# 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  • MassConcentrationCondition specifies a boundary condition for MassTransportPDEComponent.
• MassConcentrationCondition is typically used to set a mass species concentrations on the boundary. Common examples include a mass species inflow condition.
• • MassConcentrationCondition sets a specific mass species concentration on the boundary with dependent variable , independent variables and time variable .
• Stationary variables vars are vars={c[x1,,xn],{x1,,xn}}.
• Time-dependent variables vars are vars={c[t,x1,,xn],t,{x1,,xn}}.
• The mass concentration condition MassConcentrationCondition models .
• • Model parameters pars as specified for MassTransportPDEComponent.
• The following additional model parameters pars can be given:
•  parameter default symbol "MassConcentration" 0 , mass concentration in • MassConcentrationCondition evaluates to a DirichletCondition.
• The boundary predicate pred can be specified as in DirichletCondition.
• If the MassConcentrationCondition depends on parameters that are specified in the association pars as ,keypi,pivi,], the parameters are replaced with .

# Examples

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## Basic Examples(3)

Set up a mass concentration boundary condition:

Compute the mass concentration with model variables and parameters 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: Set up the stationary mass transport model variables :

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 : Set up the mass transport model variables :

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 : Set up the mass transport model variables :

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: Set up the stationary mass transport model variables :

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: Set up the mass transport model variables :

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: Set up the mass transport model variables :

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: