Natural Convection between Two Vertical Plates

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The dimensionless vertical velocity inside two vertical plates at distance and temperatures and is computed for specified Grashov number , where is the velocity , is the distance in meters, is the kinematic viscosity in , is the gravitational acceleration in , and is the volumetric coefficient of thermal expansion in.


For a fixed Grashov number, determines black points on the curve, followed by the numerical values of . Thus for any and the precise values of the velocity are available.

The frame ticks change with Grashov number , which conveniently lets you observe that the shape of the velocity distribution did not change.


Contributed by: Mikhail Dimitrov Mikhailov (March 2011)
Open content licensed under CC BY-NC-SA



The vertical velocity of an incompressible Boussinesq fluid with constant properties inside two vertical plates at distance and temperatures and is determined assuming zero pressure gradient and that the temperature and velocity depend only on the horizontal coordinate .

The models for temperature and velocity are

where is the gravitational acceleration , is the volumetric coefficient of thermal expansion , is the kinematic viscosity , and is the average temperature .

To reduce the number of parameters, we introduce the dimensionless quantities

, , , ,

where is the dimensionless horizontal coordinate, is dimensionless temperature, is the Grashnov number, and is the dimensionless vertical velocity.

Then the temperature and velocity models become

The solutions of the models are

, .

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