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Analytical solutions to the Stefan problem with internal heat generation
(Elsevier B.V., 2016-06-25)
A first-order, ordinary differential equation modeling the Stefan problem (solid-liquid phase change) with internal heat generation in a plane wall is derived and the solutions are compared to the results of a computational ...
Two-phase Stefan problem with nonlinear thermal coefficients and a convective boundary condition
(Pergamon-Elsevier Science Ltd, 2021-04)
A solidification process for a semi-infinite material is presented through a non-linear two-phase unidimensional Stefan problem, where a convective boundary condition is imposed at the fixed face x=0. The volumetric heat ...
A new equivalence of Stefan’s problems for the time fractional diffusion equation
(Springer, 2014-06)
A fractional Stefan’s problem with a boundary convective condition is solved, where the fractional derivative of order α ∈ (0, 1) is taken in the Caputo sense. Then an equivalence with other two fractional Stefan’s problems ...
Explicit solutions to fractional Stefan-like problems for Caputo and Riemann–Liouville derivatives
(Elsevier Science, 2020-11)
Two fractional two-phase Stefan-like problems are considered by using Riemann-Liouville and Caputo derivatives of order α ∈ (0, 1) verifying that they coincide with the same classical Stefan problem at the limit case when ...
Determination of unknown thermal coefficients in a Stefan problem for Storm’s type materials
(Sociedade Brasileira de Matemática Aplicada e Computacional, 2018-09)
We consider a nonlinear one-dimensional Stefan problem for a semi-infinite material x> 0 , with phase change temperature Tf. We assume that the heat capacity and the thermal conductivity satisfy a Storm’s condition. A ...
One-Dimensional Nonlinear Stefan Problems in Storm's Materials
(MDPI, 2014-01)
We consider two one-phase nonlinear one-dimensional Stefan problems for a semi-infinite material x > 0; with phase change temperature Tf : We assume that the heat capacity and the thermal conductivity satisfy a Storm’s ...
A generalized neumann solution for the two-phase fractional lame-clapeyron-stefan problem
(Gakkotosho, 2014-04)
We obtain a generalized Neumann solution for the two-phase fractional Lam´eClapeyron-Stefan problem for a semi-infinite material with constant boundary and initial conditions. In this problem, the two governing equations ...
Two Stefan problems for a non-classical heat equation with nonlinear thermal coefficients
(Khayyam Publishing, 2014-11)
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 ...
Relationship between Neumann solutions for two-phase Lamé-Clapeyron-Stefan problems with convective and temperature boundary conditions
(Vinca Inst Nuclear Sci, 2017-01)
We obtain for the two-phase Lamé-Clapeyron-Stefan problem for a semi-infinite material an equivalence between the temperature and convective boundary conditions at the fixed face in the case that an inequality for the ...
One-phase Stefan problem with temperature-dependent thermal conductivity and a boundary condition of Robin type
(De Gruyter, 2015-12)
We study a one-phase Stefan problem for a semi-in nite material with temperature-dependent thermal conductivity with a boundary condition of Robin type at the xed face x = 0. We obtain su cient conditions for data in order ...