MassTransferValue

✖
`MassTransferValue`

✖

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

✖

MassTransferValue[pred,vars,pars,lkey]

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

Details

MassTransferValue specifies a boundary condition for MassTransportPDEComponent and is used as part of the modeling equation:

MassTransferValue is typically used to model the effect of a reactive flow outside the simulation domain.
MassFluxValue models mass species transferred across some part of the boundary with dependent variable in [ $TemplateBox[{InterpretationBox[, 1], {"mol", , "/", , {"m", ^, 3}}, moles per meter cubed, {{(, "Moles", )}, /, {(, {"Meters", ^, 3}, )}}}, QuantityTF]$ ], independent variables in [] and time variable in [].
Stationary variables vars are vars={c[x₁,…,x_n],{x₁,…,x_n}}.
Time-dependent variables vars are vars={c[t,x₁,…,x_n],t,{x₁,…,x_n}}.
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:

The mass transfer value MassTransferValue with mass transfer coefficient [], external mass concentration [ $TemplateBox[{InterpretationBox[, 1], {"mol", , "/", , {"m", ^, 3}}, moles per meter cubed, {{(, "Moles", )}, /, {(, {"Meters", ^, 3}, )}}}, QuantityTF]$ ] and boundary unit normal models:

Model parameters pars as specified for MassTransportPDEComponent.
The following additional model parameters pars can be given:

parameter	default	symbol
"AmbientConcentration"	0	, external mass concentration [ $TemplateBox[{InterpretationBox[, 1], {"mol", , "/", , {"m", ^, 3}}, moles per meter cubed, {{(, "Moles", )}, /, {(, {"Meters", ^, 3}, )}}}, QuantityTF]$ ]
"MassTransferCoefficient"	1	, mass transfer coefficient []

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.
MassTransferValue is a special case of a MassFluxValue.
MassTransferValue evaluates to a generalized NeumannValue.
The boundary predicate pred can be specified as in NeumannValue.
If the MassTransferValue depends on parameters that are specified in the association pars as …,keyp_i…,p_iv_i,…], the parameters are replaced with .

Examples

open allclose all

Basic Examples (2)Summary of the most common use cases

Set up a mass transfer boundary condition:

In[1]:=1

✖

https://wolfram.com/xid/0mk5bsy8hwd2-vw7olo

Out[1]=1

Set up a system of mass transfer boundary conditions:

In[1]:=1

✖

https://wolfram.com/xid/0mk5bsy8hwd2-6qc2mq

Out[1]=1

Scope (3)Survey of the scope of standard use cases

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

In[1]:=1

✖

https://wolfram.com/xid/0mk5bsy8hwd2-glqeii

Out[3]=3

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

In[1]:=1

✖

https://wolfram.com/xid/0mk5bsy8hwd2-uwpzeb

In[2]:=2

✖

https://wolfram.com/xid/0mk5bsy8hwd2-hwq3hg

Out[2]=2

In[3]:=3

✖

https://wolfram.com/xid/0mk5bsy8hwd2-zk0k6a

Out[3]=3

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 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 :