Shown below are initial concentrations (mg/liter at 4 nodes of a 1 dimensional t

Question

Shown below are initial concentrations (mg/liter at 4 nodes of a 1 dimensional transport system. We wish to use flux boundary conditions to solve this system. In this problem, you need to find the values of the imaginary nodes to finish the line of initial conditions (time, t-0). At the right side, there is no transport across the boundaries. On the left side, the transport into the system is constant at 0.8 mg/s. Fick's law is Q A a dC/dx, diffusivity is 0.2 cm 2/s, dx 2 cm and A 1 cm 2. Left Right imag [4] [7] [8] [11] imag

Explanation / Answer

fick's law

Q=A*a*dC/dx   Q=mass flow=0.8mg/s

Q/A=J=mass flux=0.8mg/1cm^2 s

J=a*dC/dx a=diffusivity=0.2cm2/s

for C1,3 dx=2cm

dC=J*dx/a =(0.8mg/1cm^2 s)*(2cm)/(0.2cm2/s)=8 mg/cm^3

At C1,4 dx=4cm

dC=J*dx/a =(0.8mg/1cm^2 s)*(4cm)/(0.2cm2/s)=16 mg/cm^3

At C1.5 dx=6cm

dC=J*dx/a =(0.8mg/1cm^2 s)*(6cm)/(0.2cm2/s)= 24mg/cm^3

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