FEM ME422 Homework #6 Distributed: January 28, 2008 Due: February 5, 2008 Problem 1: Consider quenching of a steel slab. Initially, the slab is at a temperature T0 . It is suddenly plunged into oil at Toil .
to infinity
w
slab T2 T1 T3
convection (oil) ho Toil
to infinity
k cp ho Toil T0 W = 15 w/mK = 7817 kg/m3 = 460 J/kgK = 6000 W/m2 K = 20 C = 900 C = 0.01 m 1
These are the real properties for steel, and fairly reasonable values for the convection coefficient for quenching. Based on your engineering intuition, is the centerline temperature more likely to drop to about 450 C in (a) 1 day (b) 1 minute or (c) 1 microsecond ? Describe any experiences you have had that back up your answer. (Just give me a few lines here you don't have to write a long description. Pretend you are trying to explain your reasoning to your boss.) Problem 2: Use 2 linear finite elements along with Euler backward time integration to solve for the temperatures in the slab as a function of time. (Note: T /n = 0 at the centerline of the slab.) a. Find the 33 stiffness matrix for the problem. Don't forget the convection term. b. Find the 33 mass matrix. c. Find the forcing vector (3 terms). d. For Euler backward integration, we can write ^ ^ KT|n = F ^ ^ Find K and F for this problem. e. Solve for T as a function of time and plot T1 (t), T2 (t), and T3 (t). Run your calculation until T1 T0 +Toil . 2 f. Did your answer agree with your estimate from Problem 1? Fix something if it doesn't agree.
Problem 3: Now do the same problem in 2-D in Ansys. Plot the temperature contours at time=1 second so I'll know that you were able to get this to run. Also, make sure that temperatures the you get here agree with what you estimated in Problem 1, as well as have some reasonable correlation with the answers you got on Problem 2. This is our first transient analysis, so I have what I hope will be some helpful hints: Use any planar (Quad or Triangle) Thermal Mass Solid element Now we need to specify that the analysis is transient: Solution > Analysis Type > New Analysis > Transient 2
Solution method Full Use lumped mass No Don't forget to define the initial condition using Solution > Define Loads > Apply > Initial Condit'n > Define. We need to save the results at every time: Solution > Load Step Opts > Output Ctrls > DB/Results File > All items Every substep All entities We need to specify a time step size and a total time to run the analysis: Loads > Load Step Opts > Time/Frequency > Time - Time Step TIME Time at End (total time) DELTIM Time Step Size (t) KBC Stepped B.C. Automatic Time Stepping Off No Res...