Adriana C. Briozzo

Determination of unknown thermal coefficients for Storm's-type materials through a phase-change process

Abstract Unknown thermal coefficients of a semi-infinite material of Storm’s type through a phase-change process with an overspecified condition on the fixed face are determined. We follow the ideas developed in C. Rogers (Int. J. Non-Linear Mech. 21 (1986) 249–256) and in Tarzia (Adv. Appl. Math. 3 (1982) 74–82; Int. J. Heat Mass Transfer 26 (1983) 1151–1157). We also find formulae for the unknown coefficients and, the necessary and sufficient conditions for the existence of a similarity solution.

Explicit solution of a free boundary problem for a nonlinear absorption model of mixed saturated-unsaturated flow

In wet soils, zones of saturation naturally develop in the vicinity of impermeable strata, surface ponds and subterranean cavities. Hydrology must be then concerned with transient flow through coexisting unsaturated and saturated zones. The models of advancing saturated zones necessarily involve a nonlinear free boundary problem. A closed-form analytic solution is presented for a nonlinear diffusion model under conditions of ponding at the surface. The soil water diffusivity is restricted to the special functional form D(θ) = a(b − θ)2, where θ is the water content field to be determined and a, b are positive constants. The explicit solution depends on a parameter C (determined by the data of the problem), according to two cases: 1 < C < C1 or C ≥ C1, where C1 is a constant which is obtained as the unique solution of an equation. This result complements the study given in P. Broadbridge, Water Resources Research, 1990, 26, 2435–2443, in order to established when the explicit solution is available. The behavior of the bifurcation parameter C1 as a function of the driving potential is studied with the corresponding limits for small and large values. Moreover, the sorptivity is proven to be continuously differentiable function of the variable C.

A one-phase Stefan problem for a non-classical heat equation with a heat flux condition on the fixed face

We prove the existence and uniqueness, local in time, of the solution of a one-phase Stefan problem for a non-classical heat equation for a semi-infinite material with a heat flux boundary condition at the fixed face x=0. Here the heat source depends on the temperature at the fixed face x=0. We use the Friedman-Rubinstein integral representation method and the Banach contraction theorem in order to solve an equivalent system of two Volterra integral equations.

Exact Solutions for Nonclassical Stefan Problems

We consider one-phase nonclassical unidimensional Stefan problems for a source function which depends on the heat flux, or the temperature on the fixed face . In the first case, we assume a temperature boundary condition, and in the second case we assume a heat flux boundary condition or a convective boundary condition at the fixed face. Exact solutions of a similarity type are obtained in all cases.

One-phase Stefan problem with temperature-dependent thermal conductivity and a boundary condition of Robin type

Abstract We study a one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conductivity with a boundary condition of Robin type at the fixed face x = 0. We obtain sufficient conditions for data in order to have a parametric representation of the solution of similarity type for t ≥ t0 > 0 with t0 an arbitrary positive time. This explicit solution is obtained through the unique solution of an integral equation with the time as a parameter.

A Stefan problem for a non-classical heat equation with a convective condition

We prove the existence and uniqueness, local in time, of the solution of a one-phase Stefan problem for a non-classical heat equation for a semi-infinite material with a convective boundary condition at the fixed face x = 0. Here the heat source depends on the temperature at the fixed face x = 0 that provides a heating or cooling effect depending on the properties of the source term. We use the Friedman–Rubinstein integral representation method and the Banach contraction theorem in order to solve an equivalent system of two Volterra integral equations. We also obtain a comparison result of the solution (the temperature and the free boundary) with respect to the one corresponding with null source term.

Existence, Uniqueness and an Explicit Solution for a One-Phase Stefan Problem for a Non-classical Heat Equation

Existence and uniqueness, local in time, of the solution of a one-phase Stefan problem for a non-classical heat equation for a semi-infinite material is obtained by using the Friedman-Rubinstein integral representation method through an equivalent system of two Volterra integral equations. Moreover, an explicit solution of a similarity type is presented for a non-classical heat source depending on time and heat flux on the fixed face x = 0.