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{ 1D_CYLINDER_TRANSIENT.PDE

 

 This problem analyzes the diffusive loss of a solute from a solvent due to leakage

 across an outer boundary using 1D cylindrical coordinates.

 

}

 

title '1D time dependent diffusion in a Cylinder'

 

coordinates

   cylinder1("R")

 

variables

   C

 

definitions

   D = 1

   source = 0

   b = 1

   a = 2

   C0 = 10

   diss = 0.01     ! dissolution coefficient

   Cext = 0       ! external sink concentration

   Flux = -D*dr(C)

 

initial values

   C = C0

 

equations

   C: div(D*grad(C)) + source = dt(C)

 

boundaries

  region 1

      start (b)   point load(C)=0

      line to (a) point load(C)=diss*(Cext-C) !outer leakage rate

 

time 0 to 10

 

monitors

  for cycle=1

      elevation(C) from (b) to (a)

 

plots

  for cycle=10

      elevation(C) from (b) to (a)

      elevation(Flux) from (b) to (a) range=(0,0.01) {minimum plot range}

  history(C) at (b) ((b+a)/2) (a)

  history(Flux) at (b) ((b+a)/2) (a)

 

end