Editing Rayleigh number (section)

===Solidifying alloys===
The Rayleigh number can also be used as a criterion to predict convectional instabilities, such as [[A-segregates]], in the mushy zone of a solidifying alloy. The mushy zone Rayleigh number is defined as:

<math display="block">\mathrm{Ra} = \frac{\frac{\Delta \rho}{\rho_0}g \bar{K} L}{\alpha \nu} = \frac{\frac{\Delta \rho}{\rho_0}g \bar{K} }{R \nu}</math>

where:
*''<span style="text-decoration: overline">K</span>'' is the mean permeability (of the initial portion of the mush)
*''L'' is the characteristic length scale 
*''α'' is the thermal diffusivity 
*''ν'' is the kinematic viscosity 
*''R'' is the solidification or isotherm speed.<ref name="ReferenceA">{{cite journal |last1=Torabi Rad |first1=M. |last2=Kotas |first2=P. |last3=Beckermann |first3=C. |author3-link=Christoph Beckermann |title=Rayleigh number criterion for formation of A-Segregates in steel castings and ingots |journal=Metall. Mater. Trans. A |date=2013 |volume=44A |issue=9 |pages=4266–4281|doi=10.1007/s11661-013-1761-4 |bibcode=2013MMTA...44.4266R |s2cid=137652216 }}</ref>

A-segregates are predicted to form when the Rayleigh number exceeds a certain critical value. This critical value is independent of the composition of the alloy, and this is the main advantage of the Rayleigh number criterion over other criteria for prediction of convectional instabilities, such as Suzuki criterion.

Torabi Rad et al. showed that for steel alloys the critical Rayleigh number is 17.<ref name="ReferenceA"/> Pickering et al. explored Torabi Rad's criterion, and further verified its effectiveness. Critical Rayleigh numbers for lead–tin and nickel-based super-alloys were also developed.<ref>{{cite journal |last1=Pickering |first1=E.J. |last2=Al-Bermani |first2=S. |last3=Talamantes-Silva |first3=J. |title=Application of criterion for A-segregation in steel ingots |journal=Materials Science and Technology |date=2014|volume=31 |issue=11 |page=1313 |doi=10.1179/1743284714Y.0000000692 |bibcode=2015MatST..31.1313P |s2cid=137549220 }}</ref>