Transient Heat Transfer

Summary

Solves a transient heat conduction problem with a boundary parameterized by a heat transfer coefficient that exchanges heat with a thermal reservoir.

Description

This problem solves the transient heat equation with strong form:

where , , , and , subject to the initial condition .

In this example, we solve this using the weak form

where

Example File

[Mesh]
  type = MFEMMesh
  file = gold/mug.e
  dim = 3
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
  []
[]

[Variables]
  [temperature]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[Functions]
  [reservoir_far_temperature]
    type = ParsedFunction
    expression = 0.5
  []
  [heat_transfer_coefficient]
    type = ParsedFunction
    expression = 5.0
  []
[]

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = temperature
    coefficient = thermal_conductivity
  []  
  [dT_dt]
    type = MFEMTimeDerivativeMassKernel
    variable = temperature
    coefficient = volumetric_heat_capacity
  []    
[]

[BCs]
  [bottom]
    type = MFEMScalarDirichletBC
    variable = temperature
    boundary = '1'
    value = 1.0
  []
  [top]
    type = MFEMConvectiveHeatFluxBC
    variable = temperature
    boundary = '2'
    T_infinity = reservoir_far_temperature
    heat_transfer_coefficient = heat_transfer_coefficient
  []
[]

[Materials]
  [Substance]
    type = MFEMGenericConstantMaterial
    prop_names = 'thermal_conductivity volumetric_heat_capacity'
    prop_values = '1.0 1.0'
  []
[]

[Preconditioner]
  [boomeramg]
    type = MFEMHypreBoomerAMG
  []
[]

[Solver]
  type = MFEMHypreGMRES
  preconditioner = boomeramg
  l_tol = 1e-16
  l_max_its = 1000  
[]

[Executioner]
  type = MFEMTransient
  device = cpu
  dt = 2.0
  start_time = 0.0
  end_time = 6.0
[]

[Outputs]
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/HeatTransfer
    vtk_format = ASCII
  []
[]
(test/tests/kernels/heattransfer.i)