Free Convection past an Isothermal Vertical Plate

Consider the free convection past a vertical flat plate or wall maintained at a constant temperature with > , where is the fluid temperature far from the wall. W. M. Deen derived the governing equations for such a problem (see the reference):
and with and ,
where is the dimensionless temperature, is the Prandtl number (a dimensionless number that gives the rate of viscous momentum transfer relative to heat conduction), and is proportional to the fluid velocity ( is a modified stream function). One has to use the shooting technique to solve this split boundary value problem. This Demonstration displays the temperature and velocity profiles for various values of the Prandtl number versus a similarity variable , where is the Grashof number. When is reduced, the dimensionless temperature variations extend farther from the wall (an indication of higher rates of heat conduction).


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


W. M. Deen, Analysis of Transport Phenomena, New York: Oxford University Press, 1998.
    • 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+