Lab 3 Heat Transfer Along a Rod.docx

Lab 3 Heat Transfer Along a Rod.docx - Lab 3 Temperature...

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Lab 3: Temperature Gradient Along a 1-D Rod A. Background Information Have you ever cooked on a stove with a pan with a metal handle? If you have, you may have noticed that when you start cooking, the handle is cool and everything is great. However, as you leave the pan on the stove, the handle gradually warms up. If you leave the pan on the stove for long enough, eventually the handle will be as hot as the stove itself! This is a phenomenon known as heat transfer. Just like water likes to flow from areas of higher elevation (and higher potential energy) to areas of lower elevation (and lower potential energy), heat energy tries to travel from areas of high temperature (higher energy) to areas of lower temperature (lower energy). In addition, heat energy attempts to equalize the temperature along an entire medium. This is why the handle of your pan will eventually reach the same temperature as the stove: as more heat energy is added to the pan that energy transfers throughout the pan in an attempt to equalize the temperature throughout. For our purposes, we are going to investigate the temperature gradient along a 1-D rod where we are not continually adding heat to the system. As you know, if there was a real rod we were working with, there would be an infinite number of points along the length of the rod and thus an infinite number of temperature values to deal with. As we know from our DAQ experiments, the computer cannot handle an infinite number of points. Instead, we need to break the length of the rod into a finite set of sections to estimate how the temperature changes along the length of the rod. We simply assume that the temperature in each section is the average temperature in that region. Figure 1: Continuous Temperature Gradient (top) versus Discrete Temperature Gradient (bottom) If we are going to model this situation in MATLAB, we need a structure that is similar. For this, we will use a 1-D array. Each element in the array will represent one of the sections along the length of the 1-D rod and the value of the array will represent the temperature of the rod for that section. This is a common practice in engineering when performing simulations of systems. A more complicated version of this same basic procedure is called Finite Element Analysis (FEA), in which a complicated object is broken down into a number of smaller sections (usually a grid). The interaction between each smaller section is known and can be easily calculated. The object can then be run through simulations by performing calculations based on the smaller sections rather than trying to perform a complex calculation on the overall object. This technique is used in a wide variety of application areas, from simulating automotive crashes, stress and strain forces on buildings and structural members, and predicting electromagnetic radiation patterns.
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B. Understand the Process
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