LBS290F                                                      Fall 1991

                     ASSIGNMENT 22 - PHYSICS/HEAT FLOW

Due Date: 11:59 PM Tuesday 12/3/91

The purpose of this program is to simulate heat flow in a solid metal bar.

The bar to be simulated will be 100 centimeters long.  The bar will start
at 30.0 degrees Celsius across the whole bar.

There will be heat and cold sources placed at various points on the bar 
as follows:

  Position     Temperature of source
  ----------------------------------
    1cm           100.0 Celsius (Boiling)
    16cm          10.0 Celsius
    65cm          80.0 Celsius
    100cm          0.0 Celsius

We are to simulate the flow of heat from these sources as a function of
time and calculate the temperature at all the positions of the bar for
successive time steps.

You are to print out the temperature at the following positions on the
bar:

   25cm, 50cm, 75cm, and 99cm

Print out these positions after 1, 5, 40, 50, and 100 time steps.

The output of the program should be as follows (your numbers might
be slightly different):

Time step 1 bar[25] = 30.00 bar[50] = 30.00 bar[75] = 30.00 bar[99] = 20.00
Time step 5 bar[25] = 29.94 bar[50] = 30.00 bar[75] = 30.06 bar[99] = 10.37
Time step 40 bar[25] = 26.50 bar[50] = 30.46 bar[75] = 36.70 bar[99] = 3.77
Time step 50 bar[25] = 25.59 bar[50] = 31.11 bar[75] = 38.78 bar[99] = 3.38
Time step 100 bar[25] = 22.45 bar[50] = 35.96 bar[75] = 46.17 bar[99] = 2.43

The back of this handout shows how an example of this might work.



            EXAMPLE OF HEAT FLOW IN A 10 CM BAR

The following will show how the program needs to work assuming a 10 cm bar
with 100.0 degree Celsius heat source at 1 cm and 10.0 degree Celsius heat 
source at 8 cm and 10.0 degree Celsius heat source at 10 cm.  The rest 
of the bar is at 30.0 degrees Celsius initially.

Before time step 0, the bar will have the following temperatures:

Temp    100.0   30.0   30.0   30.0   30.0   30.0  30.0  10.0  30.0   10.0
        -----------------------------------------------------------------
Pos       1      2      3      4      5      6     7     8     9     10

For each time step go from positions 2 through 9 and calculate the new
temperature at the poition based on the average of the old temperature 
at the position, and the temperature of the positions at the 
immediate left and right.

So for time step 1, the temperature at position 2 is:

   ( 100.0 + 30.0 + 30.0 ) / 3.0  or 53.33
Pos    1       2     3

The temperature at position 3 is:

   ( 53.33 + 30.0 + 30.0 ) / 3.0 or 37.78
Pos    2      3       4

Note that the new temperature at position 3 is used in the calculation.

This calculation is not done for positions 1, 8, or 10 because these are 
assumed to be infinite sources of heat able to keep their section of the
bar at 100.0 and 10.0 degrees regardless of heat flow.

After the time step 1, the bar will have the following temperatures:

Temp    100.00 53.33  37.78 32.59  30.86  30.29  23.43  10.00  16.67  10.00 
        -----------------------------------------------------------------
Pos       1      2      3      4      5      6     7      8      9     10


After the time step 2, the bar will have the following temperatures:

Temp    100.00 63.70  44.69  36.05  32.40  28.71 20.71  10.00  12.22  10.00  
        -----------------------------------------------------------------
Pos       1      2      3      4      5      6     7      8      9     10

Note that positions 1, 8, and 10 do not change.