Tutorial 1: Heat conduction in a slabProblem SpecificationStep 1: Specifying the Problem TypeStep 2: Creating the GeometryStep 3: MeshingStep 4: Defining Material Properties and Initial ConditionStep 5: Defining Boundary ConditionsStep 6: Specifying Solver ParametersStep 7: PostprocessingStep 8: Save and ExitTutorial 1: Heat conduction in a slab2007 Cornell UniversityBEE453, Professor Ashim DattaAuthored by Vineet Rakesh and Frank KungSoftware: COMSOL 3.3Tutorial 1: Heat conduction in a slab............................................................................................... 1Problem Specification.................................................................................................................. 1Step 1: Specifying the Problem Type..........................................................................................2Step 2: Creating the Geometry.................................................................................................... 4Step 3: Meshing.......................................................................................................................... 5Step 4: Defining Material Properties and Initial Condition...........................................................7Step 5: Defining Boundary Conditions......................................................................................... 8Step 6: Specifying Solver Parameters......................................................................................... 9Step 7: Postprocessing............................................................................................................. 11Step 8: Save and Exit................................................................................................................ 15Problem SpecificationThis is the first of a series of examples intended for a gentle introduction to COMSOL. Ourgoal here is to compute transient temperatures profiles for 1-D heat conduction in the slabbelow during the heating process. The temperature in both bottom and top surfaces of theslab are kept constant and equal to 90 0C and 20 0C respectively. The sides of the slab areassumed to be insulated. The thickness of the slab is 4 cm. The initial temperature is 20 C.The density is 900 kg/m3. The thermal conductivity is 0.55 W/mK. The specific heat is 3800J/kg K.1Step 1: Specifying the Problem TypeThe problem in this case is transient heat conduction in a 1D setting. We will first setCOMSOL up for this type of problemThe model you specify determine the Governing Equations that will be used. Starting from theenergy transport equation:sourcepdiff usionpconvectiontransientcQxTckxTutT 22 (1)For our problem, the temperatures are dependant on time; there is no fluid flow and no sourceterms. The only mode of heat transfer is by diffusion. So the problem is a transient diffusionproblem with no convection and heat source. So the governing equation changes to:22xTcktTp (2)21. Start COMSOL by doubleclicking on the COMSOLMultiphysics icon on theDesktop2. Select 2D next to Space Dimension(Note: COMSOL can do 1D problems, however to give you a better understanding of COMSOL we’ll model the problem as 2D)3. Single Click on COMSOL Multiphysics >> Heat Transfer>> Conduction >> Transient Analysis. Transient Analysis under conduction is selected as we intend to solve a time dependent conduction problem (Equation 2).4. Click on the Settings Tab5. Set the Unit system to SI6. Click OK. COMSOL Window opens up.7. Under File, click on Save as…8. Create your own folder using your NetID in the My Documents folder and save your work there. Specify the file name (e.g. cond.mph) andsave it as .mph file.34Step 2: Creating the GeometryThe geometry in this case is a 1D slab that is 4 cm high (along y axis). We are modeling theproblem as 2D and so we assume the dimension of 2 cm in the other direction (i.e. along xaxis). In this example (in contrast with the drug delivery example) we will draw out the slabdirectly without specifying the grid.1. Click on Draw >> Specify Objects >>Rectangle. Rectangle window opensup.2. Specify width as 0.02 and height as 0.04. These are the dimensions of the slab in m.3. Click on OK.4. Click on Zoom Extents to fit the geometry in the window.The geometry that is created is shown inthe figure. 5Step 3: MeshingMeshing is dividing the geometry into small elements. We can mesh the face directly, but inthis case, we will mesh the edges first and then the face. This method is used to control thenumber of elements in certain parts of the geometry like the boundaries and interfaces. Inmany cases we need a finer mesh near the boundary and so we mesh the edge accordinglyand what we get is a non-uniform mesh. However in this case we mesh the geometry with auniform mesh with a spacing of 0.002 between the nodes.61. Under Mesh, click on MappedMesh Parameters…2. Click on the Boundary Tab3. In Boundary Selection, select 1 and 4 by left clicking and holding the Ctrl key. We will specify 20 elements each on the left and right edges.4. Check the box for Constrainededge element distribution5. Click on Number of edgeelements, and type in 20 in thebox below.6. For boundary 2 and 3, use number of edge elements as 10. We specify 10 elements each on the top and bottom edges.7. Press the ‘Remesh’ Button on thebottom. The mesh that isobtained is shown in the figure.8. Click ‘Ok’79. Your screen should now look likethis.8Step 4: Defining Material Properties and Initial ConditionWe are solving the energy equation and so we need to provide the solver with the appropriatematerial property values required for the analysis. These properties are:(i) Density (): The density of the material of the slab is 900 kgm-3(ii) Thermal Conductivity (k): The thermal conductivity is 0.55 W(mK)-1(iii) Specific Heat (cp): The specific heat is 3800 J (kgK)-1The Slab is initially at a temperature of 200C initially. We will also specify this in the software inthis step. 1. Under Physics, click onSubdomain Settings…2. Click on 1 to select the slab.3. Left click on the text field nextto Thermal Conductivity andtype 0.554. Left click on the text field nextto Density and type 9005. Left click on the text field nextto Heat Capacity and type 38006. Click on the Init Tab7. In the box under