Details

The temperature variation in the direction is assumed to be linear:

, where is the space between the two walls.

The density is not constant and varies according to , where is the density at the mean temperature, .

The governing equation is given by .

It is possible to derive an analytical expression of the dimensionless velocity using the built-in Mathematica function DSolve:

,

where is the dimensionless velocity, the dimensionless length, and the Grashof number, a dimensionless number that arises in problems on free convection.