As explained in earlier chapters, fins, or extended surfaces, commonly are used in a var...

As explained in earlier chapters, fins, or extended surfaces, commonly are used in a variety of engineering applications to enhance cooling. Common examples include a motorcycle engine head, a lawn mower engine head, heat sinks used in electronic equipment, and finned tube heat exchangers in room heating and cooling applications. For long fins, the temperature distribution along the fin is given by:

What are the dependent and independent variables?

Next, consider aluminum fins of a rectangular profile shown in the accompanying figure, which are used to remove heat from a surface whose temperature is 100° C. The temperature of the ambient air is 20°C.

Plot the temperature distribution along the fin using the following data: k = 180 W/m · K, h 15 W/m² · K, a = 0.05 m, and b = 0.015 m. Vary x from zero to 0.015 m. What is the temperature of the tip of the fin? Plot the temperature of the tip as a function of k. Vary the k value from 180 to 350 W/m · K.