4.3 Grashof and Prandtl numbers

We give expressions for the numbers Gr and Pr.

Where , , a is the coefficient of volume expansion, kinematic viscosity and thermal diffusivity of a gas or liquid, g is the acceleration of gravity, T ₁ and T ₂ are the temperature of the plates, L is the distance between the plates.

By changing the parameters (T ₁ -T ₂ ), L, or the medium between the plates, i.e. the parameters , , a, we will change the value of the product Gr * Pr = k. At a certain value k = k _cr > 10 ³ , which we call critical, the volume of matter starts moving: the heated fluid areas expand, float up, cool and descend again to the bottom. There is a convective movement. Surprisingly, this movement takes place in a well-ordered manner: the liquid is structured in the form of small cells called Benard cells. The cause of convective movement is the different density of heated and cold fluid layers (the parameter is responsible ) and gravity (parameter g is responsible). Movement will be stabilized by viscosity ( a) fluid, since the internal forces of friction are directed against the movement. As a result of this play of forces with values ​​of k <10 ^{3, there is} no convective motion.