16.26 Problem Set #5	3/21/97
	Due 4/4/97

1. One side of a plate is held at the reference temperature To, while the other side is held at T1. The conductivity of the plate is
   
   
   
   Find an expression for T(x) in the steady state. Express your answer in terms of dimensionless temperature, distance, and conductivities
   
   
   
   
   
   Make a chart of the results, showing q vs x for several values of k (from - to +, and including 0).
   
   
   
   
2. If To = 0 ·F and T1 = 200 ·F, predict the stresses in the plate described above, which is made of 2024-T3 aluminum. First assume that the material properties are constant (use RT values) except for the variation in k, which, looking at the charts, can be approximated nicely as linearly varying with T. Then solve the same problem including the (roughly linear) variations in E and alpha as well. Assume free edges and small deflections.
   
   
3. A 2" x 2" 2024-T3 Aluminum plate, 1/8" thick, initially at 70·F, is restrained on all sides, and exposed to on the top and bottom surfaces to a turbulent fluid (hc = 1000 w/m2K) at temperature T, where
   
   T, = 70·F + (0.01·F/sec) t
   
   and t is the time in seconds. Predict as accurately as you can the stress in the plate as a function of time from t = 0 to t = 63000 seconds.