10.16         Heat_Conduction_Model: Generalized Heat Conduction Model

 

HEAT_CONDUCTION

 

 

            Material_name = HEAT_CONDUCTION   

                  Material_set_number = mset ,  etc...

 

 

            The generalized heat conduction model is defined as follows.

 

Note    Variable Name              Type  Default   Description

 

            Material_set_number   integer    [1]       Material set number  Numat

 

            Mass_density                 real     [0.0]     Mass density  (matrix/bulk material)

 

            Reference_temperature  real  [273.15]  Reference temperature T0

 

            Relaxation_time_1         real     [0.0]     First relaxation time t1

 

            Relaxation_time_2         real     [0.0]     Second relaxation time t2

 

            Specific_heat                  real     [0.0]     Specific heat c (matrix/bulk material)

 

(1)        Coefficient_c1               real     [0.0]     Nonlinear Specific Heat Multiplier c1

            Coefficient_c2               real     [0.0]     Nonlinear Specific Heat Multiplier c2

            Coefficient_c3               real     [0.0]     Nonlinear Specific Heat Multiplier c3

            Coefficient_c4               real     [0.0]     Nonlinear Specific Heat Multiplier c4

            Coefficient_c5               real     [0.0]     Nonlinear Specific Heat Multiplier c5

           

• Thermal Conductivity

            Thermal_Conductivity    list     [none]    Thermal conductivity (matrix/bulk material)

 

            Type                                list       [*]       Form of thermal conductivity matrix:

               isotropic / anisotropic                           if isotropic only k11 need be specified.

 

            k_11                               real     [0.0]     Conductivity k11

            k_22                               real     [0.0]     Conductivity k22

            k_33                               real     [0.0]     Conductivity k33

            k_12                               real     [0.0]     Conductivity k12

            k_23                               real     [0.0]     Conductivity k23

            k_13                               real     [0.0]     Conductivity k13

 

(2)        Coefficient_cd1             real     [0.0]     Nonlinear Conductivity Multiplier cd1

            Coefficient_cd2             real     [0.0]     Nonlinear Conductivity Multiplier cd2

            Coefficient_cd3             real     [0.0]     Nonlinear Conductivity Multiplier cd3

            Coefficient_cd4             real     [0.0]     Nonlinear Conductivity Multiplier cd4

            Coefficient_cd5             real     [0.0]     Nonlinear Conductivity Multiplier cd5

 

 

(cont'd)

 

(cont’d)

 

Note    Variable Name              Type  Default   Description

 

• Thermal Coefficient

            Thermal_coefficient        list     [none]    Thermal Moduli

 

            Type                                list       [*]       Form of thermal coefficient matrix:

               isotropic / anisotropic                            if isotropic only 11 need be specified.

 

(3)        Beta_11                          real     [0.0]     Thermal Coefficient 11

            Beta_22                          real     [0.0]     Thermal Coefficient 22

            Beta_33                          real     [0.0]     Thermal Coefficient 33

            Beta_12                          real     [0.0]     Thermal Coefficient 12

            Beta_23                          real     [0.0]     Thermal Coefficient 23

            Beta_13                          real     [0.0]     Thermal Coefficient 13

 

(4)        Coefficient_cb1             real     [0.0]     Nonlinear Thermal Multiplier cb1

            Coefficient_cb2             real     [0.0]     Nonlinear Thermal Multiplier cb2

 

• Thermal Expansion Coefficient

            Thermal_Expansion        list     [none]    Thermal Expansion Moduli

 

            Type                                list       [*]       Form of thermal coefficient matrix:

               isotropic / anisotropic                            if isotropic only 11 need be specified.

 

(5)        Alpha_11                        real     [0.0]     Thermal Expansion 11

            Alpha_22                        real     [0.0]     Thermal Expansion 22

            Alpha_33                        real     [0.0]     Thermal Expansion 33

            Alpha_12                        real     [0.0]     Thermal Expansion 12

            Alpha_23                        real     [0.0]     Thermal Expansion 23

            Alpha_13                        real     [0.0]     Thermal Expansion 13

 

(4)        Coefficient_cb1             real     [0.0]     Nonlinear Thermal Multiplier cb1

            Coefficient_cb2             real     [0.0]     Nonlinear Thermal Multiplier cb2

 

 

EXAMPLE

            Heat_conduction_model  /

                 material_type = Linear  /

                 material_name = heat_conduction

                     material_set_number = 1  /

                     reference_temperature = 1.0  /

                     mass_density = 1.0  /

                     specific_heat = 1.0e-6  /

                     thermal_conductivity  /

                          type = isotropic  /

                          k_11 = 1.60e-3  /

                     thermal_coefficient  /

                          type = isotropic  /

                          beta_11 = 1.00

Notes/

(1)        The nonlinear specific heat c(T) is computed by the following equation:

 

           

 

where T =  = absolute temperature.

 

(2)        The nonlinear thermal conductivity k(T) is computed by the following equation:

 

           

 

where T =   = absolute temperature.

 

(3)        In the linear isotropic case, the thermal modulus  is related to the usual coefficient of thermal expansion  via:

 

           

 

where E = Young's modulus, and  = Poisson's ratio.

 

(4)        The nonlinear thermal modulus  is computed by the following equation:

 

           

 

where T =   = absolute temperature.

 

(5)        The thermal moduli  are computed from the thermal expansion moduli  via:

 

           

 

where E denotes the linear elasticity tensor.

 

 

10.16.1      Multi-Phase Fluid Flow

 

         For multi-phase fluid flow problems (see Section 9.2.0.16), the following material data must also be provided for each phase.

 

 

Note    Variable Name                 Type     Default      Description

 

            Phase_number                integer       [1]          Phase number

 

            Specific_heat                     real        [0.0]        Specific heat CP

 

·         Thermal Conductivity

 

      Thermal conductivity         list        [none]       Thermal conductivity

 

            Type                                   list          [*]          Form of thermal conductivity matrix:

               isotropic / anisotropic                                    if isotropic only k11 need be specified.

 

            k_11                                  real        [0.0]        Conductivity k11

            k_22                                  real        [0.0]        Conductivity k22

            k_33                                  real        [0.0]        Conductivity k33

            k_12                                  real        [0.0]        Conductivity k12

            k_23                                  real        [0.0]        Conductivity k23

            k_13                                  real        [0.0]        Conductivity k13

 

 

 

 

Notes . .