch of applied mathematicians having lots of fun trying to solve real problems, is that Uncle Tobys have initiated a major study of their cereal cooking processes, purchasing equipment and funding further engineering and mathematical studies. They are building on theseresults to help improve and modernise the way they put the snap, crackle and pop onto your breakfast table.

Dr Mark McGuinness is with the School of Mathematical and Computing Sciences at Victoria University