scholarly journals The classical one-phase Stefan problem with temperature-dependent thermal conductivity and a convective term

MAT Serie A ◽  
2008 ◽  
Vol 15 ◽  
pp. 1-16 ◽  
Author(s):  
María Fernanda Natale ◽  
Domingo A. Tarzia
Keyword(s):  
Thermal Conductivity ◽  
Stefan Problem ◽  
Convective Term ◽  
Temperature Dependent ◽  
Temperature Dependent Thermal Conductivity

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

2015 ◽  
Vol 21 (2) ◽  
Author(s):  
Adriana C. Briozzo ◽  
María Fernanda Natale
Keyword(s):  
Thermal Conductivity ◽  
Boundary Condition ◽  
Stefan Problem ◽  
Temperature Dependent ◽  
Temperature Dependent Thermal Conductivity

AbstractWe 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

scholarly journals On the Stefan Problem With Nonlinear Thermal Conductivity

2021 ◽  
Author(s):  
Lazhar Bougoffa ◽  
Ammar Khanfer
Keyword(s):  
Thermal Conductivity ◽  
Stefan Problem ◽  
Nonlinear Boundary ◽  
Error Function ◽  
Temperature Dependent ◽  
Nonlinear Temperature ◽  
Infinite Line ◽  
Two Parameters ◽  
Nonlinear Thermal Conductivity ◽  
Temperature Dependent Thermal Conductivity

The solution is obtained and validated by an existence and uniqueness theorem for the following nonlinear boundary value problem \[ \frac{d}{dx}(1+\delta y+\gamma y^{2})^{n}\frac{dy}{dx}]+2x\frac{dy}{dx}=0,\,\,\,x>0,\,\,y(0)=0,\,\,\,y(\infty)=1, \] which was proposed in 1974 by [1] to represent a Stefan problem with a nonlinear temperature-dependent thermal conductivity on the semi-infinite line (0;1). The modified error function of two parameters $\varphi_{\delta,\gamma}$ is introduced to represent the solution of the problem above, and some properties of the function are established. This generalizes the results obtained in [3, 4].

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