Navier Stokes Solid Heat Transfer / PNSFVSolidHeatTransfer

Equation

This Physics object creates the kernels and boundary conditions to solve the heat transfer equation for the solid phase in a porous media flow problem.

where:

• is the solid specific enthalpy, computed from the specific heat and the solid temperature

• is the solid density

• is the porosity

• is the solid temperature

• is the fluid temperature

• the solid thermal conductivity

• is the source term, corresponding to energy deposited directly in the solid phase

• is the ambient convection volumetric heat transfer coefficient

The enthalpy is used in lieu of to be able to model solids with temperature dependent specific heat.

The kernels potentially created for this equation are:

• INSFVEnergyTimeDerivative for the time derivative of the energy

• PINSFVEnergyDiffusion for energy diffusion with an isotropic thermal diffusivity

• PINSFVEnergyAnisotropicDiffusion for energy diffusion with an anisotropic thermal diffusivity

• FVCoupledForce for the energy source term

• PINSFVEnergyAmbientConvection for the volumetric ambient convection term, if present

Automatically created variables

The PNSFVSolidHeatTransferPhysics by default will automatically create a nonlinear variable for the solid phase temperature. It should be named as follows:

static const std::string T_solidus = "T_solidus";

Coupling with other Physics

In the presence of fluid flow, a Navier Stokes Fluid Heat Transfer / WCNSFVFluidHeatTransferPhysics should be created using the [Physics/NavierStokes/FluidHeatTransfer/<name>] syntax. The following input performs the coupling between the fluid equations and the solid temperature equations. The coupling between the fluid and solid domain is performed through a volumetric ambient convection term.

[Physics<<<{"href": "../../syntax/Physics/index.html"}>>>]
  [NavierStokes<<<{"href": "../../syntax/Physics/NavierStokes/index.html"}>>>]
    [Flow<<<{"href": "../../syntax/Physics/NavierStokes/Flow/index.html"}>>>]
      [flow]
        compressibility<<<{"description": "Compressibility constraint for the Navier-Stokes equations."}>>> = 'weakly-compressible'
        porous_medium_treatment<<<{"description": "Whether to use porous medium kernels or not."}>>> = true
        define_variables<<<{"description": "Whether to define variables if the variables with the specified names do not exist. Note that if the variables are defined externally from the Physics, the initial conditions will not be created in the Physics either."}>>> = true

        pressure_variable<<<{"description": "If supplied, the system checks for available pressure variable. Otherwise, it is created within the action."}>>> = 'pressure'

        density<<<{"description": "The name of the density. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'rho'
        dynamic_viscosity<<<{"description": "The name of the dynamic viscosity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'mu'

        initial_velocity<<<{"description": "The initial velocity, assumed constant everywhere"}>>> = '${u_inlet} 1e-6 0'
        initial_pressure<<<{"description": "The initial pressure, assumed constant everywhere"}>>> = '${p_outlet}'

        inlet_boundaries<<<{"description": "Names of inlet boundaries"}>>> = 'left'
        momentum_inlet_types<<<{"description": "Types of inlet boundaries for the momentum equation."}>>> = 'fixed-velocity'
        momentum_inlet_function = '${u_inlet} 0'

        wall_boundaries<<<{"description": "Names of wall boundaries"}>>> = 'top bottom'
        momentum_wall_types<<<{"description": "Types of wall boundaries for the momentum equation"}>>> = 'noslip symmetry'

        outlet_boundaries<<<{"description": "Names of outlet boundaries"}>>> = 'right'
        momentum_outlet_types<<<{"description": "Types of outlet boundaries for the momentum equation"}>>> = 'fixed-pressure'
        pressure_function = '${p_outlet}'

        mass_advection_interpolation<<<{"description": "The numerical scheme to use for interpolating density, as an advected quantity, to the face."}>>> = 'average'
        momentum_advection_interpolation<<<{"description": "The numerical scheme to use for interpolating momentum/velocity, as an advected quantity, to the face."}>>> = 'average'
      []
    []
    [FluidHeatTransfer<<<{"href": "../../syntax/Physics/NavierStokes/FluidHeatTransfer/index.html"}>>>]
      [fluid]
        thermal_conductivity<<<{"description": "The name of the fluid thermal conductivity for each block. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'k'
        effective_conductivity<<<{"description": "Whether the conductivity should be multiplied by porosity, or whether the provided conductivity is an effective conductivity taking porosity effects into account"}>>> = true
        specific_heat<<<{"description": "The name of the specific heat. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'cp'

        initial_temperature<<<{"description": "The initial temperature, assumed constant everywhere"}>>> = '${T_inlet}'

        # See 'flow' for inlet boundaries
        energy_inlet_types<<<{"description": "Types for the inlet boundaries for the energy equation."}>>> = 'fixed-temperature'
        energy_inlet_function = '${T_inlet}'

        # See 'flow' for wall boundaries
        energy_wall_types<<<{"description": "Types for the wall boundaries for the energy equation."}>>> = 'heatflux heatflux'
        energy_wall_function = '0 0'

        ambient_convection_alpha<<<{"description": "The heat exchange coefficients for each block in 'ambient_convection_blocks'. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'h_cv'
        ambient_temperature<<<{"description": "The ambient temperature for each block in 'ambient_convection_blocks'. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'T_solid'

        energy_advection_interpolation<<<{"description": "The numerical scheme to use for interpolating energy/temperature, as an advected quantity, to the face."}>>> = 'average'
      []
    []

    [SolidHeatTransfer<<<{"href": "../../syntax/Physics/NavierStokes/SolidHeatTransfer/index.html"}>>>]
      [solid]
        block<<<{"description": "Blocks (subdomains) that this Physics is active on."}>>> = 0
        initial_temperature<<<{"description": "Initial value of the temperature variable"}>>> = 100
        transient<<<{"description": "Whether the physics is to be solved as a transient"}>>> = true
        # To match the previous test results
        solid_temperature_two_term_bc_expansion<<<{"description": "If a two-term Taylor expansion is needed for the determination of the boundary valuesof the temperature/energy."}>>> = true

        thermal_conductivity_solid<<<{"description": "Thermal conductivity, which may have different names depending on the subdomain. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = '${k_s}'
        cp_solid<<<{"description": "Specific heat functor. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = ${cp_s}
        rho_solid<<<{"description": "Density functor. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = ${rho_s}

        fixed_temperature_boundaries<<<{"description": "Boundaries on which to apply a fixed temperature"}>>> = 'top'
        boundary_temperatures<<<{"description": "Functors to compute the heat flux on each boundary in 'fixed_temperature_boundaries'. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = '${top_side_temperature}'

        ambient_convection_alpha<<<{"description": "The heat exchange coefficients for each block in 'ambient_convection_blocks'. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'h_cv'
        ambient_convection_temperature<<<{"description": "The fluid temperature for each block in 'ambient_convection_blocks'. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'T_fluid'
        verbose<<<{"description": "Flag to facilitate debugging a Physics"}>>> = true
      []
    []
  []
[]

Input Parameters