Gelfand-type problem for two-phase porous media

Area of Science:

• Chemical Engineering
• Materials Science
• Thermodynamics

Background:

• The Gelfand problem is a key model in Frank-Kamenetskii theory for thermal explosion.
• Classical models often use a single temperature, which is insufficient for multi-phase systems.
• Two-phase materials require distinct temperature descriptions for accurate modeling.

Purpose of the Study:

• To generalize the Gelfand problem for two-phase materials.
• To analyze the conditions leading to thermal explosion in these systems.
• To investigate the effect of interphase heat exchange on explosion dynamics.

Main Methods:

• Mathematical modeling of thermal processes in two-phase media.
• Analysis of stationary temperature distributions.
• Asymptotic analysis in the limit of infinite interphase heat exchange.

Main Results:

• Thermal explosion in two-phase systems is driven by the absence of stationary temperature states.
• Interphase heat exchange acts as a delaying factor for thermal explosion.
• Under conditions of infinite interphase heat exchange, the problem simplifies to the classical Gelfand problem with modified constants.

Conclusions:

• The study extends thermal explosion theory to two-phase materials.
• Interphase heat exchange significantly influences the onset and dynamics of thermal explosion.
• The findings provide a theoretical basis for understanding thermal safety in composite materials.