MATHEMATICAL MODELING OF FILTRATION COMBUSTION IN A WET POROUS MEDIUM CONSIDERING TEMPERATURE-DEPENDENT

Abstract:

This research delved into examining the impact of temperature-dependent thermal conductivity and diffusion coefficients on filtration combustion within a moist porous medium. The presented model, predicated on a series of assumptions and rooted in the conservation principles of total mass, chemical species, and energy under transient state conditions, governed the observed phenomenon. The existence of a unique solution to the problem was explored through an actual solution method. Subsequently, the solution’s properties were thoroughly investigated.

The intertwined nonlinear governing equations, governing the temperature and concentration fields, were analytically solved using methods such as parameter expansion, direct integration, and eigenfunction expansion. The investigation scrutinized the influence of dimensionless parameters, including scaled thermal conductivity, species diffusion coefficient, and the Frank-Kamenetskii parameter (Peclet mass number), on filtration combustion. The thesis concluded that the maximum temperature is reached at a point where the scaled thermal conductivity equals 0.5 for a fixed time, t.

Simulation results uncovered the creation of a high-temperature front due to combustion. Moreover, the molar fractions of oxygen, vapor, and passive gas, as well as the molar concentrations of solid fuel and liquid, exhibited considerable dependence on the values of the involved parameters.