A numerical method for oxygen diffusion and absorption in a sike cell

摘要

Oxygen diffusion in a sike cell with simultaneous absorption is an important problem and has a wide range of medical applications. The problem mathematically formulated through two different stages, the present paper, concerns mainly on the second stage, in which, the injected oxygen through the cell starts absorbing. The basic idea of the proposed numerical method is to form a double linear system of equations, each of dimension (4 × 4). The first system is formed through applying first, second, third and fourth moments and using assumed profile for the concentration containing four unknowns functions of time. Numerical solution through a proposed scheme leads to the unknown functions. The second system is formed through applying the boundary conditions given in addition to another assumed condition, that is the concentration at x = 0 is unknown function of time. The results of the first system becomes an entry data for the second one leading to the concentration at the fixed surface x = 0. The results obtained by the present method were compared with two different methods and the results gave a good agreement.