E. Balakrishnan

A SEMENOV MODEL OF SELF-HEATING IN COMPOST PILES

In this paper we model the thermal behaviour of cellulosic materials in the presence of micro-organisms undergoing exothermic reactions. For simplicity we consider a spatially uniform model which is based upon Semenovs theory for thermal explosions. The singularity theory has been used to investigate the generic properties of the model. We consider first the case in which chemical reactions are absent, which represents heat generation in low-oxygen-containing environments. Here we show that 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 jumps in the steady temperature. We then investigate the full model, which is shown to have three generic steady-state diagrams. If the energy released from the chemical reaction is sufficiently small, then the steady-state diagram may contain an elevated temperature branch, which is the feature of practical interest in facilities such as industrial compost heaps and municipal tips. If the chemical reaction is too strong the energy released by biological action increases the local temperature sufficiently high that spontaneous ignition of the cellulosic material occurs. For a given degree of chemical activity it is possible to predict the biological activity at which combustion is initiated.

A fundamental analysis of continuous flow bioreactor and membrane reactor models with tessier kinetics

In this research we analyze the steady-state operation of a continuous flow bioreactor, with or without recycle, and an idealized or nonidealized continuous flow membrane reactor. The model extends to include a fixed bed reactor where a fraction of the biomass is detached by the flow. The reaction is assumed to be governed by Tessier growth kinetics. We show that a flow reactor with idealized recycle has the same performance as an idealized membrane reactor and that the performance of a nonidealized membrane reactor is identical to that of an appropriately defined continuous flow bioreactor with nonidealized recycle. The performance of all three reactor types can therefore be obtained by analyzing a flow reactor with recycle. The steady states of the recycle model are found and their stability determined as a function of the residence time. The performance of the reactor at large residence times is obtained.

THE MULTIPLICITY OF STEADY-STATE SOLUTIONS ARISING FROM MICROWAVE HEATING. I. INFINITE BIOT NUMBER AND SMALL PENETRATION DEPTH

Microwave heating of porous solid materials has received considerable attention in recent years because of its widespread use in industry. In this study, the microwave power absorption term is modelled as the product of an exponential temperature function with a function that decays exponentially with distance. The latter describes the penetration of the material by the microwaves. We investigate the phenomena of multiplicity in class A geometries, paying particular attention to how the penetration function affects the behaviour of the system. We explain why the phase-plane techniques which have been used in the case when the penetration term is constant do not extend to non-constant penetration.

Microwave assisted ignition to achieve combustion synthesis

The use of microwave heating to initiate combustion synthesis has been increasingly investigated in recent years because of its advantages over traditional methods. A simple mathematical model is used to model these experiments. The microwave power absorption term is modelled as the product of an Arrhenius reaction term with a function that decays exponentially with distance. The former represents the temperature-dependent absorption of the microwaves whereas the latter describes the penetration of the material by the microwaves. Combustion kinetics are modelled as a first-order Arrhenius reaction.

An analysis of a standard reactor cascade and a step- feed reactor cascade for biological processes described by monod kinetics

Abstract We analyse the steady-state operation of two types of reactor cascade without recycle. The first is a standard reactor cascade in which the feed stream enters into the first reactor. The second is a step-feed reactor cascade in which an equal proportion of the feed stream enters each reactor in the cascade. The reaction is assumed to be a biological process governed by Monod growth kinetics with a decay coefficient for the microorganisms. The steady-states of both models are found for an arbitrary number of reactors and their stability determined as a function of the residence time. We show that in a step-feed reactor cascade the substrate and biomass concentrations leaving the reactor of the cascade are identical to those leaving the first reactor of the cascade. We further show that this result is true for a general specific growth rate of the form μ (S,X). Thus for such processes the non-standard cascade offers no advantage over that of a single reactor. This is surprising because the use of a non-standard cascade has been proposed as a mechanism to improve the biological treatment of wastewater.

Radiative ignition of combustible materials I. Polymeric materials undergoing nonflaming thermal degradation-the critical storage problem

The critical storage problem for a self-heating combustible material exposed to an external radiative heat source is investigated. The reaction kinetics are denied in terms of a characteristic temperature and an activation energy, linking small-scale experimental techniques to mediumscale flarmmability tests. The model is nondimensionalised in such a way that material properties of fundamental interest are retained as distinct continuation parameters.