Gas-phase and heat-exchange effects on the ignition of high- and low-exothermicity porous solids subject to constant heating

This article investigates the ignition of low-exothermicity reactive porous solids exposed to a maintained source of heat (hotspot), without oxygen limitation. The gas flow within the solid, particularly in response to pressure gradients (Darcy’s law), is accounted for. Numerical experiments related to the ignition of low-exothermicity porous materials are presented. Gas and solid products of reaction are included. The first stage of the paper examines the (pseudo-homogeneous) assumption of a single temperature for both phases, amounting to an infinite rate of heat exchange between the two. Isolating the effect of gas production and flow in this manner, the effect of each on the ignition time is studied. In such cases, ignition is conveniently defined by the birth of a self-sustained combustion wave. It is found that gas production decreases the ignition time, compared to equivalent systems in which the gas-dynamic problem is effectively neglected. The reason for this is quite simple; the smaller heat capacity of the gas allows the overall temperature to attain a higher value in a similar time, and so speeds up the ignition process. Next, numerical results using a two-temperature (heterogeneous) model, allowing for local heat exchange between the phases, are presented. The pseudo-homogeneous results are recovered in the limit of infinite heat exchange. For a finite value of heat exchange, the ignition time is lower when compared to the single-temperature limit, decreasing as the rate of heat exchange decreases. However, the decrease is only mild, of the order of a few percent, indicating that the pseudo-homogeneous model is in fact a rather A. A. Shah (B) · J. Brindley Applied Mathematics Department, Leeds University, Leeds LS29JT, UK e-mail: [email protected] Present Address: A. A. Shah Department of Mathematics, Simon Fraser University, 8888 University Drive, B.C. Canada V5A 1S6 A. C. McIntosh SPEME, Leeds University, Leeds LS29JT, UK J. Griffiths School of Chemistry, Leeds University, Leeds LS29JT, UK 162 J Eng Math (2006) 56:161–177 good approximation, at least for a constant heat-exchange rate. The relationships between the ignition time and a number of physico-chemical parameters of the system are also investigated.