ex.05

Example 5

September 2013 5.1 Version 15.0.0

EXAMPLE 5

SOLID/SOLID HEAT CONDUCTION PROBLEM

DESCRIPTION

All previous examples involved a single domain calculation: one set of equations with one set of material parameters have been solved over the whole domain. Here we wish to introduce the new concept of multi-domain calculation: distinct sets of equations are solved on non-overlapping subdomains. This example involves a heat transfer calculation between two solids. In Fig. 1, we illustrate the heat transfer problem between solid 1 and solid 2, with their respective thermal conductivities k1 (= 400 W/m/C) and k2 (= 50 W/m/C), and their

respective boundary conditions. In particular, we note that the geometry of the problem consists of two non-overlapping subdomains.

T = 100 T = 20

insulated

insulated

k = 4001

k = 502

subdomain I

(boundary 1)

(boundary 2)

(boundary 3)

(boundary 4)

subdomain II

Fig. 1. Solid/solid heat conduction problem and boundary conditions.

The mesh is included in the box x = [0, 0.3], y = [0, 0.8].

Example 5

September 2013 5.2 Version 15.0.0

KEYWORDS

heat transfer in solids, multi-domain calculation

FILENAMES

solsol.mdf, solsol.msh, solsol.dat, solsol.cons, solsol.lst, res, cfx.res

NEW CONCEPTS

We introduce here the new concept of multi-domain calculation: distinct sets of equations are solved on non-overlapping subdomains. In Polydata, we will define one single task for solving two coupled heat conduction problems. Each problem is described in a sub-task, but the two sub-tasks are part of the same task.

POLYDATA SESSION

- Read a mesh: solsol.msh - Create a new task: 2D planar, steady-state.

Create a sub-task: Heat Conduction Domain: S1 Material data Thermal conductivity: K = 400 Thermal boundary conditions S2: interface see note 1 BS1: insulated boundary BS3: insulated boundary BS4: temperature imposed: Tp = 100 C

Create a sub-task: Heat Conduction Domain: S2 Material data Thermal conductivity: K = 50 Thermal boundary conditions S1: interface see note 1 BS1: insulated boundary BS2: temperature imposed: Tp = 20 C BS3: insulated boundary - Outputs - Default output : CFD-Post - System of units for CFD-Post: metric_MKSA+Celsius

Example 5

September 2013 5.3 Version 15.0.0

- Probe (optional) probe 1: prefix: solsol_1 location: (0.1, 0.4) probe 2: prefix: solsol_2 location: (0.2, 0.4)

Save and Exit - Mesh file: solsol.msh - Data file: solsol.dat - Result file: res - CFD-Post: cfx.res

Note 1 : Interface between subdomains

Since a heat conduction problem is solved on both subdomains, interface boundary conditions must be specified along their intersection. For the energy equation, such a boundary condition ensures the continuity of the temperature field and of the heat flux. In the present case, it is a non-moving interface.

RUNNING POLYFLOW

At the present stage, we have two input files for POLYFLOW: a mesh file and a data file. In view of our filename syntax, their names are SOLSOL.MSH and SOLSOL.DAT, respectively. This last file will be used as standard input file for POLYFLOW. As standard output file, the listing, we select the name SOLSOL.LST. A result file named RES is also generated, which can be used for a future restart.

Graphic post-processing

Mesh and result files for graphic post-processing are generated. In Fig. 2.a, we display the temperature contour lines over the whole domain. The effects arising from different thermal conductivities are apparent. In Fig. 2.b, we display the temperature profiles on several horizontal lines crossing the mesh.

Example 5

September 2013 5.4 Version 15.0.0

a) b)

Fig. 2. Solid/solid heat conduction problem:

a) Temperature contour lines (init. val. = 20, incr. = 5, fin. val. = 100), b) Temperature profiles along various horizontal lines (y=0.45, y=0.4 and y=0.35).