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.
The students are now assigned about 10 problems to do. These include
- 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)
- finding the rate of change of temperature to calculate rate at which is heat is stored in the cylinder (involves numerical differentiation)
- prediction of temperatures from solution of ordinary differential equations
- 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