Types of boundaries for temperature

CrysMAS will support you in specifying a boundary condition for each line and for each variable. In the Boundaries dialog you can choose between three types of boundary conditions: Dirichlet, Neumann and Poincaré. Boundaries can be displayed in the drawing.

Neumann boundary

The Neumann boundary specifies a constant flux density of the variable normal to the line, for temperature the heat flux density. You can specify an adiabatic boundary condition setting the flux = 0.

The flux density can be constant along the line or may have a dependency along the line, on radial, or on axial coordinate. In the latter cases, it is a function f(l), where l is 0 at the start point and 1 at the end point of the line, or a function f(r) or f(z) if it should depend on radius or axial coordinate, resp.

Dirichlet boundary

The Dirichlet boundary specifies fixed values for the variable along the line. The boundary will be displayed in the drawing as variable name (D = value). The Dirichlet boundary for temperature, for instance, is displayed as Temperature (D = 300).

Values which are not constant along the line can be defined in two ways:

  • by a f(l/z/r) function (as for Neumann boundaries)

  • by specifying the values along the line in a profile file ( *.pro file).

The *.pro file has two rows divided into columns.

The first row specifies the number of points and their positions along the line. The position is the distance between the start point and the actual position in relation to the length of the line. This distance can adopt values between 0 and 1 .

Points along the boundary line 

Figure 34. Points along the boundary line

The first column of the second row is reserved for time-dependent computation and must contain the time values. In the remaining columns the values for the variable in each point are specified. CrysMAS will set values between these points by linear interpolation. The *.pro file shall not contain any additional comments.

col 1

col 2 (point 1)

col 3 (point 2)

col 4 (point 3)

3

0.2

0.5

0.7

0

300

350

370

If this boundary is specified for time-dependent computation, the *.pro file will have one line for each time step. The first column always contains the time value. The boundary values between the time steps will be automatically calculated by linear interpolation.

Tip

In the beginning the coordinates of the start point are usually not known. You can easily determine them by using the Monitor/Write Profile dialog, see Monitor/Write Profile. You select the boundary line and the coordinates of start and end points will be listed in the output file.

You can also see the direction of the boundary line pressing the show button for displaying the boundaries for the variable selected or the show all button for displaying the boundaries for all variables. Boundaries will be drawn in red, with an arrow indicating their direction.

Poincaré boundary

The Poincaré boundary specifies that the flux of a variable is proportional to the difference between the value of the variable on the line and a given reference value.

In case of temperature, the reference value is the temperature of the surrounding media (Ref Value = f(l)) and the proportional coefficient is called the heat transfer coefficient (Coeff = f(x)). The parser understands x as the current selected variable, the one for each we apply the boundary condition.

RefRad boundary

The RefRad boundary specifies a heatflux corresponding to radiation towards a reference temperature, which can be given as function of l, r or z.

ExternalFlux, ExternalTemperature

used for coupling with other programs, please contact CGL_support@iisb.fraunhofer.de for more information.

Temperature dependent Poincaré and Dirichlet boundary

The temperature dependent Poincaré and Dirichlet boundary types have the same behavior as their "normal" counterparts described in before. The major difference is, that the coefficients or values used in this types are functions of the temperature f(T) at the corresponding point on the region line.

Boundaries of this type are particularly useful for modeling evaporation or dissolution of a chemical species at a boundary of a fluid region. As these boundary types are redundant for the variable temperature, they cannot be set for this variable.