Gelfand-type problem for two-phase porous media

We consider a generalization of the Gelfand problem arising in Frank-Kamenetskii theory of thermal explosion. This generalization is a natural extension of the Gelfand problem to two-phase materials, where, in contrast to the classical Gelfand problem which uses a single temperature approach, the state of the system is described by two different temperatures. We show that similar to the classical Gelfand problem the thermal explosion occurs exclusively owing to the absence of stationary temperature distribution. We also show that the presence of interphase heat exchange delays a thermal explosion. Moreover, we prove that in the limit of infinite heat exchange between phases the problem of thermal explosion in two-phase porous media reduces to the classical Gelfand problem with renormalized constants.

Studies on the Effects of Interphase Heat Exchange during Thermal Explosion in a Combustible Dusty Gas with General Arrhenius Reaction-Rate Laws

A mathematical model for thermal explosion in a combustible dusty gas containing fuel droplets with general Arrhenius reaction-rate laws, convective and radiative heat losses, and interphase heat exchange between gas and inert solid particles is investigated. The objective of the study is to examine the effects of interphase heat exchange between the gas and solid particles on (i) ignition of reacting gas, (ii) accumulation of heat by the solid particles during combustion process (iii) evaporation of the liquid fuel droplets, and (iv) consumption of reacting gas concentration. The equations governing the physical model with realistic assumptions are stated and nondimensionalised leading to an intractable system of first-order coupled nonlinear differential equations, which is not amenable to exact methods of solution. Therefore, we present numerical solutions as well as different qualitative effects of varying interphase heat exchange parameter. Graphs and Table feature prominently to explain the results obtained.

Investigation of a wave impulse passing from a gas into a saturated porous medium

The reflection of the wave pulse from the gas-porous medium boundary is studied. The cases of ”open“ and ”closed“ boundaries of a porous medium are considered. The dependence of the reflection coefficient of the incident pulse on the pore sizes and the interphase heat exchange is taken into account.

A Heuristic Evaluation of the Governing Mode of Heat Transfer in a Liquid–Liquid Spray Column

A steady-state one-dimensional multiphase flow model is developed to describe the characteristics of a spray column type direct-contact liquid–liquid heat exchanger. Several models are assumed to describe the interphase heat exchange between water as the continuous phase and organic liquids as the dispersed phase. For small-diameter droplets, it is shown that existing experimental data are best described by a model that assumes the heat transfer is controlled by conduction within the drops.