# MassFluxValue

MassFluxValue[pred,vars,pars]

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

MassFluxValue[pred,vars,pars,lkey]

represents a mass flux boundary condition with local parameters specified in pars[lkey].

# Details

• MassFluxValue specifies a boundary condition for MassTransportPDEComponent and is used as part of the modeling equation:
• MassFluxValue is typically used to model mass species flow through a boundary caused by a species source or sink outside of the domain.
• A flow rate is the flow of a quantity like energy or mass per time. Flux is the flow rate through the boundary and is measured in the units of the quantity per area per time. A millimeter of rain per cross section of opening area per hour is a rain flux.
• MassFluxValue models the rate of mass species flowing through some part of the boundary with dependent variable in [], independent variables in [] and time variable in [].
• Stationary variables vars are vars={c[x1,,xn],{x1,,xn}}.
• Time-dependent variables vars are vars={c[t,x1,,xn],t,{x1,,xn}}.
• The non-conservative time-dependent mass transport model MassTransportPDEComponent is based on a convection-diffusion model with mass diffusivity , mass convection velocity vector , mass reaction rate and mass source term :
• The conservative time-dependent mass transport model MassTransportPDEComponent is based on a conservative convection-diffusion model given by:
• In the non-conservative form, MassFluxValue with mass flux in and boundary unit normal models:
• In the conservative form, MassFluxValue models:
• Model parameters pars as specified for MassTransportPDEComponent.
• The following additional model parameters pars can be given:
•  parameter default symbol "BoundaryUnitNormal" Automatic "MassFlux" 0 , mass flux [] "ModelForm" "NonConservative" -
• All model parameters may depend on any of , and , as well as other dependent variables.
• To localize model parameters, a key lkey can be specified, and values from association pars[lkey] are used for model parameters.
• MassFluxValue evaluates to a NeumannValue.
• The boundary predicate pred can be specified as in NeumannValue.
• If the MassFluxValue 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(2)

Set up a mass flux boundary condition in non-conservative form:

Set up a mass flux boundary condition in conservative form:

## Scope(10)

### Basic Examples(2)

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 the center of the left boundary, while the right boundary is subject to a parallel species flow with a 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 length at the center of the left surface:

Set up a mass transfer boundary on the right surface:

Set up an outflow flux 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:

### Time Dependent(1)

Model a 1D non-conservative chemical species field and a mass flux through part of the boundary with:

Set up the time-dependent mass transport model variables :

Set up a region :

Specify the mass transport model parameters mass diffusivity and mass convection velocity :

Set up the equation with a mass flux of at the left end for the first 50 seconds:

Solve the PDE with an initial condition of a zero concentration:

Visualize the solution:

### Nonlinear Time Dependent(1)

Model a 1D non-conservative chemical species field with a nonlinear diffusivity coefficient 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:

### Coupled Time Dependent(2)

Model a 1D coupled non-conservative dual chemical species field with corresponding mass flux through the left parts of the boundary:

Set up the time dependent mass transport model variables for the and species, respectively:

Set up a uniform region :

Specify the mass transport model parameters mass diffusivity and for the and species:

Set up the boundary conditions with a mass flux of and for and at the left end for the first 50 seconds:

Set up the equation:

Set up initial conditions:

Solve the PDEs:

Visualize the solution:

Model a 1D coupled chemical species field with a convection velocity and a mass flux through the left boundary:

Set up the time-dependent mass transport model variables for and species, respectively:

Set up a uniform region :

Specify the mass transport model parameters mass diffusivity and for the and species:

Set up the equation with a mass flux of 6 and 12 for and at the left end for the first 50 seconds:

Set up the equation:

Set up initial conditions:

Solve the PDEs:

Visualize the solution:

## Applications(2)

### Single Equation(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 the center of the 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 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:

### Coupled Equations(1)

Solve a coupled heat transfer and mass transport model with a thermal transfer value and a mass flux value on the boundary:

Set up the heat transfer mass transport model variables :

Set up a region :

Specify heat transfer and mass transport model parameters, heat source , thermal conductivity , mass diffusivity and mass source :

Specify boundary condition parameters for a thermal convection value with an external flow temperature of 1000 K and a heat transfer coefficient of :

Specify the equation:

Set up initial conditions:

Solve the model:

Visualize the solution:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_massfluxvalue, author="Wolfram Research", title="{MassFluxValue}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/MassFluxValue.html}", note=[Accessed: 13-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_massfluxvalue, organization={Wolfram Research}, title={MassFluxValue}, year={2020}, url={https://reference.wolfram.com/language/ref/MassFluxValue.html}, note=[Accessed: 13-September-2024 ]}