scholarly journals PROBLEM FROM THE THEORY OF BRIDGE EROSION

2018 ◽  
pp. 68-74
Author(s):  
S.N. Kharin ◽  
S.A. Kassabek ◽  
M. Slyamkhan
Keyword(s):  
Exact Solution ◽  
Mathematical Models ◽  
Stefan Problem ◽  
Error Function ◽  
Two Phase ◽  
Bridge Problem ◽  
Radial Heat ◽  
Integral Error

In this paper, we represent the exact solution of a two phase Stefan problem. Radial heat polynomialsand integral error function are used for solving bridge problem. The recurrent expressions for the coefficients of these series are presented. The mathematical models describe the dynamics of contact opening and bridging. Keywords: radial heat polynomials, Stefan problem.

scholarly journals ABOUT THE EXACT SOLUTION IN TWO PHASE-STEFAN PROBLEM

2007 ◽  
Vol 6 (2) ◽  
pp. 70 ◽  
Author(s):  
A. C. Boucíguez ◽  
R. F. Lozano ◽  
M. A. Lara
Keyword(s):  
Boundary Condition ◽  
Exact Solution ◽  
Stefan Problem ◽  
Two Phase ◽  
Flux Boundary Condition ◽  
Temperature Boundary ◽  
Infinite Slab ◽  
Heat Flux Boundary Condition ◽  
The Relationship ◽  
Temperature Boundary Condition

Two cases of the two - phase Stefan problem in a semi - infinite slab are presented here: one has heat flux boundary condition proportional to t−½ and the other has constant temperature boundary condition. In these two cases the exact solution exists, the relationship between the two boundary conditions is presented here, and the equivalence between the two problems is shown.

Exact solution for a two-phase Stefan problem with power-type latent heat

2017 ◽  
Vol 110 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Yang Zhou ◽  
Xiang-you Shi ◽  
Guo-qing Zhou
Keyword(s):  
Exact Solution ◽  
Latent Heat ◽  
Stefan Problem ◽  
Power Type ◽  
Two Phase

scholarly journals Exact solution of the one phase inverse Stefan problem

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 985-990
Author(s):  
Merey Sarsengeldin ◽  
Stanislav Kharin ◽  
Samat Kassabek ◽  
Zamanbek Mukambetkazin
Keyword(s):  
Heat Flux ◽  
Exact Solution ◽  
Maximum Principle ◽  
Error Estimate ◽  
Stefan Problem ◽  
Test Problem ◽  
Solution Function ◽  
Flux Function ◽  
Integral Error ◽  
The One

Exact solution of inverse one phase Stefan problem is represented in the form of linear combination of integral error functions. Heat flux function is reconstructed and coefficients of solution function are found exactly. Test problem was considered for engineering purposes and it was shown that by collocation method the error for three points does not exceed 0:01%. Error estimate was calculated by maximum principle.

scholarly journals An Accurate Approximation of the Two-Phase Stefan Problem with Coefficient Smoothing

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1924
Author(s):  
Vasily Vasil’ev ◽  
Maria Vasilyeva
Keyword(s):  
Phase Change ◽  
Stefan Problem ◽  
Error Function ◽  
Discontinuous Coefficients ◽  
Two Phase ◽  
Spatial Interval ◽  
The One ◽  
Transfer Problems ◽  
The Mathematical Model ◽  
The Given

In this work, we consider the heat transfer problems with phase change. The mathematical model is described through a two-phase Stefan problem and defined in the whole domain that contains frozen and thawed subdomains. For the numerical solution of the problem, we present three schemes based on different smoothing of the sharp phase change interface. We propose the method using smooth coefficient approximation based on the analytical smoothing of discontinuous coefficients through an error function with a given smoothing interval. The second method is based on smoothing in one spatial interval (cell) and provides a minimal length of smoothing calculated automatically for the given values of temperatures on the mesh. The third scheme is a convenient scheme using a linear approximation of the coefficient on the smoothing interval. The results of the numerical computations on a model problem with an exact solution are presented for the one-dimensional formulation. The extension of the method is presented for the solution of the two-dimensional problem with numerical results.

Exact solution of two phase spherical Stefan problem with two free boundaries

2016 ◽  
Author(s):  
Alexey A. Kavokin ◽  
Targyn Nauryz ◽  
Nazerke T. Bizhigitova
Keyword(s):  
Exact Solution ◽  
Stefan Problem ◽  
Free Boundaries ◽  
Two Phase

scholarly journals On the Two-phase Fractional Stefan Problem

2020 ◽  
Vol 20 (2) ◽  
pp. 437-458 ◽  
Author(s):  
Félix del Teso ◽  
Jørgen Endal ◽  
Juan Luis Vázquez
Keyword(s):  
Free Boundary ◽  
Stefan Problem ◽  
Free Boundary Problems ◽  
Classical Problem ◽  
Nonlocal Diffusion ◽  
Two Phase ◽  
Boundary Problems ◽  
Numerical Studies ◽  
The One ◽  
Evolution Type

AbstractThe classical Stefan problem is one of the most studied free boundary problems of evolution type. Recently, there has been interest in treating the corresponding free boundary problem with nonlocal diffusion. We start the paper by reviewing the main properties of the classical problem that are of interest to us. Then we introduce the fractional Stefan problem and develop the basic theory. After that we center our attention on selfsimilar solutions, their properties and consequences. We first discuss the results of the one-phase fractional Stefan problem, which have recently been studied by the authors. Finally, we address the theory of the two-phase fractional Stefan problem, which contains the main original contributions of this paper. Rigorous numerical studies support our results and claims.

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