Interactive Self-Study Module: Lumped Capacitance Method for Analyzing Transient Conduction Problems
Overview:
This module uses screencasts and interactive simulations to explain how you can calculate the temperature of an object that warms up or cools down over time. The object is surrounded by a warm or cool fluid, such as air or water, which causes the temperature of the object to change over time. In this module we are going to assume that the temperature of the entire object is uniform. In other words, we are going to assume that the inside of the object warms up or cools down at the same time as the exterior. However, this is a major limitation. In reality the outside of the object will warm up or cool down faster than the inside. We will study this effect in a subsequent module.
Your retention of material in this module will increase if you write down reasons for your answers to ConcepTests, questions in screencasts, and questions to answer before using interactive simulations, and you try to solve the example problems before watching the screencast solutions.
We suggest using the learning resources in the following order:
- Attempt to answer the multiple choice ConcepTest and solve the example problem before watching the screencasts or working with the simulations.
- Watch the screencasts that describe how you can use lumped capacitance to estimate the temperature of an object over time.
- Review the important equations for lumped capacitance analysis.
- Use the interactive simulation to further understand how you can predict the temperature of an object over time.
- Try to solve the example problems before watching the solutions in the screencasts.
- Answer the ConcepTests.
- Look at the list of key points, but only after you try to list the key points yourself.
Motivation:
- Engineers often need to estimate the temperature of an object as a function of time. If the object is relatively small and has a relatively high thermal conductivity, you can assume that the temperature throughout that object is relatively uniform. This makes the math much easier. One example is the tip of a thermocouple. It is small and is made of metal that has a high thermal conductivity. It needs to equilibrate to the surrounding temperature before it can provide an accurate reading. If the thermocouple tip does not equilibrate quickly, the user might not wait long enough and will report an incorrect reading. You can use lumped capacitance to predict how long this will take.
- This module is primarily intended for a Heat Transfer course.
Before studying this module, you should be able to:
- Draw and work with control volumes.
- Write a transient energy balance equation for a control volume.
- Explain the meaning of a heat transfer coefficient.
- Use dimensionless parameters, such as the Reynolds number.
- Discuss differential equations and specify an initial condition.
After studying this module, you should be able to:
- Identify whether lumped capacitance is appropriate in a given scenario.
- Sketch a qualitatively-accurate graph of the temperature of an object as a function of time.
- Predict when an object will reach a specified temperature.