3D Building

In this example, we estimate an apartment with 5 rooms using the stationary heat equation.

1. Running the case

The command line to run this case is

mpirun -np 4 feelpp_toolbox_heat --case "github:{repo:toolbox,path:examples/modules/heat/examples/3Dbuilding}"

Case option

--case "github:{repo:toolbox,path:examples/modules/heat/examples/3Dbuilding}"

2. Data files

The case data files are available in Github here

CFG file - [Edit the file]
JSON file - [Edit the file]

3. Geometry

The mesh can be found on Girder

4. Input parameters

Name	Description	Unit
\(k\)	thermal conductivity	\(W \cdot m^{-1} \cdot K^{-1}\)
\(T\)	temperature	\(K\)
\(T_{ext}\)	external temperature	\(K\)
\(h\)	transfer coefficient	\(W\cdot m^{-2}\cdot K^{-1}\)

Name

Description

Unit

\(k\)

thermal conductivity

\(W \cdot m^{-1} \cdot K^{-1}\)

\(T\)

temperature

\(K\)

\(T_{ext}\)

external temperature

\(K\)

\(h\)

transfer coefficient

\(W\cdot m^{-2}\cdot K^{-1}\)

5. Materials

    "Materials":
    {
        "air":
        {
	    "markers":"air",
            "k":"1"//[ W/(m*K) ]
            //"Cp":"1000.005", //[ J/(kg*K) ]
            //"rho":"1.205" //[ kg/(m^3) ]
        },
        "internal-walls":
        {
	    "markers":"internal-walls",
            "k":"0.25"
        },
        "internal-doors":
        {
	    "markers":"internal-doors",
            "k":"0.13"
        }
    },

6. Boundary Conditions

The boundary conditions for this thermal probleme are introduced Dirichlet boundary conditions and Robin boundary conditions.

    "BoundaryConditions":
    {
        "temperature":
        {
            "Dirichlet":
            {
                "heater-livingroom": { "expr":"325" },
                "heater-kitchen": { "expr":"320" },
                "heater-bedroom1": { "expr":"315" },
                "heater-bedroom2": { "expr":"312" },
                "heater-bathroom": { "expr":"298" }
            },
            "Robin":
            {
                "exterior-walls":
                {
                    "expr1":"1.0/(0.06+0.01/0.5 + 0.3/0.8 + 0.20/0.032 +0.016/0.313 +0.14)",// h coeff
                    "expr2":"275"// temperature exterior
                },
                "front-door":
                {
                    "expr1":"1.0/(0.06+0.06/0.150+0.1/0.029+0.14)", // h coeff
                    "expr2":"275"// temperature exterior
                }
            }
        }
    },

7. Output

The field of interest for this example is the temperature.

    "PostProcess":
    {
	"Exports":
	{
            "fields":["temperature"]
	}
    }

From the result of ParaView, we can see that the temperature is dissipated along the 5 heaters.