Preface

The following case study develops several models to help understand how to uniformly and accurately cook whole grains for the manufacture of breakfast cereals. During the cooking process, heat and moisture must enter the grain. These two transport processes are modelled by diffusion equations. Linear diffusion is appropriate for the heat transport. A nonlinear diffusion model is examined for the more complex process of water uptake in the grain. The times to heat and wet the grain can be estimated using both numerical and analytic approaches. The mean action time proves to be a very powerful way of estimating the speed of the wetting front. The degree of overcooking in the present manufacturing process can also be estimated. Finally, some recommendations for improving the cooking process are suggested.

The work outlined here was part of the analysis carried out at the 1996 Mathematics-in-Industry Study Group at the University of Melbourne, Australia. Some extensions of the work have been carried out by various groups ([3], [5]). Only the basic analysis is presented here; extensions are suggested as projects. The collaboration with the company is ongoing.

Introduction

Starch crops, such as cereals, pulses, and tubers, account for over half the total food produced and consumed in the world. Humans find it easiest to digest starch after it has been cooked. The application of both heat and moisture to starch causes it to gelatinise – this allows the starch to be able to be digested by enzymes.

The cooking of intact whole grains (e.g. wheat, corn, rice) is industrially important in breakfast cereal manufacture.