Laboratory Waterbath with Proportional Control

A laboratory waterbath consists of a heater, a nearby sensor, the thermostated object further downstream, a cooling coil covering the bottom of the container, and a stirrer that circulates and mixes. It is modeled here by a set of differential equations describing the heat flow in each of 11 radial sectors of the waterbath when the object temperature is initially dropped to 19 °C from the temperature setting of 20 °C.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The best configuration is for the sensor to be very near the heater, and for the object to be farther downstream. To simulate an off-on control, reduce the spread between the variables and , which represent the upper and lower limits of the proportioning range.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+