MassConcentrationCondition

MassConcentrationCondition[pred,vars,pars]

represents a mass concentration boundary condition for PDEs with predicate pred indicating where it applies, with model variables vars and global parameters pars.

MassConcentrationCondition[pred,vars,pars,lkey]

represents a thermal surface boundary condition with local parameters specified in pars[lkey].

Details

Examples

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Basic Examples  (3)

Set up a mass concentration boundary condition:

Compute the mass concentration with model variables vars and parameters pars with a mass concentration of at the left boundary:

Set up the equation:

Solve the PDE:

Visualize the solution and note the sinusoidal mass change on the left:

Set up a system of mass concentration boundary conditions:

Scope  (7)

Define model variables vars for a transient species field with model parameters pars and a specific boundary condition parameter:

Define model variables vars for a transient species field with model parameters pars and multiple specific parameter boundary conditions:

1D  (1)

Model a 1D chemical species field in an incompressible fluid whose right side and left side are subjected to a mass concentration and inflow condition, respectively:

 del .(-d del c(x))+v^->.del c(x)^(︷^(       mass transport model       )) =|_(Gamma_(x=0))q(x)^(︷^( mass flux value  ))

Set up the stationary mass transport model variables vars:

Set up a region :

Specify the mass transport model parameters species diffusivity and fluid flow velocity :

Specify a species flux boundary condition:

Specify a mass concentration boundary condition:

Set up the equation:

Solve the PDE:

Visualize the solution:

2D  (1)

Model mass transport of a pollutant in a 2D rectangular region in an isotropic homogeneous medium. Initially, the pollutant concentration is zero throughout the region of interest. A concentration of 3000 is maintained at a strip with dimension 0.2 located at center of the left boundary, while the right boundary is subject to a parallel species flow with constant concentration of 1500 , allowing for mass transfer. A pollutant outflow of 100 is applied at both the top and bottom boundaries. A diffusion coefficient of 0.833 is distributed uniformly with a uniform horizontal velocity of 0.01 :

 del .(-d del c(x,y))+v^->.del c(x,y)^(︷^(           mass transport model              )) =|_(Gamma_(y=0, y=10))q(x,y)^(︷^(    mass flux value     ))+|_(Gamma_(x=20))h (c_(ext)(x,y)-c(x,y))^(︷^(         mass transfer value       ))

Set up the mass transport model variables vars:

Set up a rectangular domain with a width of and a height of :

Specify model parameters species diffusivity and fluid flow velocity :

Set up a species concentration source of 0.2 in length at the center of the left surface:

Set up a mass transfer boundary on the right surface:

Set up an outflow flux q of on the top and bottom surfaces:

Set up the equation:

Solve the PDE:

Visualize the solution:

3D  (1)

Model a non-conservative chemical species field in a unit cubic domain, with two mass conditions at two lateral surfaces and a mass inflow through a circle with radius 0.2 at the center of the top surface, as well as an orthotropic mass diffusivity :

 del .(-d del c(x,y,z))+v^->.del c(x,y,z)^(︷^(                              mass transport model                        )) =|_(Gamma_(z=1& (x-0.5)^2+(y-0.5)^2<=0.04))q(x,y,z)^(︷^(                          mass flux value                      ))

Set up the mass transport model variables vars:

Set up a region :

Specify a diffusivity and a flow velocity field :

Specify mass concentrations:

Specify a flux condition of through a regional circle on the top surface:

Set up the equation:

Solve the PDE:

Visualize the solution:

Material Regions  (1)

Model a 1D chemical species transport through different material with a reaction rate in one. The right side and left side are subjected to a mass concentration and inflow condition, respectively:

 del .(-d del c(x))+a c(x)^(︷^(           mass transport model              )) =|_(Gamma_(x=0))q(x)^(︷^( mass flux value  ))

Set up the stationary mass transport model variables vars:

Set up a region :

Specify the mass transport model parameters species diffusivity and a reaction rate active in the region :

Specify a species flux boundary condition:

Specify a mass concentration boundary condition:

Set up the equation:

Solve the PDE:

Visualize the solution:

Nonlinear Time Dependent  (1)

Model a 1D non-conservative chemical species field with a nonlinear diffusivity coefficient d and an outflow condition through part of the boundary, which is expressed as follows:

 (partialc(t,x))/(partialt)+del .(-d del c(t,x))^(︷^(          diffusion term       )) +v^->.del c(t,x))^(︷^(  convection term)) =|_(Gamma_(x=0.2))q(t,x)^(︷^( mass flux boundary ))

Set up the mass transport model variables vars:

Set up a region :

Specify a nonlinear species diffusivity and fluid flow velocity :

Specify an outflow flux of applied at the right end:

Specify a time-dependent mass concentration surface condition:

Set up an initial condition:

Set up the equation:

Solve the PDE:

Visualize the solution:

Applications  (1)

Model mass transport of a pollutant in a 2D rectangular region in an isotropic homogeneous medium. Initially, the pollutant concentration is zero throughout the region of interest. A concentration of 3000 is maintained at a strip with dimension 0.2 located at center of left boundary, while a pollutant outflow of 100 is applied at both the top and bottom boundaries. A diffusion coefficient of 0.833 is distributed uniformly, but both horizontal and vertical velocity are spatial dependent:

 del .(-d del c(x,y))+v^->.del c(x,y)^(︷^(           mass transport model              )) =|_(Gamma_(y=0, y=10))q(x,y)^(︷^(    mass flux value     ))

Set up the mass transport model variables vars:

Set up a rectangular domain with a width of and a height of :

Specify model parameters species diffusivity and fluid flow velocity :

Set up a species concentration source of 0.2 in length at the center of the left surface:

Set up an outflow flux of on the top and bottom surfaces:

Set up the equation:

Solve the PDE:

Visualize the solution:

Wolfram Research (2020), MassConcentrationCondition, Wolfram Language function, https://reference.wolfram.com/language/ref/MassConcentrationCondition.html.

Text

Wolfram Research (2020), MassConcentrationCondition, Wolfram Language function, https://reference.wolfram.com/language/ref/MassConcentrationCondition.html.

BibTeX

@misc{reference.wolfram_2020_massconcentrationcondition, author="Wolfram Research", title="{MassConcentrationCondition}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/MassConcentrationCondition.html}", note=[Accessed: 18-April-2021 ]}

BibLaTeX

@online{reference.wolfram_2020_massconcentrationcondition, organization={Wolfram Research}, title={MassConcentrationCondition}, year={2020}, url={https://reference.wolfram.com/language/ref/MassConcentrationCondition.html}, note=[Accessed: 18-April-2021 ]}

CMS

Wolfram Language. 2020. "MassConcentrationCondition." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MassConcentrationCondition.html.

APA

Wolfram Language. (2020). MassConcentrationCondition. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MassConcentrationCondition.html