An exact solution to a Stefan problem with variable thermal conductivity and a Robin boundary condition

In this article it is proved the existence of similarity solutions for a one-phase Stefan problem with temperature-dependent thermal conductivity and a Robin condition at the fixed face. The temperature distribution is obtained through a generalized modified error function which is defined as the so...

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Autores principales: Ceretani, Andrea Noemí, Salva, Natalia Nieves, Tarzia, Domingo Alberto
Formato: Articulo article acceptedVersion
Lenguaje:Inglés
Publicado: Elsevier 2018
Materias:
Stefan problems
Exact solutions
Temperature dependent thermal
Conductivity
Convective boundary conditions
Modified error function
Phase-change processes
Ciencias de la Tierra y Medio Ambiente
Acceso en línea:http://rdi.uncoma.edu.ar/handle/uncomaid/17283
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Repositorio Institucional UNCo de Universidad Nacional del Comahue
id I22-R178-uncomaid-17283
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spelling I22-R178-uncomaid-172832023-10-18T12:56:51Z An exact solution to a Stefan problem with variable thermal conductivity and a Robin boundary condition Ceretani, Andrea Noemí Salva, Natalia Nieves Tarzia, Domingo Alberto Stefan problems Exact solutions Temperature dependent thermal Conductivity Convective boundary conditions Modified error function Phase-change processes Ciencias de la Tierra y Medio Ambiente In this article it is proved the existence of similarity solutions for a one-phase Stefan problem with temperature-dependent thermal conductivity and a Robin condition at the fixed face. The temperature distribution is obtained through a generalized modified error function which is defined as the solution to a nonlinear ordinary differential problem of second order. It is proved that the latter has a unique nonnegative bounded analytic solution when the parameter on which it depends assumes small positive values. Moreover, it is shown that the generalized modified error function is concave and increasing, and explicit approximations are proposed for it. Relation between the Stefan problem considered in this article with those with either constant thermal conductivity or a temperature boundary condition is also analysed. En este artículo se demuestra la existencia de soluciones de similitud para un problema de Stefan monofásico con conductividad térmica dependiente de la temperatura y una condición de Robin en la cara fija. La distribución de temperatura se obtiene mediante una función de error modificada generalizada que se define como la solución a un problema diferencial ordinario no lineal de segundo orden. Está demostrado que este último tiene una única solución analítica acotada no negativa cuando el parámetro del que depende asume pequeños valores positivos. Además, se muestra que la función de error modificada generalizada es cóncava y creciente, y se proponen aproximaciones explícitas para ella. También se analiza la relación entre el problema de Stefan considerado en este artículo con aquellos con conductividad térmica constante o una condición límite de temperatura. Fil: Ceretani, Andrea Noemí. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemática; Argentina. Fil: Ceretani, Andrea Noemí. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Fil: Ceretani, Andrea Noemí. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Departamento de Matemática; Argentina. Fil: Salva, Natalia Nieves. Universidad Nacional del Comahue. Centro Regional Universitario Bariloche. Departamento de Matemática; Argentina. Fil: Salva, Natalia Nieves. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche. Departamento de Mecánica Computacional; Argentina. Fil: Tarzia, Domingo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Fil: Tarzia, Domingo Alberto. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemática; Argentina. 2018-04 2023-06-22T14:40:10Z 2023-06-22T14:40:10Z Articulo article acceptedVersion 1468-1218 http://rdi.uncoma.edu.ar/handle/uncomaid/17283 eng https://doi.org/10.1016/j.nonrwa.2017.09.002 Atribución-NoComercial-CompartirIgual 2.5 Argentina https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ application/pdf pp. 243-259 application/pdf Elsevier Nonlinear Analysis: Real World Applications 40 (2018)
institution Universidad Nacional del Comahue
institution_str I-22
repository_str R-178
collection Repositorio Institucional UNCo
language Inglés
topic Stefan problems
Exact solutions
Temperature dependent thermal
Conductivity
Convective boundary conditions
Modified error function
Phase-change processes
Ciencias de la Tierra y Medio Ambiente
spellingShingle Stefan problems
Exact solutions
Temperature dependent thermal
Conductivity
Convective boundary conditions
Modified error function
Phase-change processes
Ciencias de la Tierra y Medio Ambiente
Ceretani, Andrea Noemí
Salva, Natalia Nieves
Tarzia, Domingo Alberto
An exact solution to a Stefan problem with variable thermal conductivity and a Robin boundary condition
topic_facet Stefan problems
Exact solutions
Temperature dependent thermal
Conductivity
Convective boundary conditions
Modified error function
Phase-change processes
Ciencias de la Tierra y Medio Ambiente
description In this article it is proved the existence of similarity solutions for a one-phase Stefan problem with temperature-dependent thermal conductivity and a Robin condition at the fixed face. The temperature distribution is obtained through a generalized modified error function which is defined as the solution to a nonlinear ordinary differential problem of second order. It is proved that the latter has a unique nonnegative bounded analytic solution when the parameter on which it depends assumes small positive values. Moreover, it is shown that the generalized modified error function is concave and increasing, and explicit approximations are proposed for it. Relation between the Stefan problem considered in this article with those with either constant thermal conductivity or a temperature boundary condition is also analysed.
format Articulo
article
acceptedVersion
author Ceretani, Andrea Noemí
Salva, Natalia Nieves
Tarzia, Domingo Alberto
author_facet Ceretani, Andrea Noemí
Salva, Natalia Nieves
Tarzia, Domingo Alberto
author_sort Ceretani, Andrea Noemí
title An exact solution to a Stefan problem with variable thermal conductivity and a Robin boundary condition
title_short An exact solution to a Stefan problem with variable thermal conductivity and a Robin boundary condition
title_full An exact solution to a Stefan problem with variable thermal conductivity and a Robin boundary condition
title_fullStr An exact solution to a Stefan problem with variable thermal conductivity and a Robin boundary condition
title_full_unstemmed An exact solution to a Stefan problem with variable thermal conductivity and a Robin boundary condition
title_sort exact solution to a stefan problem with variable thermal conductivity and a robin boundary condition
publisher Elsevier
publishDate 2018
url http://rdi.uncoma.edu.ar/handle/uncomaid/17283
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