Talk:Rayleigh number

What is x?

What is x? It is not defined. — Preceding unsigned comment added by Michael C Price (talk • contribs) 14:56, 6 May 2006 (UTC)

x is the position. The article does mention this. The parameter changes along the length of the wall, so you need a local value at a particular x position. There is no fixed characteristic length. —Preceding unsigned comment added by 129.162.1.42 (talk) 18:42, 7 January 2008 (UTC)

The property x is the "characteristic length". In the context of convection from a vertical plane, for example, two sources I've found state that the characteristic length is the height of the plane. The article qualified the definition of x with the text: "(in this case, the distance from the leading edge)". I removed this, principally as it appeared to be referring to a specific physical situation. (It also didn't necessarily clarify the definition and wasn't referenced.) For the same reason, I removed the qualifying text for the surface temperature definition, which referred to a "wall". Pololei (talk) 17:05, 23 September 2015 (UTC)

Critical Rayleigh number

The critical Rayleigh number's interpretation is not as simple as saying "conduction dominates" or "convection tominates". Under certain geometries, the critical Rayleigh number may be define in a way which considers Prandtl's Number's influence for determining whether the boundary layer is laminar or turbulent. I believe it's empiracle how you define Ra_c for a particular geometry and thermohydraulic conditions, which may be Gr or Pr sensitive. — Preceding unsigned comment added by Martin James Turner (talk • contribs) 08:14, 4 May 2008 (UTC)

Opening paragraph, Rayleigh number and Nusselt number

The lede contains the following sentence: "When the Rayleigh number is below a critical value for that fluid, heat transfer is primarily in the form of conduction; when it exceeds the critical value, heat transfer is primarily in the form of convection."

I'm happy to be corrected, but I would have said that the critical Rayleigh number is the point at which the fluid system becomes unstable to convection. A state of marginal convection might not be very vigorous, and I can imagine that it might be insufficient to tip the primary mode of heat transfer from conduction to convection. That ratio would be more appropriately measured by the Nusselt number. Only when convection is rather vigorous is the Nusselt number great than 1. Is this right? Attic Salt (talk) 13:23, 2 April 2019 (UTC)

I agree, Attic Salt. There doesn't appear to be a universal concept of a 'critical' Rayleigh number; an author can of course attach the word critical to any event occurring on the Rayleigh number scale. That said, the academic texts I've seen all use it only when referring to the onset of convective fluid motion (in a heated fluid transitioning from pure conduction)—or, as you more precisely put it, at the point of instabiliy.

If any event is to be mentioned in the article—especially if it's to have the word critical attached to it—it ought to be the onset of convection. (Another noteworthy event is the transition from laminar to turbulent flow.) Regarding the Nusselt number, my understanding is that it has the value of one for pure conduction; anything higher denotes convection. (Convection is the combined effect of conduction and advection.) Pololei (talk) 01:09, 4 April 2019 (UTC)

Have amended the article's lead paragraph in accordance with the above discussion (whilst also putting emphasis on the Rayleigh number's role in describing the flow regime of a fluid). Pololei (talk) 21:19, 9 April 2019 (UTC)

I agree that the webpage is now better, sorry I should have phrased my original edits better. I agree that 'critical' Rayleigh numbers are defined by the start of convection, eg in Lord Rayleigh's original 1916 paper he derived a critical value of Ra above which there is convection (flow), and below which there is no convection. At this value Nu = 1 so transport is still dominated by diffusion; it is only at values of Ra much larger than the critical value that transport is dominated by convection (Nu >> 1). Rayleigh found the critical Rayleigh number in this sense for a specific geometry. As I understand it, in other geometries there is no critical Ra, i.e., convection increases continuously from a flow speed of zero (work of Gu and coworkers Gu, Yang (2018). "Measurement and mitigation of free convection in microfluidic gradient generators". Lab on a Chip. doi:10.1039/C8LC00526E. is an example where convection is driven by a solute not temperature gradient but the two situations are analogous). So perhaps it would worthwhile emphasising the more general feature of Rayleigh numbers which is that for sufficiently large values convection dominates diffusion, while for sufficiently small values convection is either absent or so slow that it is irrelevant for transport. Rpsear (talk) 00:26, 25 April 2019 (UTC)

Don't worry, Rpsear—your contributions are all part of the collaborative process. Let me come back to you on this. In the meantime, if you have any—ideally, freely available—reliable sources that discuss or exemplify this kind of use of the Rayleigh number (i.e. as indicator of dominance of either convection or conduction), please let me know. Pololei (talk) 10:28, 27 April 2019 (UTC)

The difficulty, it seems, is that it's fundamentally incorrect to speak of the relative dominance of conduction (i.e. diffusion) or convection in a fluid of a certain Rayleigh number. That's because convection implicitly involves conduction. It's the combination of conduction and advection. Below a certain "critical" value of Rayleigh number, heat transfer across the fluid is by pure conduction; above that value, heat transfer is by convection. It's either one or the other.

Likewise, when the Nusselt number is one, heat transfer is by pure conduction. (It's not dominated by conduction.) Anything above unity is convection (i.e. conduction plus advection). The Nusselt number is sometimes described as the ratio of convective heat transfer to conductive heat transfer, but it's truer to say that it represents the enhancement of heat transfer due to convection.

Is it possible that you're thinking of conduction and advection? Pololei (talk) 00:56, 30 April 2019 (UTC)