This is a program to simulate temperature distribution of a thin plate, the thin plate is thermally isolated in the way that heat can not flow through the two faces parellel to the screen, there is neither heat source nor sink in the plate and heat can only flow in and out through the four edges of the thin plate. Immediately after we put a thin plate of a certain initial temperature into an envornement which fixes the temperatures of the four edges of the thin plate to some values, the temperatures within the thin plate shall change spatially and temporally. Finally the temperatures shall reach a steady-state condition when they no longer change in terms of time and space. This program shows the temperature distribution in equilibrium condition and a very special case how the equilibrium condition is reached in terms of time and space. Features of the program SLIDERS There are five temperature sliders to enable users to set four fixed edge temperatures and one initial plate temperature: lefttemp Left edge temperature toptemp Top edge temperature rightte Right edge temperature bottomt Bottom edge temperature inplate Initial plate temperature There is one slider used to set the length of the thin plate, the number of the slider is the percentage of the thin plate of the screen-size. scale Percentage of plate to screen-size The last slider is used together with man-go button, it varies the speed to reach equilibrium condition and the resulotion of the result: step Increment size BUTTONS There are three buttons with the following functions: setup Initializing all conditions auto-go To execute automatically man-go To execute manually show-heat-flow To show heat flow lines hide-heat-flow To hide heat flow lines after "show-heat-flow" button is pressed MONITORS Three monitors are used to give user some important information: timer A clock maxvariation The maximum temperature variation of all patches for the latest two calculations temp-at 0 0 The temperature at the center, a rule is that the value of it should be the average of the four edge temperatures, this gives users a rough idea on how close the condition is to the steady-state condition. HOW TO SIMULATE Manually 1. Set the five temperatures by temperature sliders; 2. Set the size of the plate by the scale slider; 3. Press "setup" button and then "man-go" button and adjust "step" slider to speed up or slow down the simulation process; 4. Press "man-go" button to stop simulation process whenever desired results are got; 5. Press "show-heat-flow" button to see heat flow lines. Automatically 1. Set the five temperatures by temperature sliders; 2. Set the size of the plate by the scale slider; 3. Press "setup" button and then "auto-go" button; 4. Press "auto-go" button to stop simualtion whenever desired results are got; 5. Press "show-heat-flow" button to show heat flow lines. WHAT TO OBSERVE 1. The equilibrium temperature distribution for different edge temperature settings. 2. The process how the equilibrium is reached. UNIT There are three units used in this simulation, time, temperature and length, users are supposed to keep track of the units they input and calibrations can be made to show real units with similirity rules. SOME EXAMPLES SETTINGS TO OBSERVE ITEM TOP RIGHT BOTTOM LEFT 1 100 0 0 0 2 0 100 100 100 3 0 33 66 99 4 25 0 25 100 CAUTION To avoid singularity and infinite loop, please do not set all the five temperatures at one single value. WHAT TO DEVELOP Now, the model this program simulates is the most typical classic problem with a square thin plate being the most common shape, and the boundary conditions are the simplest. When users are familier with this model, they can try some more complex ones in terms of shape and boundary conditions, such as rectangular, circle, ovel and any shape other than primative shapes mentioned above, as boundary conditions are concerned, they can try derivative and combined conditions.