arXiv subjects

Julieta Bollati

Publications and source records attributed to Julieta Bollati.

23 records · Page 2Linked to original sources

arXiv2018

Exact solution for a two-phase Stefan problem with variable latent heat and a convective boundary condition at the fixed face

Recently it was obtained in [Tarzia, Thermal Sci. 21A (2017) 1-11] for the classical two-phase Lamé-Clapeyron-Stefan problem an equivalence between the temperature and convective boundary conditions at the fixed face under a certain restriction. Motivated by this article we study the two-phase Stefan problem for a semi-infinite material with a latent heat defined as a power function of the position and a convective boundary condition at the fixed face. An exact solution is constructed using Kummer functions in case that an inequality for the convective transfer coefficient is satisfied generalizing recent works for the corresponding one-phase free boundary problem. We also consider the limit to our problem when that coefficient goes to infinity obtaining a new free boundary problem, which has been recently studied in [Zhou-Shi-Zhou, J. Engng. Math. (2017) DOI 10.1007/s10665-017-9921-y].

math-ph↗

arXiv2018

Heat balance integral methods applied to the one-phase Stefan problem with a convective boundary condition at the fixed face

In this paper we consider a one-dimensional one-phase Stefan problem corresponding to the solidification process of a semi-infinite material with a convective boundary condition at the fixed face. The exact solution of this problem, available recently in the literature, enable us to test the accuracy of the approximate solutions obtained by applying the classical technique of the heat balance integral method and the refined integral method, assuming a quadratic temperature profile in space. We develop variations of these methods which turn out to be optimal in some cases. Throughout this paper, a dimensionless analysis is carried out by using the parameters: Stefan number (Ste) and the generalized Biot number (Bi). In addition it is studied the case when Bi goes to infinity, recovering the approximate solutions when a Dirichlet condition is imposed at the fixed face. Some numerical simulations are provided in order to estimate the errors committed by each approach for the corresponding free boundary and temperature profiles.

math.AP↗

arXiv2017

Mathematical model for acid water neutralization with anomalous and fast diffusion

In this paper we model the neutralization of an acid solution in which the hydrogen ions are transported according to Cattaneo's diffusion. The latter is a modification of classical Fickian diffusion in which the flux adjusts to the gradient with a positive relaxation time. Accordingly the evolution of the ions concentration is governed by the hyperbolic telegraph equation instead of the classical heat equation. We focus on the specific case of a marble slab reacting with a sulphuric acid solution and we consider a one-dimensional geometry. We show that the problem is multi-scale in time, with a reaction time scale that is larger than the diffusive time scale, so that the governing equation is reduced to the one-dimensional wave equation. The mathematical problem turns out to be a hyperbolic free boundary problem where the consumption of the slab is described by a nonlinear differential equation. Global well posedness is proved and some numerical simulations are provided.

physics.chem-ph↗

arXiv2017

One-phase Stefan problem with a latent heat depending on the position of the free boundary and its rate of change

From the one-dimensional consolidation of fine-grained soils with threshold gradient, it can be derived a special type of Stefan problems where the seepage front, due to the presence of this threshold gradient, exhibits the features of a moving boundary. In this kind of problems, in contrast with the classical Stefan problem, the latent heat is considered to depend inversely with the rate of change of the seepage front. In this paper a one-phase Stefan problem with a latent heat that not only depends on the rate of change of the free boundary but also on its position is studied. The aim of this analysis is to extend prior results, finding an analytical solution that recovers, by specifying some parameters, the solutions that have already been examined in the literature regarding Stefan problems with variable latent heat. Computational examples will be presented in order to examine the effect of this parameters on the free boundary.

math.AP↗

arXiv2016

Explicit solution for Stefan problem with latent heat depending on the position and a convective boundary condition at the fixed face using Kummer functions

An explicit solution of a similarity type is obtained for a one-phase Stefan problem in a semi-infinite material using Kummer functions. Motivated by [D.A. Tarzia, Relationship between Neumann solutions for two phase Lamé-Clapeyron-Stefan problems with convective and temperature boundary conditions, Thermal Sci.(2016) DOI 10.2298/TSCI 140607003T, In press], and [Y. Zhou, L.J. Xia, Exact solution for Stefan problem with general power-type latent heat using Kummer function, Int. J. Heat Mass Transfer, 84 (2015) 114-118], we consider a phase-change problem with a latent heat defined as a power function of the position with a non-negative real exponent and a convective boundary condition at the fixed face $x=0$. Existence and uniqueness of the solution is proved. Relationship between this problem and the problems already solved by Zhou and Xia with temperature and flux boundary condition is analysed. Furthermore it is studied the limit behaviour of the solution when the coefficient which characterizes the heat transfer at the fixed boundary tends to infinity. Numerical computation of the solution is done over certain examples, with a view to comparing this results with those obtained by general algorithms that solve Stefan problems.

math.AP↗