9873

Heating of Bodies in a Limited Volume of Well-Stirred Fluid

Consider long cylinders of radius placed in a limited volume of well-stirred fluid. The uniform temperature of the fluid varies because heat is exchanged by convection with the long cylinders. Initially the fluid and the bodies are at dimensionless temperatures equal to 1 and 0, respectively.
The dimensionless constant , a measure of the heat storage capacity of the bodies relative to the fluid, is given by: , where is the number of long cylinders, , , and are the fluid's specific heat, density and volume, respectively, and , , and are the body's specific heat, density and volume, respectively.
The Biot number is defined as , where is the heat transfer coefficient of the fluid, the thermal conductivity of the long cylinder, and its radius.
This Demonstration displays the average temperature in the bodies (the blue curve) and the fluid's temperature (the orange curve) as a function of time for various Biot numbers. For low Biot numbers, the two temperatures will become equal only after a long time, as expected, because the fluid's heat transfer coefficient is very low. Again as expected, the temperatures of the fluid and the bodies are both equal to if . As increases, the steady-state fluid's temperature and the steady-state bodies' average temperature will be smaller.

SNAPSHOTS

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

DETAILS

Reference: M. D. Mikhailov and M. N. Özisik, Unified Analysis and Solutions of Heat and Mass Diffusion, New York: Dover, 1994.
    • 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.









 
RELATED RESOURCES
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 © 2014 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+