A mathematical model for change of phase is presented, accounting for the presence of regions in which liquid and solid coexist. The basic variables are temperature θ and solid fraction v . We start from a relationship of the type θ = θ ( v ), supposed valid in thermodynamical equilibrium. Then for dynamical processes we introduce a perturbation causing v to be less than its equilibrium value in any solidification process. This solid fraction deficiency is governed by an ordinary differential equation containing θ t , in the forcing term. The heat-balance equation is in turn coupled to the ordinary differential equation through the term λ v t , (λ is latent heat). Some existence and uniqueness results are proved and some monotonicity properties are described for pure melting or pure solidification processes.

A phase-change model with a zone of coexistence of phases / A. FASANO; PRIMICERIO M.. - In: IMA JOURNAL OF APPLIED MATHEMATICS. - ISSN 0272-4960. - STAMPA. - 41:(1988), pp. 31-46. [10.1093/imamat/41.1.31]

### A phase-change model with a zone of coexistence of phases

#### Abstract

A mathematical model for change of phase is presented, accounting for the presence of regions in which liquid and solid coexist. The basic variables are temperature θ and solid fraction v . We start from a relationship of the type θ = θ ( v ), supposed valid in thermodynamical equilibrium. Then for dynamical processes we introduce a perturbation causing v to be less than its equilibrium value in any solidification process. This solid fraction deficiency is governed by an ordinary differential equation containing θ t , in the forcing term. The heat-balance equation is in turn coupled to the ordinary differential equation through the term λ v t , (λ is latent heat). Some existence and uniqueness results are proved and some monotonicity properties are described for pure melting or pure solidification processes.
##### Scheda breve Scheda completa Scheda completa (DC)
1988
41
31
46
A. FASANO; PRIMICERIO M.
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Utilizza questo identificatore per citare o creare un link a questa risorsa: `https://hdl.handle.net/2158/209679`
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