scholarly journals COMPUTATION OF ONE DIMENSIONAL ONE PHASE STEFAN PROBLEMS

2020 ◽  
Author(s):  
V.G. Naidu ◽  
P. Kanakadurga Devi
Keyword(s):  
Single Phase ◽  
Moving Boundary ◽  
Moving Boundary Problem ◽  
Initial Time ◽  
Neumann Condition ◽  
Type Problem ◽  
Governing Equations ◽  
Accurate Analysis ◽  
One Dimensional ◽  
Stefan Problems

To design an efficient device or to calculate the performance of existing device requires an accurate analysis of parameters involved in the system. In this work, an efficient front tracking finite difference method is developed to solve one dimensional single phase moving boundary problem with Neumann condition. The basic difficulty apart from the need to find the moving boundary presented, that there is no domain for the first phase at initial time. This difficulty is handled by the age old principle of basic mathematics. Naturally, giving symbolic names to the unknowns by modelling the problem, governing equations are developed with the conditions of the Stefan type problem, solved it and compared the obtained solutions with existing results wherever possible.

scholarly journals One Phase Moving Boundary Problem

2019 ◽  
Vol 9 (2) ◽  
pp. 3427-3431
Keyword(s):  
Boundary Problem ◽  
Moving Boundary ◽  
Moving Boundary Problem ◽  
Initial Time ◽  
Step Method ◽  
Time Step ◽  
Spherical Droplet ◽  
Variable Time ◽  
Variable Time Step ◽  
Time Step Method

In this paper we introduced a variable time step method to obtain interface to moving boundary problem for Slab and Sphere. We present the basic difficulty, apart from the need to find the moving boundary, that there is no domain for the space variable. This difficulty is handled by the age old principles of basic mathematics. Naturally, giving symbolic names to the unknowns develop equations involving them and solve it using the conditions of the problem. High order accurate initial time step sizes for given space step size are obtained with the help of Green’s theorem. The Subsequent time steps are obtained by an iterative scheme. This variable time step method handles Dirichlet’s problem of freezing or melting of a Slab and spherical droplet.

One-dimensional Consolidation of Thawing Soils

1971 ◽  
Vol 8 (4) ◽  
pp. 558-565 ◽  
Author(s):  
N. R. Morgenstern ◽  
J. F. Nixon
Keyword(s):  
Moving Boundary ◽  
Practical Interest ◽  
Moving Boundary Problem ◽  
One Dimensional ◽  
Closed Form Solutions ◽  
Pressure Distributions ◽  
Thaw Consolidation ◽  
Degree Of Consolidation ◽  
Compressible Soil ◽  
Excess Pore Pressures

The physics of consolidation of a thawing soil is formulated in terms of the well-known theories of heat conduction and of linear consolidation of a compressible soil. A moving boundary problem results, and closed form solutions have been obtained for several cases of practical interest. The results are presented in terms of normalized pore pressure distributions. It is shown that the excess pore pressures and the degree of consolidation in thawing soils depend primarily on the thaw consolidation ratio.

Nodal Integral and Finite Difference Solution of One-Dimensional Stefan Problem

2003 ◽  
Vol 125 (3) ◽  
pp. 523-527 ◽  
Author(s):  
James Caldwell ◽  
Svetislav Savovic´ ◽  
Yuen-Yick Kwan
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Moving Boundary ◽  
Finite Difference Methods ◽  
Melting Process ◽  
Time Dependent ◽  
One Dimensional ◽  
Stefan Problems ◽  
Finite Difference Solution ◽  
Very High

The nodal integral and finite difference methods are useful in the solution of one-dimensional Stefan problems describing the melting process. However, very few explicit analytical solutions are available in the literature for such problems, particularly with time-dependent boundary conditions. Benchmark cases are presented involving two test examples with the aim of producing very high accuracy when validated against the exact solutions. Test example 1 (time-independent boundary conditions) is followed by the more difficult test example 2 (time-dependent boundary conditions). As a result, the temperature distribution, position of the moving boundary and the velocity are evaluated and the results are validated.

A Four-Step Fixed-Grid Method for 1D Stefan Problems

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
M. Tadi
Keyword(s):  
Free Boundary ◽  
Moving Boundary ◽  
Free Boundary Problems ◽  
Grid Method ◽  
Moving Boundary Problems ◽  
Boundary Problems ◽  
One Dimensional ◽  
Nonlinear Part ◽  
Stefan Problems ◽  
Fixed Grid

This note is concerned with a fixed-grid finite difference method for the solution of one-dimensional free boundary problems. The method solves for the field variables and the location of the boundary in separate steps. As a result of this decoupling, the nonlinear part of the algorithm involves only a scalar unknown, which is the location of the moving boundary. A number of examples are used to study the applicability of the method. The method is particularly useful for moving boundary problems with various conditions at the front.

Similarity Analysis of Condensing Flow in a Fluid-Driven Fracture

1988 ◽  
Vol 110 (3) ◽  
pp. 754-762 ◽  
Author(s):  
S. K. Griffiths ◽  
R. H. Nilson
Keyword(s):  
Single Phase ◽  
Dimensionless Parameter ◽  
Nuclear Explosion ◽  
Similarity Solutions ◽  
Pure Substance ◽  
Underground Nuclear Explosion ◽  
Governing Equations ◽  
Opening Displacement ◽  
One Dimensional ◽  
Fracture Length

Similarity solutions are derived for some fundamental problems of condensing flow in a hydraulically driven fracture. The governing equations describe one-dimensional homogeneous turbulent flow along a wedge-shaped hydraulic fracture in an elastic medium. The instantaneous fracture speed is determined as an analytical function of fracture length, material properties, process parameters, and a single eigenvalue, which is calculated by solving a system of ordinary differential equations for the variation of pressure, energy, velocity, and opening displacement along the fracture. Results are presented for abrupt condensation of a pure substance and for gradual condensation of air/water mixtures. The rate of condensation is controlled by the rate of heat transfer to the fracture wall, which depends upon a single dimensionless parameter. For small and large values of this parameter the present multiphase solutions are in agreement with previous solutions for single-phase flows of vapors and liquids. Although most of the results are presented in dimensionless form, some numerical examples are given for steam-driven fractures emanating from the cavity resulting from an underground nuclear explosion.

Two methods to solve a fractional single phase moving boundary problem

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Xicheng Li ◽  
Shaowei Wang ◽  
Moli Zhao
Keyword(s):  
Mathematical Model ◽  
Exact Solution ◽  
Heat Equation ◽  
Fractional Derivative ◽  
Boundary Problem ◽  
Single Phase ◽  
Moving Boundary ◽  
Moving Boundary Problem ◽  
Moving Boundary Problems ◽  
Boundary Problems

AbstractA moving boundary problem of a melting problem is considered in this study. A mathematical model using the Caputo fractional derivative heat equation is proposed in the paper. Since moving boundary problems are difficult to solve for the exact solution, two methods are presented to approximate the evolution of the temperature. To simplify the computation, a similarity variable is adopted in order to reduce the partial differential equations to ordinary ones.

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