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
open allclose allBasic Examples (2)
Scope (10)
Basic Examples (2)
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 :
Specify the mass transport model parameters species diffusivity and fluid flow velocity :
Specify a species flux boundary condition:
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:
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 :
Specify a diffusivity and a flow velocity field :
Specify a flux condition of through a regional circle on the top surface:
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 :
Specify the mass transport model parameters species diffusivity and a reaction rate active in the region :
Specify a species flux boundary condition:
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 :
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:
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 :
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:
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:
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:
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:
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:
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:
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 :
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 :
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