A simple model for the propagation of a combustion wave is proposed and the speed of propagation is predicted. It is assumed that the reactant ignites at a specified temperature and then burns until depleted with reaction rate dependent on temperature and reactant concentration. The exact solution and linear stability are determined in the case of constant heat generation and a numerical scheme is developed to generate traveling wave solutions in the more general case. This numerical method is applied to the case where the temperature dependence of the reaction rate is modeled by the Arrhenius function.

The steady-state heating of a two-dimensional slab by the TE10 mode in a microwave cavity is considered. The cavity contains an iris with a variable aperture and is closed by a short. Resonance can occur in the cavity, which is dependent on the short position, the aperture width and the temperature of the heated slab.

The governing equations for the slab are steady-state versions of the forced heat equation and Maxwell's equations while fixed-temperature boundary conditions are used. An Arrhenius temperature dependency is assumed for both the electrical conductivity and the thermal absorptivity. Semi-analytical solutions, valid for small thermal absorptivity, are found for the steady-state temperature and the electric-field amplitude in the slab using the Galerkin method.

With no-iris (a semi-infinite waveguide) the usual S-shaped power versus temperature curve occurs. As the aperture width is varied however, the critical power level at which thermal runaway occurs and the temperature response on the upper branch of the S-shaped curve are both changed. This is due to the interaction between the radiation, the cavity and the heated slab. An example is presented to illustrate these aperture effects. Also, it is shown that an optimal aperture setting and short position exists which minimises the input power needed to obtain a given temperature.

In a recent paper Weber et al. [9] examined the propagation of combustion waves in a semi-infinite gaseous or solid medium. Whereas their main concern was the behaviour of waves once they had been initiated, we concentrate here on the initiation of such waves in a solid medium and have not examined in detail the steadiness or otherwise of the waves subsequent to their formation. The investigation includes calculations for finite systems. The results for a slab, cylinder and sphere are compared.

Critical conditions for initiation of ignition by a power source are established. For a slab the energy input is spread uniformly over one boundary surface. In the case of cylindrical or spherical symmetry it originates from a cylindrical core or from a small, central sphere, respectively. The size of source and reactant body is important in the last two cases. With the exception of the initial temperature distribution, the equations investigated are similar in form to those of Weber et al. [5,9] and, as a prelude to the present study, with very simple adaptation, it has been possible to reproduce the results of the earlier work. We then go on to report the result of calculations for the initiation of ignition under different geometries with various initial and boundary conditions.

Self-heating in packed paniculate that is exothermically reactive is a major cause of fire and explosion in the powder industry. This study is focused on part of the Auckland development of a mathematical model dealing with this hazardous process in industry using milk powder as an example. Milk powder is a primary powdered food product around the world.

An update of the detailed mathematical model is given here, and predictions are made using the model to simulate the basket-heating behaviour of a milk powder in the laboratory (so the model can thus be validated). Basket heating in an oven is a standard laboratory technique for measuring the exothermic reactivity of a solid material.

After a favorable comparison with the laboratory results, several aspects of basket-heating were investigated with a view to further improving the technique. Firstly, the model was used to explore the effect of elevated ambient humidity and initial sample water content upon the heating process in the basket. Secondly, the model was used to explore the cross over phenomenon which is related to a novel procedure for measuring activation energy and exothermicity (that is, the Crossing-Point-Temperature (CPT) method, which is a new version of the basket heating technique). The predictions together with the experimental evidence show that the reaction kinetics obtained using the Heat Release (HR) method (another version of the basket heating technique well published in the literature) may not be correct, especially for those measured at elevated oven temperatures and for larger basket sizes. Thirdly, simulations were performed to illustrate that the CPT phenomenon does not just occur at the center of the basket but also occurs everywhere else in the sample. This can become a significant advantage for further development of the CPT method in terms of reducing experimental duration and improving reproducibility.