Comparative study between two numerical methods for oxygen diffusion problem

2009 ◽  
Vol 25 (8) ◽  
pp. 855-863 ◽  
Author(s):  
Vildan Gülkaç
Keyword(s):  
Numerical Methods ◽  
Comparative Study ◽  
Oxygen Diffusion ◽  
Diffusion Problem

An improved formulation of the oxygen-diffusion problem and its application to Zircaloy oxidation by steam

1997 ◽  
Vol 47 (5-6) ◽  
pp. 427-444 ◽  
Author(s):  
S. K. Wong ◽  
C. C. Chan ◽  
S. K. Crusher Wong
Keyword(s):  
Oxygen Diffusion ◽  
Diffusion Problem

scholarly journals The New Approximate Analytic Solution for Oxygen Diffusion Problem with Time-Fractional Derivative

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Vildan Gülkaç
Keyword(s):  
Oxygen Diffusion ◽  
Moving Boundary ◽  
Essential Feature ◽  
Power Series Expansion ◽  
Approximate Solutions ◽  
Convergent Series ◽  
Diffusion Problem ◽  
Approximate Analytic Solution ◽  
Stable Case ◽  
Modified Method

Oxygen diffusion into the cells with simultaneous absorption is an important problem and it is of great importance in medical applications. The problem is mathematically formulated in two different stages. At the first stage, the stable case having no oxygen transition in the isolated cell is investigated, whereas at the second stage the moving boundary problem of oxygen absorbed by the tissues in the cell is investigated. In oxygen diffusion problem, a moving boundary is essential feature of the problem. This paper extends a homotopy perturbation method with time-fractional derivatives to obtain solution for oxygen diffusion problem. The method used in dealing with the solution is considered as a power series expansion that rapidly converges to the nonlinear problem. The new approximate analytical process is based on two-iterative levels. The modified method allows approximate solutions in the form of convergent series with simply computable components.

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