An experiment to illustrate numerical differentiation, integration, regression and ODEs

Starting Summer 2007, five experiments have been introduced in the course in Numerical Methods at USF. I will discuss each experiment in a separate blog as the

summer trods along.

Experiment#1: Cooling an aluminum cylinder

The first experiment illustrates use of numerical differentiation, numerical integration, regression and ordinary differential equations. In this experiment, an aluminum cylinder is immersed in a bath of iced water. As you can see in the figure, two thermocouples are attached to the cylinder and are connected to a temperature indicator. Readings of temperature as a function of time are taken in intervals of 5 seconds for a total of 40 seconds. The temperature of the iced-water bath is also noted.

If you just want the data for a typical experiment conducted in class, click here and here for data.

The students are now assigned about 10 problems to do. These include

1. finding the convection coefficient (involves nonlinear regression – it is also a good example of where the data for a nonlinear model does not need to be transformed to use linear regression)
2. finding the rate of change of temperature to calculate rate at which is heat is stored in the cylinder (involves numerical differentiation)
3. prediction of temperatures from solution of ordinary differential equations
4. finding reduction in the diameter of the aluminum cylinder (involves numerical integration as the thermal expansion coefficient is a function of temperature)

This post brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://nm.mathforcollege.com