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}"

mpirun

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"
        }
    },

json

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
                }
            }
        }
    },

json

7. Output

The field of interest for this example is the temperature.

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

json

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