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}"

2. Data files

The case data files are available in Github here

3. Geometry

heat 3d

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

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

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.