Maria Fernanda Natale - Academia.edu (original) (raw)

Papers by Maria Fernanda Natale

Research paper thumbnail of An exact solution for a one-phase Stefan problem with nonlinear thermal coefficient

Research paper thumbnail of Approximate solutions to the one-phase Stefan problem with non-linear temperature-dependent thermal conductivity

arXiv (Cornell University), Feb 25, 2019

In this chapter we consider different approximations for the onedimensional one-phase Stefan prob... more In this chapter we consider different approximations for the onedimensional one-phase Stefan problem corresponding to the fusion process of a semi-infinite material with a temperature boundary condition at the fixed face and non-linear temperature-dependent thermal conductivity. The knowledge of the exact solution of this problem, allows to compare it directly with the approximate solutions obtained by applying the heat balance integral method, an alternative form to it and the refined balance integral method, assuming a quadratic temperature profile in space. In all cases, the analysis is carried out in a dimensionless way by the Stefan number (Ste) parameter.

Research paper thumbnail of An integral equation in order to solve a one-phase Stefan problem with nonlinear thermal conductivity

MAT Serie A, 2004

We study a one-phase Stefan problem for a semi-in¯nite material with temperaturedependent thermal... more We study a one-phase Stefan problem for a semi-in¯nite material with temperaturedependent thermal conductivity with a constant temperature or a heat°ux condition of the type ¡q 0 = p t (q 0 > 0) at the¯xed face x = 0. We obtain in both cases su±cient conditions for data in order to have a parametric representation of the solution of the similarity type for t¸t 0 > 0 with t 0 an arbitrary positive time. These explicit solutions are obtained through the unique solution of an integral equation with the time as a parameter.

Research paper thumbnail of Simultaneous determination of two unknown thermal coefficients through an inverse one-phase Lamé-Clapeyron (Stefan) problem with an overspecified condition on the fixed face

International Journal of Heat and Mass Transfer, 1983

Formulas are obtained for the simultaneous determination oftwo of the four coefficients,k (therma... more Formulas are obtained for the simultaneous determination oftwo of the four coefficients,k (thermal conductivity),/ (latent heat of fusion), c (specific heat) , p (mass den sity), of a material occupying a semi-infinite medium. This determination is obtained through an inverse one-phase Lame-Clapeyron (Stefan) problem with an overspecified condition on the fixed face of the phase ch ange material. To so lve this problem, we assume th at the coefficients /'0,CT, 0 0 > 0 are known from experiments (where h o characterizes the heat flux through the fixed face, CT characterizes the mo ving boundary and 0 0 is the temperature on the fixed face). Denoting th e temperature by 0,the results we obtain concerning the associated moving boundary problem are the following : (i) When one of the triples {O,k,/}, {O,k,p} is to be found, the corresponding moving boundary problem always has a solution of the Lame-Clapeyron-Neumann typ e. (ii) If one of the triples {O,k,e}, {O,/,e}, {O,/,p}, and {O,c,p} has to be determined , the above property is satisfied if and only if a complementary condition for the data is verified, Formulas are also obtained for the simult aneous determination of other physical coefficients a nd the inequality~2 < Slej2(Ste :Stefan number) for the coefficient~of the free boundary 5(t) = 2a~t 1/2 of the Lame-Clapeyron solution of the one-phase Stefan problem without unknown coefficients.

Research paper thumbnail of Explicit solution for non-classical one-phase Stefan problem with variable thermal coefficients and two different heat source terms

A one-phase Stefan problem for a semi-infinite material is studied for special functional forms o... more A one-phase Stefan problem for a semi-infinite material is studied for special functional forms of the thermal conductivity and specific heat depending on the temperature of the phase-change material. Using the similarity transformation technique, an explicit solution for these situations are shown. The mathematical analysis is made for two different kinds of heat source terms, and the existence and uniqueness of the solutions are proved.

Research paper thumbnail of Integral balance methods applied to non-classical Stefan problems

Thermal Science, 2018

We consider two different Stefan problems for a semi-infinite material for the non-classical heat... more We consider two different Stefan problems for a semi-infinite material for the non-classical heat equation with a source that depends on the heat flux at the fixed face. One of them, with constant temperature at the fixed face, was already studied in literature and the other, with a convective boundary condition at the fixed face, is presented in this work. Due to the complexity of the exact solution it is of interest to compare with approximate solutions obtained by applying heat balance integral methods, assuming a quadratic temperature profile in space. A dimensionless analysis is carried out by using the parameters: Stefan number and the generalized Biot number. In addition it is studied the case when Biot number 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 verify the accuracy of the approximate methods.

Research paper thumbnail of Existence and uniqueness of the p-generalized modified error function

Electronic Journal of Differential Equations

In this article, we define a p-generalized modified error function as the solution to a non-linea... more In this article, we define a p-generalized modified error function as the solution to a non-linear ordinary differential equation of second order, with a Robin type boundary condition at x=0. We prove existence and uniqueness of a non-negative \(C^{\infty}\) solution by using a fixed point argument. We show that the p-generalized modified error function converges to the p-modified error function defined as the solution to a similar problem with a Dirichlet boundary condition. In both problems, for p=1, the generalized modified error function and the modified error function are recovered. In addition, we analyze the existence and uniqueness of solution to a problem with a Neumann boundary condition. For more information see https://ejde.math.txstate.edu/Volumes/2020/35/abstr.html

Research paper thumbnail of Analytical solution for a cylinder glaciation model with variable latent heat and thermal diffusivity

International Journal of Non-Linear Mechanics

Research paper thumbnail of Two Stefan problems for a non-classical heat equation with nonlinear thermal coefficients

Differential and Integral Equations

The mathematical analysis of two one-phase unidimensional and non-classical Stefan problems with ... more The mathematical analysis of two one-phase unidimensional and non-classical Stefan problems with nonlinear thermal coecients is obtained. Two related cases are considered, one of them has a temperature condition on the fixed face x = 0 and the other one has a flux condition of the type q0= p t (q0 > 0) : In the first case, the source function depends on the heat flux at the fixed face x = 0; and in the other case it depends on the temperature at the fixed face x = 0: In both cases, we obtain sufficient conditions in order to have the existence of an explicit solution of a similarity type, which is given by using a double fixed point.Fil: Briozzo, Adriana Clotilde. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Austral. Facultad de Cs.empresariales. Departamento de Matemáticas; ArgentinaFil: Natale, María Fernanda. Universidad Austral. Facultad de Cs.empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Research paper thumbnail of Two-phase Stefan problem with nonlinear thermal coefficients and a convective boundary condition

Authorea

We consider a non-linear two-phase unidimensional Stefan problem, which consists on a solidificat... more We consider a non-linear two-phase unidimensional Stefan problem, which consists on a solidification process, for a semi-infinite material x > 0, with phase change temperature T 1 , an initial temperature T 2 > T 1 and a convective boundary condition imposed at the fixed face x = 0 characterized by a heat transfer coefficient h > 0. We assume that the volumetric heat capacity and the thermal conductivity are particular nonlinear functions of the temperature in both solid and liquid phases and they verify a Storm-type relation. A certain inequality on the coefficient h is established in order to get an instantaneous phase change process. We determine sufficient conditions on the parameters of the problem in order to prove the existence and uniqueness of a parametric explicit solution for the Stefan problem.

Research paper thumbnail of On a two‐phase Stefan problem with convective boundary condition including a density jump at the free boundary

Mathematical Methods in the Applied Sciences, 2020

We consider a two‐phase Stefan problem for a semi‐infinite body with a convective boundary condit... more We consider a two‐phase Stefan problem for a semi‐infinite body with a convective boundary condition including a density jump at the free boundary with a time‐dependent heat transfer coefficient of the type , whose solution was given in D. A. Tarzia, PAMM. Proc. Appl. Math. Mech. 7, 1040307–1040308 (2007). We demonstrate that the solution to this problem converges to the solution to the analogous one with a temperature boundary condition when the heat transfer coefficient . Moreover, we analyze the dependence of the free boundary respecting to the jump density.

Research paper thumbnail of Existence and uniqueness of solution for two one-phase Stefan problems with variable thermal coefficients

Nonlinear Analysis: Real World Applications, 2020

One dimensional Stefan problems for a semi-infinite material with temperature dependent thermal c... more One dimensional Stefan problems for a semi-infinite material with temperature dependent thermal coefficients are considered. Existence and uniqueness of solution are obtained imposing a Dirichlet or a Robin type condition at fixed face x = 0. Moreover, it is proved that the solution of the problem with the Robin type condition converges to the solution of the problem with the Dirichlet condition at the fixed face. Computational examples are provided.

Research paper thumbnail of Non-classical Stefan problem with nonlinear thermal coefficients and a Robin boundary condition

Nonlinear Analysis: Real World Applications, 2019

A non-classical one dimensional Stefan problem with thermal coefficients temperature dependent an... more A non-classical one dimensional Stefan problem with thermal coefficients temperature dependent and a Robin type condition at fixed face x = 0 for a semi-infinite material is considered. The source function depends on the evolution the heat flux at the fixed face x = 0. Existence of a similarity type solution is obtained and the asymptotic behaviour of free boundary with respect to latent heat fusion is studied. The analysis of several particular cases are given.

Research paper thumbnail of The classical one-phase Stefan problem with temperature-dependent thermal conductivity and a convective term

MAT Serie A, 2008

We study a one-phase Stefan problem for a semi-infinite material with temperaturedependent therma... more We study a one-phase Stefan problem for a semi-infinite material with temperaturedependent thermal conductivity and a convective term with a constant temperature boundary condition or a heat flux boundary condition of the type −q 0 / √ t (q 0 > 0) at the fixed face x = 0. We obtain in both cases sufficient conditions for data in order to have a parametric representation of the solution of the similarity type for t ≥ t 0 > 0 with t 0 an arbitrary positive time. We improve the results given in

Research paper thumbnail of A one-phase Lamé-Clapeyron-Stefan problem with nonlinear thermal coefficients

Research paper thumbnail of An explicit solution for a two-phase Stefan problem with a similarity exponential heat sources

MAT Serie A, 2004

A two-phase Stefan problem with heat source terms in both liquid and solid phases for a semi-in¯n... more A two-phase Stefan problem with heat source terms in both liquid and solid phases for a semi-in¯nite phase-change material is considered. The internal heat source functions are given by g j (x; t) = (¡1) j+1 ½l t exp ³ ¡(x 2a j p t + d j) 2´(j = 1 solid phase; j = 2 liquid phase), ½ is the mass density, l is the fusion latent heat by unit of mass; a 2 j is the di®usion coe±cient, x is spatial variable, t is the temporal variable and d j 2 R. A similarity solution is obtained for any data when a temperature boundary condition is imposed at the¯xed face x = 0; when a°ux condition of the type ¡q 0 = p t (q 0 > 0) is imposed on x = 0 then there exists a similarity solution if and only if a restriction on q 0 is satis¯ed.

Research paper thumbnail of A nonlinear supercooled Stefan problem

Zeitschrift für angewandte Mathematik und Physik, 2017

We study the supercooled one-phase Stefan problem for a semi-infinite material with temperature-d... more We study the supercooled one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conductivity at the fixed face x = 0. We obtain sufficient conditions for data in order to have existence of a solution of similarity type, local in time and finite-time blow-up occurs. This explicit solution is obtained through the unique solution of an integral equation with the time as a parameter.

Research paper thumbnail of Nonlinear Stefan problem with convective boundary condition in Storm’s materials

Zeitschrift für angewandte Mathematik und Physik, 2016

We consider a nonlinear one-dimensional Stefan problem for a semi-infinite material x > 0, with p... more We consider a nonlinear one-dimensional Stefan problem for a semi-infinite material x > 0, with phase change temperature T f. We assume that the heat capacity and the thermal conductivity satisfy a Storm's condition and we assume a convective boundary condition at the fixed face x = 0. An unique explicit solution of similarity type is obtained. Moreover, asymptotic behavior of the solution when h → +∞ is studied.

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

Journal of Applied Analysis, 2015

We study a one-phase Stefan problem for a semi-infinite material with temperature-dependent therm... more 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 ≥ t 0 > 0 with t 0 an arbitrary positive time. This explicit solution is obtained through the unique solution of an integral equation with the time as a parameter.

Research paper thumbnail of Explicit solutions for a one-phase Stefan problem with temperature-dependent thermal conductivity

Research paper thumbnail of An exact solution for a one-phase Stefan problem with nonlinear thermal coefficient

Research paper thumbnail of Approximate solutions to the one-phase Stefan problem with non-linear temperature-dependent thermal conductivity

arXiv (Cornell University), Feb 25, 2019

In this chapter we consider different approximations for the onedimensional one-phase Stefan prob... more In this chapter we consider different approximations for the onedimensional one-phase Stefan problem corresponding to the fusion process of a semi-infinite material with a temperature boundary condition at the fixed face and non-linear temperature-dependent thermal conductivity. The knowledge of the exact solution of this problem, allows to compare it directly with the approximate solutions obtained by applying the heat balance integral method, an alternative form to it and the refined balance integral method, assuming a quadratic temperature profile in space. In all cases, the analysis is carried out in a dimensionless way by the Stefan number (Ste) parameter.

Research paper thumbnail of An integral equation in order to solve a one-phase Stefan problem with nonlinear thermal conductivity

MAT Serie A, 2004

We study a one-phase Stefan problem for a semi-in¯nite material with temperaturedependent thermal... more We study a one-phase Stefan problem for a semi-in¯nite material with temperaturedependent thermal conductivity with a constant temperature or a heat°ux condition of the type ¡q 0 = p t (q 0 > 0) at the¯xed face x = 0. We obtain in both cases su±cient conditions for data in order to have a parametric representation of the solution of the similarity type for t¸t 0 > 0 with t 0 an arbitrary positive time. These explicit solutions are obtained through the unique solution of an integral equation with the time as a parameter.

Research paper thumbnail of Simultaneous determination of two unknown thermal coefficients through an inverse one-phase Lamé-Clapeyron (Stefan) problem with an overspecified condition on the fixed face

International Journal of Heat and Mass Transfer, 1983

Formulas are obtained for the simultaneous determination oftwo of the four coefficients,k (therma... more Formulas are obtained for the simultaneous determination oftwo of the four coefficients,k (thermal conductivity),/ (latent heat of fusion), c (specific heat) , p (mass den sity), of a material occupying a semi-infinite medium. This determination is obtained through an inverse one-phase Lame-Clapeyron (Stefan) problem with an overspecified condition on the fixed face of the phase ch ange material. To so lve this problem, we assume th at the coefficients /'0,CT, 0 0 > 0 are known from experiments (where h o characterizes the heat flux through the fixed face, CT characterizes the mo ving boundary and 0 0 is the temperature on the fixed face). Denoting th e temperature by 0,the results we obtain concerning the associated moving boundary problem are the following : (i) When one of the triples {O,k,/}, {O,k,p} is to be found, the corresponding moving boundary problem always has a solution of the Lame-Clapeyron-Neumann typ e. (ii) If one of the triples {O,k,e}, {O,/,e}, {O,/,p}, and {O,c,p} has to be determined , the above property is satisfied if and only if a complementary condition for the data is verified, Formulas are also obtained for the simult aneous determination of other physical coefficients a nd the inequality~2 < Slej2(Ste :Stefan number) for the coefficient~of the free boundary 5(t) = 2a~t 1/2 of the Lame-Clapeyron solution of the one-phase Stefan problem without unknown coefficients.

Research paper thumbnail of Explicit solution for non-classical one-phase Stefan problem with variable thermal coefficients and two different heat source terms

A one-phase Stefan problem for a semi-infinite material is studied for special functional forms o... more A one-phase Stefan problem for a semi-infinite material is studied for special functional forms of the thermal conductivity and specific heat depending on the temperature of the phase-change material. Using the similarity transformation technique, an explicit solution for these situations are shown. The mathematical analysis is made for two different kinds of heat source terms, and the existence and uniqueness of the solutions are proved.

Research paper thumbnail of Integral balance methods applied to non-classical Stefan problems

Thermal Science, 2018

We consider two different Stefan problems for a semi-infinite material for the non-classical heat... more We consider two different Stefan problems for a semi-infinite material for the non-classical heat equation with a source that depends on the heat flux at the fixed face. One of them, with constant temperature at the fixed face, was already studied in literature and the other, with a convective boundary condition at the fixed face, is presented in this work. Due to the complexity of the exact solution it is of interest to compare with approximate solutions obtained by applying heat balance integral methods, assuming a quadratic temperature profile in space. A dimensionless analysis is carried out by using the parameters: Stefan number and the generalized Biot number. In addition it is studied the case when Biot number 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 verify the accuracy of the approximate methods.

Research paper thumbnail of Existence and uniqueness of the p-generalized modified error function

Electronic Journal of Differential Equations

In this article, we define a p-generalized modified error function as the solution to a non-linea... more In this article, we define a p-generalized modified error function as the solution to a non-linear ordinary differential equation of second order, with a Robin type boundary condition at x=0. We prove existence and uniqueness of a non-negative \(C^{\infty}\) solution by using a fixed point argument. We show that the p-generalized modified error function converges to the p-modified error function defined as the solution to a similar problem with a Dirichlet boundary condition. In both problems, for p=1, the generalized modified error function and the modified error function are recovered. In addition, we analyze the existence and uniqueness of solution to a problem with a Neumann boundary condition. For more information see https://ejde.math.txstate.edu/Volumes/2020/35/abstr.html

Research paper thumbnail of Analytical solution for a cylinder glaciation model with variable latent heat and thermal diffusivity

International Journal of Non-Linear Mechanics

Research paper thumbnail of Two Stefan problems for a non-classical heat equation with nonlinear thermal coefficients

Differential and Integral Equations

The mathematical analysis of two one-phase unidimensional and non-classical Stefan problems with ... more The mathematical analysis of two one-phase unidimensional and non-classical Stefan problems with nonlinear thermal coecients is obtained. Two related cases are considered, one of them has a temperature condition on the fixed face x = 0 and the other one has a flux condition of the type q0= p t (q0 > 0) : In the first case, the source function depends on the heat flux at the fixed face x = 0; and in the other case it depends on the temperature at the fixed face x = 0: In both cases, we obtain sufficient conditions in order to have the existence of an explicit solution of a similarity type, which is given by using a double fixed point.Fil: Briozzo, Adriana Clotilde. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Austral. Facultad de Cs.empresariales. Departamento de Matemáticas; ArgentinaFil: Natale, María Fernanda. Universidad Austral. Facultad de Cs.empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Research paper thumbnail of Two-phase Stefan problem with nonlinear thermal coefficients and a convective boundary condition

Authorea

We consider a non-linear two-phase unidimensional Stefan problem, which consists on a solidificat... more We consider a non-linear two-phase unidimensional Stefan problem, which consists on a solidification process, for a semi-infinite material x > 0, with phase change temperature T 1 , an initial temperature T 2 > T 1 and a convective boundary condition imposed at the fixed face x = 0 characterized by a heat transfer coefficient h > 0. We assume that the volumetric heat capacity and the thermal conductivity are particular nonlinear functions of the temperature in both solid and liquid phases and they verify a Storm-type relation. A certain inequality on the coefficient h is established in order to get an instantaneous phase change process. We determine sufficient conditions on the parameters of the problem in order to prove the existence and uniqueness of a parametric explicit solution for the Stefan problem.

Research paper thumbnail of On a two‐phase Stefan problem with convective boundary condition including a density jump at the free boundary

Mathematical Methods in the Applied Sciences, 2020

We consider a two‐phase Stefan problem for a semi‐infinite body with a convective boundary condit... more We consider a two‐phase Stefan problem for a semi‐infinite body with a convective boundary condition including a density jump at the free boundary with a time‐dependent heat transfer coefficient of the type , whose solution was given in D. A. Tarzia, PAMM. Proc. Appl. Math. Mech. 7, 1040307–1040308 (2007). We demonstrate that the solution to this problem converges to the solution to the analogous one with a temperature boundary condition when the heat transfer coefficient . Moreover, we analyze the dependence of the free boundary respecting to the jump density.

Research paper thumbnail of Existence and uniqueness of solution for two one-phase Stefan problems with variable thermal coefficients

Nonlinear Analysis: Real World Applications, 2020

One dimensional Stefan problems for a semi-infinite material with temperature dependent thermal c... more One dimensional Stefan problems for a semi-infinite material with temperature dependent thermal coefficients are considered. Existence and uniqueness of solution are obtained imposing a Dirichlet or a Robin type condition at fixed face x = 0. Moreover, it is proved that the solution of the problem with the Robin type condition converges to the solution of the problem with the Dirichlet condition at the fixed face. Computational examples are provided.

Research paper thumbnail of Non-classical Stefan problem with nonlinear thermal coefficients and a Robin boundary condition

Nonlinear Analysis: Real World Applications, 2019

A non-classical one dimensional Stefan problem with thermal coefficients temperature dependent an... more A non-classical one dimensional Stefan problem with thermal coefficients temperature dependent and a Robin type condition at fixed face x = 0 for a semi-infinite material is considered. The source function depends on the evolution the heat flux at the fixed face x = 0. Existence of a similarity type solution is obtained and the asymptotic behaviour of free boundary with respect to latent heat fusion is studied. The analysis of several particular cases are given.

Research paper thumbnail of The classical one-phase Stefan problem with temperature-dependent thermal conductivity and a convective term

MAT Serie A, 2008

We study a one-phase Stefan problem for a semi-infinite material with temperaturedependent therma... more We study a one-phase Stefan problem for a semi-infinite material with temperaturedependent thermal conductivity and a convective term with a constant temperature boundary condition or a heat flux boundary condition of the type −q 0 / √ t (q 0 > 0) at the fixed face x = 0. We obtain in both cases sufficient conditions for data in order to have a parametric representation of the solution of the similarity type for t ≥ t 0 > 0 with t 0 an arbitrary positive time. We improve the results given in

Research paper thumbnail of A one-phase Lamé-Clapeyron-Stefan problem with nonlinear thermal coefficients

Research paper thumbnail of An explicit solution for a two-phase Stefan problem with a similarity exponential heat sources

MAT Serie A, 2004

A two-phase Stefan problem with heat source terms in both liquid and solid phases for a semi-in¯n... more A two-phase Stefan problem with heat source terms in both liquid and solid phases for a semi-in¯nite phase-change material is considered. The internal heat source functions are given by g j (x; t) = (¡1) j+1 ½l t exp ³ ¡(x 2a j p t + d j) 2´(j = 1 solid phase; j = 2 liquid phase), ½ is the mass density, l is the fusion latent heat by unit of mass; a 2 j is the di®usion coe±cient, x is spatial variable, t is the temporal variable and d j 2 R. A similarity solution is obtained for any data when a temperature boundary condition is imposed at the¯xed face x = 0; when a°ux condition of the type ¡q 0 = p t (q 0 > 0) is imposed on x = 0 then there exists a similarity solution if and only if a restriction on q 0 is satis¯ed.

Research paper thumbnail of A nonlinear supercooled Stefan problem

Zeitschrift für angewandte Mathematik und Physik, 2017

We study the supercooled one-phase Stefan problem for a semi-infinite material with temperature-d... more We study the supercooled one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conductivity at the fixed face x = 0. We obtain sufficient conditions for data in order to have existence of a solution of similarity type, local in time and finite-time blow-up occurs. This explicit solution is obtained through the unique solution of an integral equation with the time as a parameter.

Research paper thumbnail of Nonlinear Stefan problem with convective boundary condition in Storm’s materials

Zeitschrift für angewandte Mathematik und Physik, 2016

We consider a nonlinear one-dimensional Stefan problem for a semi-infinite material x > 0, with p... more We consider a nonlinear one-dimensional Stefan problem for a semi-infinite material x > 0, with phase change temperature T f. We assume that the heat capacity and the thermal conductivity satisfy a Storm's condition and we assume a convective boundary condition at the fixed face x = 0. An unique explicit solution of similarity type is obtained. Moreover, asymptotic behavior of the solution when h → +∞ is studied.

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

Journal of Applied Analysis, 2015

We study a one-phase Stefan problem for a semi-infinite material with temperature-dependent therm... more 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 ≥ t 0 > 0 with t 0 an arbitrary positive time. This explicit solution is obtained through the unique solution of an integral equation with the time as a parameter.

Research paper thumbnail of Explicit solutions for a one-phase Stefan problem with temperature-dependent thermal conductivity