Combined Free and Forced Convection

The Grashof number and the square of the Reynolds number are plotted as functions of the velocity of air as it passes over a flat plate. The plot explores natural or free convection—heat transfer that occurs between a stationary fluid and a solid—versus forced convection—heat transfer between a moving fluid and a solid. The yellow and blue areas of the plot represent regions where the ratio of (free convection dominates) and where (forced convection dominates), respectively. The dotted red line represents the user-defined velocity, and the computed Nusselt number is displayed above the plot for that velocity. The plate diagram is an idealized picture of the system. Changing the temperature of the plate and the air relative to one another helps you understand physically that the Grashof number is proportional to the difference of the two temperatures. This is why raising one of the temperatures can first decrease the free-dominated portion of the graph and then increase the same portion after the other temperature is surpassed.
  • Contributed by: Mathew L. Williams
  • (University of Colorado Boulder, Department of Chemical and Biological Engineering)


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


This Demonstration shows parameters that lead to combined forced and free convection over a flat plate. The conventional range where free and forced convection are combined is . A combined equation was used to calculate the Nusselt number for all velocities, where:
( stands for natural and for forced)
(Reynolds number)
(Grashof number)
(Rayleigh number)
, length of plate
, velocity of air
, kinematic viscosity of air
, Prandtl number ( and are approximated by fitting an equation to a range of known and numbers at corresponding temperatures for air)
, thermal expansion coefficient (approximated as )
    • 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 © 2016 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+