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user123abc
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Thread moved from the technical forums to the schoolwork forums
TL;DR Summary: Solve heat equation in a disc using fourier transforms
Carbon dioxide dissolves in the blood plasma but is not absorbed by red blood cells. As the blood returns to an alveolus, assume that it is well-mixed so that the concentration of dissolved CO2 is uniform across a cylindrical alveolar blood vessel. Model the diffusive transport of CO2 from an infinitely long cylinder of radius a containing plasma to the alveolus wall, i.e. use dc/dt = D d^2 c/dr^2 where r is the radial component, t is time, D is a diffusion constant and c(r,t) is the concentration of CO2. This is subject to initial and boundary conditions c(r,0)=c_0>1 and c(a,t)=1. Find c(r,t) using Fourier transforms.
I was given the hint to find the steady state solution first and then subtract it from the full solution to solve with FTs for homogeneous BCs. I'm stuck though, I feel like there isn't enough boundary conditions. Any insight would be great!
Carbon dioxide dissolves in the blood plasma but is not absorbed by red blood cells. As the blood returns to an alveolus, assume that it is well-mixed so that the concentration of dissolved CO2 is uniform across a cylindrical alveolar blood vessel. Model the diffusive transport of CO2 from an infinitely long cylinder of radius a containing plasma to the alveolus wall, i.e. use dc/dt = D d^2 c/dr^2 where r is the radial component, t is time, D is a diffusion constant and c(r,t) is the concentration of CO2. This is subject to initial and boundary conditions c(r,0)=c_0>1 and c(a,t)=1. Find c(r,t) using Fourier transforms.
I was given the hint to find the steady state solution first and then subtract it from the full solution to solve with FTs for homogeneous BCs. I'm stuck though, I feel like there isn't enough boundary conditions. Any insight would be great!