Mathematical model of exothermal hydride formation

We construct the model of hydride composition. A single symmetrical metal powder particle is considered. Heat releasing and sorption effects are taken into consideration. We analyze the effect of a few concurrent processes. Stages of metal saturation with hydrogen, skin appearance, “contracting envelope”, and final saturation of hydride up to the equilibrium concentration are described by the appropriate mathematical constructions. These are systems of ordinary differential equations and non-classical boundary-value problems with moving bound for the diffusion equation. Due to symmetry of the particle we can consider only one spatial variable. For the boundary-value problems we present a lattice numerical method and prove its convergence to a weak solution to the problem; therefore its existence is proved. Results of some numerical experiments are presented as an illustration; we show that the shape of the powder particles do not influence much on the sorption and heat releasing rates.