Free and Moving Boundary Problems of Heat and Mass Transfer

2018 ◽  
Vol 7 (3.27) ◽  
pp. 18
Author(s):  
P Kanakadurga Devi ◽  
V G. Naidu ◽  
K Mamatha ◽  
B Naresh
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Boundary Problem ◽  
Heat And Mass Transfer ◽  
Moving Boundary ◽  
Moving Boundary Problem ◽  
Interval Length ◽  
Bisection Method ◽  
Moving Boundary Problems ◽  
Boundary Problems

Bisection method is used to solve a moving boundary problem. This moving boundary problem was solved by the maze of mathematical manipulations by several authors. The method of using bisection is simple as compared to the lengthy mathematical manipulation of other methods. The procedure of the paper is useful in other moving boundary problems of heat and mass transfer, including boundary value problems involving ordinary differential equations with unknown interval length.  

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.

scholarly journals Improving the Accuracy of Fictitious Domain Method Using Indicator Function from Volume Intersection

2019 ◽  
Vol 2019 ◽  
pp. 1-18
Author(s):  
Guoliang Chai ◽  
Junwei Su ◽  
Le Wang ◽  
Chunlei Yu ◽  
Yigen Zhang ◽  
...  
Keyword(s):  
Circular Cylinder ◽  
Boundary Problem ◽  
Moving Boundary ◽  
Indicator Function ◽  
Fictitious Domain ◽  
Moving Boundary Problems ◽  
Fictitious Domain Method ◽  
Boundary Problems ◽  
Domain Method ◽  
Volume Intersection

Fictitious domain method (FDM) is a commonly accepted direct numerical simulation technique for moving boundary problems. Indicator function used to distinguish the solid zone and the fluid zone is an essential part concerning the whole prediction accuracy of FDM. In this work, a new indicator function through volume intersection is developed for FDM. In this method, the arbitrarily polyhedral cells across the interface between fluid and solid are located and subdivided into tetrahedrons. The fraction of the solid volume in each cell is accurately computed to achieve high precision of integration calculation in the particle domain, improving the accuracy of the whole method. The quadrature over the solid domain shows that the newly developed indicator function can provide results with high accuracy for variable integration in both stationary and moving boundary problems. Several numerical tests, including flow around a circular cylinder, a single sphere in a creeping shear flow, settlement of a circular particle in a closed container, and in-line oscillation of a circular cylinder, have been performed. The results show good accuracy and feasibility in dealing with the stationary boundary problem as well as the moving boundary problem. This method is accurate and conservative, which can be a feasible tool for studying problems with moving boundaries.

scholarly journals Numerical Investigations of the Effect of Nonlinear Quadratic Pressure Gradient Term on a Moving Boundary Problem of Radial Flow in Low-Permeable Reservoirs with Threshold Pressure Gradient

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Wenchao Liu ◽  
Jun Yao
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Pressure Gradient ◽  
Boundary Problem ◽  
Moving Boundary ◽  
Radial Flow ◽  
Moving Boundary Problem ◽  
Strong Nonlinearity ◽  
Governing Equations ◽  
Partial Differential

The existence of a TPG can generate a relatively high pressure gradient in the process of fluid flow in porous media in low-permeable reservoirs, and neglecting the QPGTs in the governing equations, by assuming a small pressure gradient for such a problem, can cause a significant error in predicting the formation pressure. Based on these concerns, in consideration of the QPGT, a moving boundary model of radial flow in low-permeable reservoirs with the TPG for the case of a constant flow rate at the inner boundary is constructed. Due to strong nonlinearity of the mathematical model, a numerical method is presented: the system of partial differential equations for the moving boundary problem is first transformed equivalently into a closed system of partial differential equations with fixed boundary conditions by a spatial coordinate transformation method; and then a stable, fully implicit finite difference method is used to obtain its numerical solution. Numerical result analysis shows that the mathematical models of radial flow in low-permeable reservoirs with TPG must take the QPGT into account in their governing equations, which is more important than those of Darcy’s flow; the sensitive effects of the QPGT for the radial flow model do not change with an increase of the dimensionless TPG.

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