Transient Thermal Conduction Example

Introduction

This tutorial was created using ANSYS 7.0 to solve a simple transient conduction problem. Special thanks to Jesse Arnold for the analytical solution shown at the end of the tutorial.

The example is constrained as shown in the following figure. Thermal conductivity (k) of the material is 5 W/m*K and the block is assumed to be infinitely long. Also, the density of the material is 920 kg/m^3 and the specific heat capacity (c) is 2.040 kJ/kg*K.

It is beneficial if the Thermal-Conduction tutorial is completed first to compare with this solution.

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Preprocessing: Defining the Problem

1. Give example a TitleUtility Menu > File > Change Title...
   /Title,Transient Thermal Conduction
2. Open preprocessor menuANSYS Main Menu > Preprocessor
   /PREP7
3. Create geometryPreprocessor > Modeling > Create > Areas > Rectangle > By 2 Corners
   X=0, Y=0, Width=1, Height=1
   BLC4,0,0,1,1
4. Define the Type of Element
Preprocessor > Element Type > Add/Edit/Delete... > click 'Add' > Select Thermal Mass Solid, Quad 4Node 55
ET,1,PLANE55For this example, we will use PLANE55 (Thermal Solid, Quad 4node 55). This element has 4 nodes and a single DOF (temperature) at each node. PLANE55 can only be used for 2 dimensional steady-state or transient thermal analysis.

5. Element Material Properties
Preprocessor > Material Props > Material Models > Thermal > Conductivity > Isotropic > KXX = 5 (Thermal conductivity)
MP,KXX,1,10Preprocessor > Material Props > Material Models > Thermal > Specific Heat > C = 2.04
MP,C,1,2.04Preprocessor > Material Props > Material Models > Thermal > Density > DENS = 920
MP,DENS,1,920

6. Mesh Size
Preprocessor > Meshing > Size Cntrls > ManualSize > Areas > All Areas > 0.05
AESIZE,ALL,0.05

7. Mesh
Preprocessor > Meshing > Mesh > Areas > Free > Pick All
AMESH,ALLAt this point, the model should look like the following:

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Solution Phase: Assigning Loads and Solving

1. Define Analysis Type
Solution > Analysis Type > New Analysis > Transient
ANTYPE,4The window shown below will pop up. We will use the defaults, so click OK.


2. Set Solution Controls
Solution > Analysis Type > Sol'n ControlsThe following window will pop up.

A) Set Time at end of loadstep to 300 and Automatic time stepping to ON.
B) Set Number of substeps to 20, Max no. of substeps to 100, Min no. of substepsto 20.
C) Set the Frequency to Write every substep.
Click on the NonLinear tab at the top and fill it in as shown

D) Set Line search to ON .
E) Set the Maximum number of iterations to 100.
For a complete description of what these options do, refer to the help file. Basically, the time at the end of the load step is how long the transient analysis will run and the number of substeps defines how the load is broken up. By writing the data at every step, you can create animations over time and the other options help the problem converge quickly.

3. Apply Constraints
For thermal problems, constraints can be in the form of Temperature, Heat Flow, Convection, Heat Flux, Heat Generation, or Radiation. In this example, 2 sides of the block have fixed temperatures and the other two are insulated.



• Solution > Define Loads > Apply
  Note that all of the -Structural- options cannot be selected. This is due to the type of element (PLANE55) selected.
• Thermal > Temperature > On Nodes
• Click the Box option (shown below) and draw a box around the nodes on the top line and then click OK.
  The following window will appear:
  
  
• Fill the window in as shown to constrain the top to a constant temperature of 500 K
• Using the same method, constrain the bottom line to a constant value of 100 KOrange triangles in the graphics window indicate the temperature contraints.


4. Apply Initial Conditions
Solution > Define Loads > Apply > Initial Condit'n > Define > Pick AllFill in the IC window as follows to set the initial temperature of the material to 100 K:


5. Solve the System
Solution > Solve > Current LS
SOLVE

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Postprocessing: Viewing the Results

1. Results Using ANSYS
Plot Temperature
General Postproc > Plot Results > Contour Plot > Nodal Solu ... > DOF solution, Temperature TEMP
Animate Results Over Time



• First, specify the contour range.Utility Menu > PlotCtrls > Style > Contours > Uniform Contours...Fill in the window as shown, with 8 contours, user specified, from 100 to 500.
  
• Then animate the data.Utility Menu > PlotCtrls > Animate > Over Time...Fill in the following window as shown (20 frames, 0 - 300 Time Range, Auto contour scaling OFF, DOF solution > TEMP)
  
You can see how the temperature rises over the area over time. The heat flows from the higher temperature to the lower temperature constraints as expected. Also, you can see how it reaches equilibrium when the time reaches approximately 200 seconds. Shown below are analytical and ANSYS generated temperature vs time curves for the center of the block. As can be seen, the curves are practically identical, thus the validity of the ANSYS simulation has been proven.

Analytical Solution

ANSYS Generated Solution

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Time History Postprocessing: Viewing the Results

1. Creating the Temperature vs. Time Graph
   
   
   • Select: Main Menu > TimeHist Postpro. The following window should open automatically.
     If it does not open automatically, select Main Menu > TimeHist Postpro > Variable Viewer
     
   • Click the add button  in the upper left corner of the window to add a variable.
   • Select Nodal Solution > DOF Solution > Temperature (as shown below) and click OK. Pick the center node on the mesh, node 261, and click OK in the 'Node for Data' window.
     
   • The Time History Variables window should now look like this:
2. Graph Results over Time
   
   
   • Ensure TEMP_2 in the Time History Variables window is highlighted.
   • Click the graphing button  in the Time History Variables window.
   • The labels on the plot are not updated by ANSYS, so you must change them manually. SelectUtility Menu > Plot Ctrls > Style > Graphs > Modify Axes and re-label the X and Y-axis appropriately.
     Note how this plot does not exactly match the plot shown above. This is because the solution has not completely converged. To cause the solution to converge, one of two things can be done: decrease the mesh size or increase the number of substeps used in the transient analysis. From experience, reducing the mesh size will do little in this case, as the mesh is adequate to capture the response. Instead, increasing the number of substeps from say 20 to 300, will cause the solution to converge. This will greatly increase the computational time required though, which is why only 20 substeps are used in this tutorial. Twenty substeps gives an adequate and quick approximation of the solution.
     
     
     

     ANSYS Command Listing

     finish
     /clear
     
     /title, Simple Conduction Example
     /PREP7    ! Enter preprocessor
     
     ! define geometry
     
     length=1.0
     height=1.0
     blc4,0,0,length, height  ! area - one corner, then width and height
     
     ! mesh 2D areas
     
     ET,1, PLANE55   ! Thermal element only
     MP,Dens,1,920   ! Density
     mp,c,1,2.040   ! Specific heat capacity
     mp,kxx,1,5   ! Thermal conductivity
     ESIZE,0.05   ! Element size
     AMESH,ALL   ! Mesh area
     
     FINISH
     /SOLU
     
     ANTYPE,4   ! Transient analysis
     
     time,300   ! Time at end = 300
     
     nropt,full   ! Newton Raphson = full
     lumpm,0    ! Lumped mass approx off
     nsubst,20   ! 20 substeps
     neqit,100   ! Max no. of iterations = 100
     autots,off   ! Auto time search on
     lnsrch,on   ! Line search on
     outres,all,all   ! Output data for all substeps
     kbc,1
     
     ! fixed temp BC's
     NSEL,S,LOC,Y,height  ! select nodes on top with y=height
     D,ALL,TEMP,500   ! apply fixed temp of 500K
     NSEL,ALL
     NSEL,s,LOC,Y,0
     D,ALL,TEMP,100   ! apply fixed temp of 100K
     NSEL,ALL
     IC,all,Temp,100   ! Initial Conditions: 100K
     
     SOLVE
     FINISH
     
     /POST1    ! Enter postprocessor
     /CONT,1,8,100,,500  ! Define a contour range
     PLNSOL,TEMP   ! Plot temperature contour
     ANTIME,20,0.5,,0,2,0,500 ! Animate temp over time