Transient Thermal Analysis of a Fin

Transcription

1 Transient Thermal Analysis of a Fin A cylindrical copper fin conducts heat away from its base at C and transfers it to a surrounding fluid at 25 0 C through convection. The convection heat transfer coefficient is 10. The copper has a thermal conductivity (k) of 398, a specific heat (C p) of 385, and a density of Determine the following: (a) the time to reach steady state (b) the steady state temperature distribution (using a transient analysis) (c) the temperature distribution after 50 seconds (d) the animated history of temperature in the fin over time (e) the steady state heat transfer rate through the base of the fin (using a transient analysis) (f) the steady state temperature distribution and heat transfer rate through the base using a steady state thermal analysis For the transient analysis, we will assume that the fin has an initial temperature of 25 0 C. At time t=0, heat will begin to flow from the base into the fin where some of the heat is stored (hence the need for the specific heat and density) and some of it is convected away. After a period of time, the temperature distribution in the fin will become steady. Steady state solutions require that the system of equations defining the model be solved only ONCE, while transient solutions require a new solution for each time step. For example, ANSYS will determine the temperature distribution at t=0.1 s based on the initial conditions. Next, ANSYS will determine the temperature distribution at t = 0.2 s based on the temperature distribution at t=0.1 s (and so on). Solution accuracy is a function of the size of the time steps as well as characteristics of the mesh. Ambient Temp = 25 0 C h= 10 W/m 2.K Base temperature = C 25 mm 400 mm

2 TRANSIENT SOLUTION Build Model: 1. Preprocessor >Element type > Add/Edit/Delete > (Add) > Thermal Mass > Solid > ( Solid 87) > OK (this 10 node tetrahedral element works well for the curved edges of the fin) 2. Preprocessor > Material properties > Material models > Thermal > Enter Conductivity > Isotropic > KXX = 398, Specific heat C = 385, Density DENS = Preprocessor >Modeling > Create > Volumes > Cylinder > Solid cylinder > WP X = 0, WP Y = 0, Radius = , Depth = 0.4 (use PlotCtrls to view an isometric of the cylinder) 4. Preprocessor > Meshing > Mesh tool > Turn on smart size to 4 > Mesh > Volumes > Mesh >(Pick the body) > OK Define Loads, Time Stepping Options, Output Options & Solve: 5. Solution > Analysis Type > New Analysis > Transient > OK > Full > OK 6. Solution > Define Loads > Apply > Thermal > Temperature > On Areas > (pick base of fin) > TEMP 100 > OK 7. Solution > Define Loads > Apply > Thermal > Convection > On Areas > (pick all of the areas except for the base there are 3 just click 3 times near the tip of the fin) > Film Coefficient = 10, Bulk Temperature = 25 > OK 8. Solution > Define Loads > Apply > Initial Condit n > Define > Pick All > Lab = TEMP, VALUE = 25 (ANSYS will remember the base temperature and the convection conditions you entered for the steady state solution, so you don t have to re enter them. You can use the List tool to view these conditions) 9. Solution > Load Step Opts > Time/Frequenc > Time Time Step > Set TIME = (at the top), KBC = stepped, AUTOTS = Prog Chosen, Minimum time step size = 0.01, maximum time step size = 200 > OK (We will let the ANSYS take charge of choosing the appropriate time step, limiting the time step to 200s) 10. Solution > Load Step Opts > Output Ctrls > DB/Results File > FREQ = every substep > OK (setting this option will allow us to see contour plots and obtain other results at any time step between t = 0 and t = 10,000s) 11. Solution > Solve > Current LS > OK It will take the model a while to run since it will require at least 50 time steps (max time = divided by maximum time step = 200)

3 Time History Post Processing: 12. Timehist postproc > Define Variables > Add > Nodal DOF Result > OK > Select a node randomly at the middle of the end of the fin > OK > NVAR = 2, DOF solution =Temp >OK 13. Timehist Postproc > Graph Variables > NVAR1 = 2 > OK (This gives the variation of temperature with respect to time at that node. Notice that steady state conditions are reached at about 3000s, with a value of 80 degrees C at the tip) 14. Timehist Postproc > List Variables >NVAR1 = 2 > OK (this lists the temperature as a function of time at the tip, as shown below) TIME TEMP TIME TEMP

4 General Post Processing: 15. General Postproc > Read Results > Last Set 16. General Postproc > Plot Results > Contour Plot > Nodal Solution > DOF Solution > Nodal Temperature > OK (this is the temperature distribution at 10,000s or the steady state temperatures) 17. General Postproc > Read Results > By Time/Freq > Enter TIME = 50 > OK 18. General Postproc > Plot Results > Contour Plot > Nodal Solution > DOF Solution > Nodal Temperature > OK (this is the temperature distribution at 50s)

5 19. General Postproc > Read results > By time/freq > Enter TIME = 180 > OK 20. General Postproc > Plot results > Contour plot > Nodal solution > DOF solution > Nodal temperature > OK (Notice the changes in the temperature distribution relative to the temperatures at 50s. Higher temperatures are moving further down the rod.) 21. PlotCtrls > Animate > Over Time > click on Time Range and enter 0 for a minimum time and 3000 for a maximum time > OK (This will show an animation of temperature with time. You can vary settings.) 22. General Postproc > Read Results > Last Set 23. General Postproc > List Results > Reaction Solu > Heat flow > OK (scroll to the bottom of the list to see that the steady state total heat flow through the base of the fin is 19.7 W) STEADY STATE SOLUTION The transient solution must converge to the steady state solution. It is important to check the transient solution using a steady state analysis. The steady state model does not rely on the heat capacity, density, or initial conditions. Build Model: 1. Preprocessor >Element type > Add/Edit/Delete > (Add) > Thermal Mass > Solid > ( Solid 87) > OK (this 10 node tetrahedral element works well for the curved edges of the fin) 2. Preprocessor > Material properties > Material models > Thermal > Enter Conductivity > Isotropic > KXX = Preprocessor >Modeling > Create > Volumes > Cylinder > Solid cylinder > WP X = 0, WP Y = 0, Radius = , Depth = 0.4 (use PlotCtrls to view an isometric of the cylinder)

6 4. Preprocessor > Meshing > Mesh tool > Turn on smart size to 4 > Mesh > Volumes > Mesh >(Pick the body) > OK Define Loads & Solve: 5. Solution > Analysis type > New analysis > Steady State > OK 6. Solution > Define Loads > Apply > Thermal > Temperature > On Areas > (pick base of fin) > TEMP 100 > OK 7. Solution > Define Loads > Apply > Thermal > Convection > On Areas > (pick all of the areas except for the base there are 3 just click 3 times near the tip of the fin) > Film Coefficient = 10, Bulk Temperature = 25 > OK 8. Solution > Solve > Current LS > OK Post Processing: 9. General Postproc > Plot Results > Contour Plot > Nodal Solu > DOF Solution > Nodal Temperature > OK (the steady state temperature of the tip is C) 10. General Postproc > List Results > Reaction Solu > Heat flow > OK (scroll to the bottom of the list to see that the total heat flow through the base of the fin is 19.7 W) Notice that the steady state results are roughly identical to the transient results after 3000 seconds. This tutorial was developed by David Hall and Sai Ravi Kanth Tummala 2008