Explicit solutions to the one-phase Stefan problem with temperature-dependent thermal conductivity and a convective term

2003 ◽  
Vol 41 (15) ◽  
pp. 1685-1698 ◽  
Author(s):  
Marı́a F. Natale ◽  
Domingo A. Tarzia
Keyword(s):  
Thermal Conductivity ◽  
Stefan Problem ◽  
Explicit Solutions ◽  
Convective Term ◽  
Temperature Dependent ◽  
The One ◽  
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 Non-Fourier Heat Conduction Analysis with Temperature-Dependent Thermal Conductivity

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
H. Rahideh ◽  
P. Malekzadeh ◽  
M. R. Golbahar Haghighi
Keyword(s):  
Thermal Conductivity ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Differential Quadrature Method ◽  
Two Dimensional ◽  
Temperature Dependent ◽  
Temporal Domain ◽  
Fourier Heat Conduction ◽  
The One ◽  
Temperature Dependent Thermal Conductivity

As a first endeavor, the one- and two-dimensional heat wave propagation in a medium subjected to different boundary conditions and with temperature-dependent thermal conductivity is studied. Both the spatial as well as the temporal domain is discretized using the differential quadrature method (DQM). This results in superior accuracy with fewer degrees of freedom than conventional finite element method (FEM). To verify this advantage through some comparison studies, a finite element solution ise also obtained. After demonstrating the convergence and accuracy of the method, the effects of different parameters on the temperature distribution of the medium are studied.

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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