less rapid with more rapid diffusion (thereby diffusing away the gradient that is causing the convection) and/or a more viscous (sticky) fluid. For thermal convection due to heating from below, as described in the boiling pot above, the equation is modified for thermal expansion and thermal diffusivity. Density variations due to thermal expansion are given by: where is the reference density, typically picked to be the average density of the medium, is the coefficient of thermal expansion, and is the temperature difference across the medium. The general diffusivity, , is redefined as a thermal diffusivity, . Inserting these substitutions produces a Rayleigh number that can be used to predict thermal convection. Turbulence The tendency of a particular naturally convective system towards turbulence relies on the Grashof number (Gr). In very sticky, viscous fluids (large ν), fluid motion is restricted, and natural convection will be non-turbulent. Following the treatment of the previous subsection, the typical fluid velocity is of the order of , up to a numerical factor depending on the geometry of the system. Therefore, Grashof number can be thought of as Reynolds number with the velocity of natural convection replacing the velocity in Reynolds number's formula. However In practice, when referring to the Reynolds number, it is understood that one is considering forced convection, and the velocity is taken as the velocity dictated by external constraints (see below). Behavior The Grashof number can be formulated for natural convection occurring due to a concentration gradient, sometimes termed thermo-solutal convection. In this case, a concentration of hot fluid diffuses into a cold fluid, in much the same way that ink poured into a container of water diffuses to dye the entire space. Then: Natural convection is highly dependent on the geometry of the hot surface, various correlations exist in order to determine the heat transfer coefficient. A general correlation that applies for a variety of geometries is The value of f4(Pr) is calculated using the following formula Nu is the Nusselt number and the values of Nu0 and the characteristic length used to calculate Ra are listed below (see also Discussion): Warning: The values indicated for the Horizontal cylinder are wrong; see discussion. Natural convection from a vertical plate One example of natural convection is heat transfer from an isothermal vertical plate immersed in a fluid, causing the fluid to move parallel to the plate. This will occur in any system