LBS290F                                                     Spring 1992

                        ASSIGNMENT 12 - Heat Flow in a Plate

Due Date: April 29, 1992 11:59 PM

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

The plate to be simulated will be 10 centimeters by 10 centimeters.  
The plate will start at 30.0 degrees Celsius across the whole plate.

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

  Y-Position   X-Position       Temperature
  ------------------------------------------
    1cm           1cm            100.0 Celsius (Boiling)
    6cm           3cm             10.0 Celsius
    5cm           1cm            80.0 Celsius
    10cm         10cm             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 plate for
successive time steps.

You will have to write 5 loops to perform the heat flow calculation.  One loop
for each edge, and one for the central portion.  For the top edge of
the plate each cell will be calculated by the average of the three
neighboring cells.  For example, to compute the new temperature of 
position  1cm, 3cm you would average the temperatures of the cells at
1,2  1,3  1,4 and 2,3.

Left
Edge

        -------------------------------------------------  Top Edge
        | 1,1       | 1,2      | 1,3      | 1,4     |
        |           |          |          |         |
        |           |          |          |         |
        |           |          |          |         |
        - - - - - - - - - - - - - - - - - - - - - - - - -
        | 2,1       | 2,2      | 2,3      | 2,4     |
        |           |          |          |         |
        |           |          |          |         |
        |           |          |          |         |
        - - - - - - - - - - - - - - - - - - - - - - - - -
        | 3,1       | 3,2      | 3,3      | 3,4     |
        |           |          |          |         |


To compute the new temperature of one of the interior cells you 
average the temperature of the cell and its four neighbors.

In the following example cell 2,3 would be computed as the average of cells

1,3 2,2 2,3 2,4 and 3,3


Left
Edge

        -------------------------------------------------  Top Edge
        | 1,1       | 1,2      | 1,3      | 1,4     |
        |           |          |          |         |
        |           |          |          |         |
        |           |          |          |         |
        - - - - - - - - - - - - - - - - - - - - - - - - -
        | 2,1       | 2,2      | 2,3      | 2,4     |
        |           |          |          |         |
        |           |          |          |         |
        |           |          |          |         |
        - - - - - - - - - - - - - - - - - - - - - - - - -
        | 3,1       | 3,2      | 3,3      | 3,4     |
        |           |          |          |         |


It is important NOT to change the temperature of the fixed temperature 
cells specified above.

Run the simulation for 10 time steps and print out the temperature at 
the following positions on the plate after each time step.

  Y-Position   X-Position
  -----------------------
    2cm           2cm
    10cm          1cm
    4cm           2cm