Biological self-heating in industrial compost piles: A modelling case study




spontaneous combustion; compost; non-linear differential equation


We consider a simple 'toy model' for the spontaneous combustion of industrial compost stockpiles. The model is a scalar non-linear differential equation which can be analysed using techniques taught in an introductory subject on non-linear ordinary differential equations. This model was used as a case study in a third year subject. We discuss how students approached some of the questions. Could they transfer their prior knowledge about differential equations to an industrial case study? How would they cope with a problem which required both pen-and-paper and numerical calculations? Students used a variety of approaches but the worked solutions only showed one. It would be beneficial for students to see that there is not one correct method to solve such problems.

  • B. Barnes and G. R. Fulford. Mathematical modelling with case studies: Using Maple and Matlab. Third edition. CRC Press, 2015. doi: 10.1201/b17896
  • M. I. Nelson, E. Balakrishnan, and X. D. Chen. A Semenov model of self-heating in compost piles. In: Process Safety Environ. Protect. 81 (2003), pp. 375–383. doi: 10.1205/095758203770224414





Proceedings Engineering Mathematics and Applications Conference