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Non-dimensional convection diffusion equations
Posted 29.06.2009, 05:29 GMT-4 0 Replies
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I've been trying to solve non-dimensionalized equations for convection-diffusion in a hollow fibre model. I'm unable to get the results to agree with the equivalent dimensional model, though Im confident the forms of my equations are right. Im using anisotropic diffusion coefficients in the r-direction. Here are my dimensionless equations:
Subdomain 1 (fibre lumen)
del(-del(c)) = -2*Pe_ax*(1-r^2) where Pe_ax is the Peclet number
Subdomain 2 (membrane)
del(-del(c)) = 0
Subdomain 3 (extracapillary space)
del(-del(c)) = -Thiele*(c/c+Km) where Thiele is the Thiele modulus (Vmax*R1^2/D*c(in)) and Km is the dimensionless Michaelis-Menten constant. I also use a step down function for small c (thanks to Peter Buchwald's pancreatic islet model) which helps with convergence
It seems c decreases more rapidly in the dimensionless model, any ideas why?
Thanks,
Adam
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Hello Adam Davidson
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