Self-heating in compost piles due to biological effects

The increase in temperature in compost piles/landfill sites due to micro-organisms undergoing exothermic reactions is modelled. A simplified model is considered in which only biological self-heating is present. The heat release rate due to biological activity is modelled by a function which is a monotonic increasing function of temperature over the range 0 ≤ T ≤ a, whilst for T ≥ a it is a monotone decreasing function of temperature. This functional dependence represents the fact that micro-organisms die or become dormant at high temperatures. The bifurcation behaviour is investigated for 1-d slab and 2-d rectangular slab geometries. In both cases there are two generic steady-state diagrams including one in which the temperature-response curve is the standard S-shaped curve familiar from combustion problems. Thus biological self-heating can cause elevated temperature raises due to jumps in the steady temperature. This problem is used to test a recently developed semi-analytical technique. For the 2-d problem a four-term expansion is found to give highly accurate results-the error of the semi-analytical solution is much smaller than the error due to uncertainty in parameter values. We conclude that the semi-analytical technique is a very promising method for the investigation of bifurcations in spatially distributed systems.