The project present treats the problem of diffusion of oxygen into meat i.e. the calculation of the oxygen concentration c(x,t) in the distance of x from the border of the meat at the time t. The theoretical basis is Fick’s second law i.e. The general equation c(x,t) is discussed but is not evaluated. The treatment of the problem is delimited to the so-called “steady state” situation where per definition the concentration of oxygen does not change in time for any value of x. The theoretical basis is thus reduced to
Since the absorption of oxygen in meat takes place via the mitochondria the mathematical model is a differential equation including a drain function f(c) i.e. In this project two versions of f(c) are discussed: A linear drain function and a non-linear drain function. The non-linear drain function is assumed biologically to model the situation where the oxygen absorption of the mitochondria is reduced due to “oxygen poisoning”. The function c(x) is evaluated analytical for the linear drain function while c(x) is evaluated numerically for the non-linear drain function using relevant parameter values. The calculations are illustrated by graphs displaying the connection between the drain functions and the corresponding functions for c(x).
|Uddannelser||Matematik, (Bachelor/kandidatuddannelse) Åben|
|Udgivelsesdato||29 maj 2017|
|Vejledere||Jesper Schmidt Hansen|