Exact solution of a stefan problem relevant to continuous casting

1982 ◽  
Vol 25 (7) ◽  
pp. 1059-1060 ◽  
Author(s):  
J.H. Blackwell ◽  
J.R. Ockendon
Keyword(s):  
Exact Solution ◽  
Continuous Casting ◽  
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.

Existence of an exact solution for a one-phase Stefan problem with nonlinear thermal coefficients from Tirskii’s method

2007 ◽  
Vol 67 (7) ◽  
pp. 1989-1998 ◽  
Author(s):  
Adriana C. Briozzo ◽  
María Fernanda Natale ◽  
Domingo A. Tarzia
Keyword(s):  
Exact Solution ◽  
Stefan Problem

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.

The Stefan Problem With an Imperfect Thermal Contact at the Interface

1982 ◽  
Vol 49 (4) ◽  
pp. 715-720 ◽  
Author(s):  
L. N. Tao
Keyword(s):  
Exact Solution ◽  
Stefan Problem ◽  
Existence And Uniqueness ◽  
Mixed Type ◽  
Thermal Contact ◽  
Mathematical Properties ◽  
Interfacial Boundary ◽  
Infinite Region ◽  
Uniformly Convergent ◽  
Basic Solutions

The Stefan problem in a semi-infinite region with arbitrarily prescribed initial and boundary conditions, subject to a condition of the mixed type at the interface is investigated. To establish the exact solution of the problem, some new basic solutions of the heat equation are offered. Their mathematical properties are also supplied. The exact solutions of the temperatures in both phases and of the interfacial boundary are derived in infinite series. The existence and uniqueness of these series are considered and proved. It is also shown that these series are absolutely and uniformly convergent. Some concluding remarks about the differences between the present problem and the classical Stefan problem are given. Also the effect of a density discontinuity at the interface is discussed.

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