Global existence for a hydrogen storage model with full energy balance

Abstract

A thermo-mechanical model describing hydrogen storage by use of metal hydrides has been recently proposed in [4] describing the formation of hydrides using the phase transition approach. By virtue of the laws of continuum thermo-mechanics, the model leads to a phase transition problem in terms of three state variables: the temperature, the phase parameter representing the fraction of one solid phase, and the pressure, and is derived within a generalization of the principle of virtual powers proposed by Frémond [11], accounting for micro-forces, responsible for the phase transition, in the whole energy balance of the system. Three coupled nonlinear partial differential equations combined with initial and boundary conditions have to be solved. The main difficulty in investigating the resulting system of partial differential equations relies on the presence of the squared time derivative of the order parameter in the energy balance equation, and actually this term was neglected in the analysis performed in [4]. Here, the global existence of a solution to the full problem is proved by exploiting known and sharp estimates on parabolic equations with right hand side in L 1 . Some complementary results on stability and steady state solutions are also given.

Thermomechanics of damageable materials under diffusion: modelling and analysis

“…[29]. Several continuum models have been proposed, accompanied by their analytical study [3,4,8,50]. Such big volume variation then often cause damage.…”

“…Poro-elastic model revisited) The poro-elastic example (3.12) does not comply with the second condition in (4.1d) unless λ, G, and M is independent of d. Also,(3…”

A phase transition model for the helium supercooling

“…In this concerning, we quote a recent result [2] obtained for a different kind of equations, accounting in the energy balance for the quadratic dissipative contribution (related to the time derivative of the phase parameter). The existence result is obtained by use of a Boccardo-Gallouet type technique.…”

Existence of Solutions for a Mathematical Model Related to Solid–Solid Phase Transitions in Shape Memory Alloys

“…Some of the authors of this article contributed to study the Frémond and other models for shape memory alloys (see, e.g., [10,11,13,16,17,19,21]). Concerning related phase transition models, we underline that a model for hydrogen storage in metal hydrides has been recently investigated in [12], by encountering the difficulty due to the term |∂ t χ | 2 in the energy balance equation, but for a simpler analytical form of the other equations. In the system studied in [12] the presence of the quadratic dissipative contribution |∂ t χ | 2 comes from a generalized form of the principle of virtual powers, accounting for micro-forces and micro-motions responsible for the phase transition.…”

“…Concerning related phase transition models, we underline that a model for hydrogen storage in metal hydrides has been recently investigated in [12], by encountering the difficulty due to the term |∂ t χ | 2 in the energy balance equation, but for a simpler analytical form of the other equations. In the system studied in [12] the presence of the quadratic dissipative contribution |∂ t χ | 2 comes from a generalized form of the principle of virtual powers, accounting for micro-forces and micro-motions responsible for the phase transition. Concerning phase change models with microscopic motions, there is a comprehensive literature originating from the Frémond theory [26,27].…”