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+# This example calculates the effective thermal conductivity across a microstructure
+# with circular second phase precipitates. Two methods are used to calculate the effective thermal conductivity,
+# the direct method that applies a temperature to one side and a heat flux to the other,
+# and the AEH method.
+[Mesh] #Sets mesh size to 10 microns by 10 microns
+  type = GeneratedMesh
+  dim = 2
+  nx = 100
+  ny = 100
+  xmax = 10
+  ymax = 10
+[]
+
+[MeshModifiers] #Adds a new node set
+  [./new_nodeset]
+    type = AddExtraNodeset
+    coord = '5 5'
+    new_boundary = 100
+  [../]
+[]
+
+[Variables] #Adds variables needed for two ways of calculating effective thermal cond.
+  [./T]
+    initial_condition = 800
+  [../]
+  [./temp_x]
+    initial_condition = 800
+    scaling = 1.0e4 #Scales residual to improve convergence
+  [../]
+  [./temp_y]
+    initial_condition = 800
+    scaling = 1.0e4  #Scales residual to improve convergence
+  [../]
+[]
+
+[AuxVariables] #Creates second constant phase
+  [./phase2]
+  [../]
+[]
+
+[ICs] #Sets the IC for the second constant phase
+  [./phase2_IC] #Creates circles with smooth interfaces at random locations
+    variable = phase2
+    type = MultiSmoothCircleIC
+    int_width = 0.3
+    numbub = 20
+    bubspac = 1.5
+    radius = 0.5
+    outvalue = 0
+    invalue = 1
+    block = 0
+  [../]
+[]
+
+[Kernels]
+  [./HtCond] #Kernel for direct calculation of thermal cond
+    type = HeatConduction
+    variable = T
+  [../]
+  [./heat_x] #All other kernels are for AEH approach to calculate thermal cond.
+    type = HeatConduction
+    variable = temp_x
+  [../]
+  [./heat_rhs_x]
+    type = HomogenizationHeatConduction
+    variable = temp_x
+    component = 0
+  [../]
+  [./heat_y]
+    type = HeatConduction
+    variable = temp_y
+  [../]
+  [./heat_rhs_y]
+    type = HomogenizationHeatConduction
+    variable = temp_y
+    component = 1
+  [../]
+[]
+
+[BCs]
+  [./Periodic]
+    [./all]
+      auto_direction = 'x y'
+      variable = 'temp_x temp_y'
+    [../]
+  [../]
+  [./left_T] #Fix temperature on the left side
+    type = PresetBC
+    variable = T
+    boundary = left
+    value = 800
+  [../]
+  [./right_flux] #Set heat flux on the right side
+    type = NeumannBC
+    variable = T
+    boundary = right
+    value = 5e-6
+  [../]
+  [./fix_x] #Fix temp_x at a single point
+    type = DirichletBC
+    variable = temp_x
+    value = 800
+    boundary = 100
+  [../]
+  [./fix_y] #Fix temp_y at a single point
+    type = DirichletBC
+    variable = temp_y
+    value = 800
+    boundary = 100
+  [../]
+[]
+
+[Materials]
+  [./thcond] #The equation defining the thermal conductivity is defined here, using two ifs
+    # The k in the bulk is k_b, in the precipitate k_p2, and across the interaface k_int
+    type = ParsedMaterial
+    block = 0
+    constant_names = 'length_scale k_b k_p2 k_int'
+    constant_expressions = '1e-6 5 1 0.1'
+    function = 'sk_b:= length_scale*k_b; sk_p2:= length_scale*k_p2; sk_int:= k_int*length_scale; if(phase2>0.1,if(phase2>0.95,sk_p2,sk_int),sk_b)'
+    outputs = exodus
+    f_name = thermal_conductivity
+    args = phase2
+  [../]
+[]
+
+[Postprocessors]
+  [./right_T]
+    type = SideAverageValue
+    variable = T
+    boundary = right
+  [../]
+  [./k_x_direct] #Effective thermal conductivity from direct method
+    # This value is lower than the AEH value because it is impacted by second phase
+    # on the right boundary
+    type = ThermalCond
+    variable = T
+    flux = 5e-6
+    length_scale = 1e-06
+    T_hot = 800
+    dx = 10
+    boundary = right
+  [../]
+  [./k_x_AEH] #Effective thermal conductivity in x-direction from AEH
+    type = HomogenizedThermalConductivity
+    variable = temp_x
+    temp_x = temp_x
+    temp_y = temp_y
+    component = 0
+    scale_factor = 1e6 #Scale due to length scale of problem
+  [../]
+  [./k_y_AEH] #Effective thermal conductivity in x-direction from AEH
+    type = HomogenizedThermalConductivity
+    variable = temp_y
+    temp_x = temp_x
+    temp_y = temp_y
+    component = 1
+    scale_factor = 1e6 #Scale due to length scale of problem
+  [../]
+[]
+
+[Preconditioning]
+  [./SMP]
+    type = SMP
+    off_diag_row = 'temp_x temp_y'
+    off_diag_column = 'temp_y temp_x'
+  [../]
+[]
+
+[Executioner]
+  type = Steady
+  l_max_its = 15
+  solve_type = NEWTON
+  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart -pc_hypre_boomeramg_strong_threshold'
+  petsc_options_value = 'hypre boomeramg 31 0.7'
+  l_tol = 1e-04
+[]
+
+[Outputs]
+  exodus = true
+  print_perf_log = true
+  csv = true
+[]