Flow in a Vertical Channel with Walls at Different Temperatures

Consider a vertical parallel-plate channel of width with walls at different temperatures and , . Two cases are studied: (1) pure free convection (i.e., the channel is closed at both ends and there is no net flow); and (2) mixed free and forced convection (a pressure gradient is present). The velocity (solution of the momentum equation) is given by
where is gravitational acceleration, is the thermal expansion coefficient, is the reference temperature taken equal to the mean temperature, is the kinematic viscosity, is the dynamic viscosity, is the pressure gradient, and is the dimensionless position.
The velocity can be expressed as , where is the mean velocity and is the maximum velocity when the pressure gradient is zero.
If and , one recovers pure free convection. When , the velocity profile is the expected parabolic profile corresponding to a Poiseuille flow. In general, mixed free and forced convection is observed.


  • [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 © 2017 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+