Heat Transfer in Porous Media
Next, set up the Heat Transfer in Porous Media interface. Similarly to the procedure used for the mass transfer interface, go through the generated feature nodes, modify and add as needed.
1
In the Model Builder window, under Monolith Reactor Model click Heat Transfer in Porous Media.
2
In the Settings window for Heat Transfer in Porous Media, locate the Domain Selection section.
3
From the Selection list, choose Heat Transfer Domains.
Fluid 1
Begin by specifying settings for convective and conductive heat transfer in the monolith channels.
1
In the Model Builder window, expand the Porous Medium 1 node, then click Fluid 1.
2
In the Settings window for Fluid, locate the Heat Conduction, Fluid section.
3
From the kf list, choose From material.
4
Locate the Thermodynamics, Fluid section. From the ρf list, choose From material.
5
From the Cp,f list, choose From material.
6
From the γ list, choose From material.
Note that the fluid properties are now defined by the Fluid subnode of the Porous Material.
Porous Matrix 1
1
In the Model Builder window, click Porous Matrix 1.
2
In the Settings window for Porous Matrix, locate the Matrix Properties section.
3
From the Define list, choose Solid phase properties.
4
Locate the Heat Conduction, Porous Matrix section. From the ks list, choose User defined. From the list, choose Diagonal.
Specifying the diagonal thermal conductivity elements allows you to represent anisotropic conductive heat transfer in the monolith channels.
5
Specify the ks matrix as
ks_radial
0
0
ks_axial
Note that apart from the conductivity, the matrix properties are defined by the Solid: Monolith Material node added to the Porous Material feature.
Initial Values 1
1
In the Model Builder window, under Monolith Reactor Model > Heat Transfer in Porous Media click Initial Values 1.
2
In the Settings window for Initial Values, locate the Initial Values section.
3
In the T text field, type T_gas_in. This parameter was previously defined in Parameters: Temperature and Monolith Parameters.
Temperature 1
1
In the Model Builder window, click Temperature 1.
2
Select Boundary 18 only.
Outflow 1
1
In the Model Builder window, click Outflow 1.
2
In the Settings window for Outflow, locate the Boundary Selection section.
3
From the Selection list, choose Flow Outlet.
Heat Source 1
Couple the Heat Source to the heat source defined by the Transport of Diluted Species in Porous Media interface. The heat source defined in this interface already accounts for the porosity and various chemical reactions on the different catalyst domains. For this coupling, it is important that the domain selections match between the Heat Source node and the Transport of Dilute Species in Porous Media Interface.
1
In the Model Builder window, under Monolith Reactor Model> Heat Transfer in Porous Media click Heat Source 1.
2
Locate the Domain Selection section. From the Selection list, choose Porous and Free Flow Domains.
3
From the Material type list, choose From material.
4
Locate the Heat Source section. From the Q0 list, choose Heat source (tds).
Continue by adding the features needed to describe the inflow boundary condition, the fluid domains, temperature boundary conditions, solid domains, porous domain, and the heat flux boundary conditions.
Inflow 1
1
In the Physics toolbar, click  Boundaries and choose Inflow.
2
In the Settings window for Inflow, locate the Boundary Selection section.
3
From the Selection list, choose Flow Inlet.
4
Locate the Upstream Properties section. In the Tustr text field, type T_gas_in.
Fluid 1
1
In the Physics toolbar, click  Domains and choose Fluid.
2
In the Settings window for Fluid, locate the Domain Selection section.
3
From the Selection list, choose Free Flow Domain.
4
Locate the Thermodynamics, Fluid section. From the Fluid type list, choose Gas/Liquid.
Fluid 2
1
In the Physics toolbar, click  Domains and choose Fluid.
2
Click in the Graphics window and then press Ctrl+A to select all domains.
3
In the Settings window for Fluid, locate the Domain Selection section.
4
From the Selection list, choose Insulating Gas.
Next, add a temperature boundary condition at the metal wall of the reactor upstream of the SCR catalyst. We assume that the temperature is the same as that of the inlet gas.
Temperature 2
1
In the Physics toolbar, click  Boundaries and choose Temperature.
2
Select Boundaries 17, 48, and 51 only.
3
In the Settings window for Temperature, locate the Temperature section.
4
In the T0 text field, type T_gas_in.
We also have to define the temperature for the reactor wall downstream of the ASC catalyst. We assume that the temperature is that of the gas exiting the ASC catalyst. Add a feature to derive the average temperature of the outlet gas, and assign it to the boundary.
Average 1 (aveop1)
1
In the Definitions toolbar, click  Nonlocal Couplings and choose Average.
2
In the Settings window for Average, locate the Source Selection section.
3
From the Geometric entity level list, choose Boundary.
4
Select Boundaries 6 and 45 only.
Temperature 3
1
In the Physics toolbar, click  Boundaries and choose Temperature.
2
Select Boundaries 14, 16, 45, and 50 only.
3
In the Settings window for Temperature, locate the Temperature section.
4
In the T0 text field, type aveop1(T).
Add a Solid feature to describe the heat transfer in the metal shell.
Solid 1
1
In the Physics toolbar, click  Domains and choose Solid.
2
In the Settings window for Solid, locate the Domain Selection section.
3
From the Selection list, choose Metal Shell Domain.
Add a Heat Flux feature to describe the heat transfer from the reactor exterior surface to the surrounding air.
Heat Flux 1
1
In the Physics toolbar, click  Boundaries and choose Heat Flux.
2
Select Boundaries 31–34 and 70 only.
3
In the Settings window for Heat Flux, locate the Material Type section.
4
From the Material type list, choose From material.
5
Locate the Heat Flux section. From the Flux type list, choose Convective heat flux.
6
In the h text field, type h_conv.
7
In the Text text field, type T_amb.
Add another Heat Flux feature to describe the heat transfer from the reactor outlet surface to the surrounding air.
Heat Flux 2
1
In the Physics toolbar, click  Boundaries and choose Heat Flux.
2
Select Boundary 15 only.
3
In the Settings window for Heat Flux, locate the Material Type section.
4
From the Material type list, choose Solid.
5
Locate the Heat Flux section. From the Flux type list, choose Convective heat flux.
6
In the h text field, type 1[W/(m^2*K)].
7
In the Text text field, type T_amb.
The final feature that is needed to describe the heat transfer in the system is a Porous Medium feature for the supportive mat domain. The fluid in the mat is, for the simplicity of this example, assumed to be exhaust gas. This is a fair assumption, and this way we can take the fluid properties from the material.
Porous Medium 2
1
In the Physics toolbar, click  Domains and choose Porous Medium.
2
In the Model Builder window, click Porous Medium 2.
3
Select Domain 14 only.
Fluid 1
1
In the Model Builder window, click Fluid 1.
2
In the Settings window for Fluid, locate the Thermodynamics, Fluid section.
3
From the γ list, choose From material.
Porous Matrix 1
1
In the Model Builder window, click Porous Matrix 1.
2
In the Settings window for Porous Matrix, locate the Matrix Properties section.
3
From the εp list, choose User defined. In the associated text field, type 0.5.
4
Locate the Heat Conduction, Porous Matrix section. From the kb list, choose User defined. In the associated text field, type 0.1.
5
Locate the Thermodynamics, Porous Matrix section. From the ρb list, choose User defined. In the associated text field, type 0.63[g/cm^3].
6
From the Cp,b list, choose User defined. In the associated text field, type 1.1[J/g/degC].
The node sequence in the Model Builder under the Heat Transfer in Porous Media interface should now match this figure:
Having finished setting up the heat transfer physics, proceed to set up the Laminar Flow interface. Model the fluid as compressible, and assume that the flow is laminar both inside the channels and in the free-flow domain between the catalysts.