### Introduction to Scientific Programming Computational Problem Solving Using: Maple and C Mathematica and C

Author:
Joseph L. Zachary
Online Resources:
Maple/C Version
Mathematica/C Version

# Rod Heating Tutorial

In this tutorial we will explore the rod heating problem that is discussed in Chapter 17.

## Simulation

We will be using a graphical simulation of rod heating throughout this tutorial. You can start it by clicking on the following button.

A Java applet should appear here

The simulation window that appears will display along the left side six controls that can be used to customize the simulation. They are, from top to bottom

1. The temperature of the left heat source.

2. The temperature of the right heat source.

3. The initial temperature of the rod.

4. The length of the rod

5. The thermal diffusivity of the rod

6. The number of segments into which the rod is divided.
In addition, below these six controls the simulation displays the calculated value of delta t.

The graph to the right of the controls shows the initial temperature distribution of the rod. Segment boundaries are plotted along the horizontal axis, and temperatures are plotted along the vertical axis. Initially, segment boundary 0 is at 70 degrees, segment boundary 10 is at 50 degrees, and the rest of the rod is at zero degrees. The same information is displayed using a color scale below the graph.

If you pull down the Animation menu and choose the Start option, you will see an animation of how the temperatures change in the rod as a function of time.

Now pull down the Animation menu and choose the Stop option, and then pull down the File menu and choose the Reset option. The graph will once again display the initial temperature distribution of the rod.

This time, click repeatedly on the Step button. Each time you click, you will see the simulated passage of delta t units of time.

Experiment with changing the six parameters and observe how it affects the simulation.