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MassTransferValue[pred,vars,pars]

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].

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MassTransferValue

MassTransferValue[pred,vars,pars]

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 [TemplateBox[{InterpretationBox[, 1], "m", meters, "Meters"}, QuantityTF]] and time variable in [TemplateBox[{InterpretationBox[, 1], "s", seconds, "Seconds"}, QuantityTF]].
  • 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:
  • The mass transfer value MassTransferValue with mass transfer coefficient [TemplateBox[{InterpretationBox[, 1], {"m", , "/", , "s"}, meters per second, {{(, "Meters", )}, /, {(, "Seconds", )}}}, QuantityTF]], 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:
  • parameterdefaultsymbol
    "AmbientConcentration"0, external mass concentration [TemplateBox[{InterpretationBox[, 1], {"mol", , "/", , {"m", ^, 3}}, moles per meter cubed, {{(, "Moles", )}, /, {(, {"Meters", ^, 3}, )}}}, QuantityTF]]
    "MassTransferCoefficient"1, mass transfer coefficient [TemplateBox[{InterpretationBox[, 1], {"m", , "/", , "s"}, meters per second, {{(, "Meters", )}, /, {(, "Seconds", )}}}, QuantityTF]]
  • 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 …,keypi…,pivi,…, the parameters are replaced with .

Examples

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Basic Examples  (2)

Set up a mass transfer boundary condition:

Wolfram Language code: MassTransferValue[x ≥ 0, {c[t, x, y], t, {x}}, <|"AmbientConcentration" -> Subscript[c, ext][t, x, y], "MassTransferCoefficient" -> k|>]

Set up a system of mass transfer boundary conditions:

Wolfram Language code: MassTransferValue[x ≥ 0, {{Subscript[c, 1][x], Subscript[c, 2][x]}, {x}}, <|"AmbientConcentration" -> {Subscript[c, ext1][t, x, y], Subscript[c, ext2][t, x, y]}, "MassTransferCoefficient" -> {Subscript[k, 1], Subscript[k, 2]}|>]

Scope  (3)

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

Wolfram Language code: vars = {c[t, x, y], t, {x, y}}; pars = <|"DiffusionCoefficient" -> 0.026, "MassConvectionVelocity" -> {0.1}, "BoundaryCondition1" -> <|"AmbientConcentration" -> c1, "MassTransferCoefficient" -> k1|>|>; MassTransferValue[x == 1, vars, pars, "BoundaryCondition1"]

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

Wolfram Language code: vars = {c[t, x, y], t, {x, y}}; pars = <|"DiffusionCoefficient" -> 0.026, "MassConvectionVelocity" -> {0.1}, "BoundaryCondition1" -> <|"AmbientConcentration" -> c1, "MassTransferCoefficient" -> k1|>, "BoundaryCondition2" -> <|"AmbientConcentration" -> c2, "MassTransferCoefficient" -> k2|>|>;
Wolfram Language code: MassTransferValue[x == 0, vars, pars, "BoundaryCondition1"]
Wolfram Language code: MassTransferValue[x == 1, vars, pars, "BoundaryCondition2"]

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 :

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:

Wolfram Language code: vars = {c[x, y], {x, y}};

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

Wolfram Language code: Ω = Rectangle[{0, 0}, {20, 10}];

Specify model parameters species diffusivity and fluid flow velocity :

Wolfram Language code: pars = <|"DiffusionCoefficient" -> 0.833, "MassConvectionVelocity" -> {0.01, 0}|>;

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

Wolfram Language code: Subscript[Γ, concentration] = MassConcentrationCondition[x == 0 && y ≤ 5.1 && y ≥ 4.9, vars, pars, <|"MassConcentration" -> 3000|>]

Set up a mass transfer boundary on the right surface:

Wolfram Language code: Subscript[Γ, transfer] = MassTransferValue[x == 20, vars, pars, <|"AmbientConcentration" -> 1500, "MassTransferCoefficient" -> 5|>]

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

Wolfram Language code: Subscript[Γ, flux] = MassFluxValue[y == 0 || y == 10, vars, pars, <|"MassFlux" -> -100|>]

Set up the equation:

Wolfram Language code: eqn = MassTransportPDEComponent[vars, pars] == Subscript[Γ, transfer] + Subscript[Γ, flux]

Solve the PDE:

Wolfram Language code: cfun = NDSolveValue[{eqn, Subscript[Γ, concentration]}, c, {x, y}∈Ω];

Visualize the solution:

Wolfram Language code: ContourPlot[cfun[x, y], {x, y}∈Ω, ...]
Wolfram Research (2020), MassTransferValue, Wolfram Language function, https://reference.wolfram.com/language/ref/MassTransferValue.html.

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_masstransfervalue, author="Wolfram Research", title="{MassTransferValue}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/MassTransferValue.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_masstransfervalue, organization={Wolfram Research}, title={MassTransferValue}, year={2020}, url={https://reference.wolfram.com/language/ref/MassTransferValue.html}, note=[Accessed: 12-June-2026]}