Talk:Nusselt number

Derivation

This newly added sub topic is seriously lacking in material, explanation and is of questionable accuracy... any suggestions?

Characteristic Length

I have went through some research papers. The equation h=K * Nu /L, all the research papers are saying, L is the characteristic length. But they did not give any equation to relate that characteristics length with geometry of the convection surfaces.

In one research paper L is considered as diameter. Then, how can we calculate nusselt number for a flat plate?????????

The characteristic length depends on the geometry.

For a circular pipe the characteristic length would be the diameter.

For non circular ducts, the characteristic length would be:

L=4A/p

where A is the cross-sectional area of the duct, P would be the wetted perimeter.

Note that for a circular pipe:

L=4*(pi*D^2/4)/(pi*D) = D

For flat plates, the characteristic length is usually the distance from the leading edge for a local Nusselt number. Average Nusselt numbers over a distance 0 to L use the L as the characteristic length. Note that most of these Nusselt number relationships (based on Reynolds and Prandlt numbers) are empirical.

• As above, Nu will in general depend on the geometry under consideration. Selection of the significant length dimension will obviously change the value of Nu. I cannot say for certain as I am not a professor of fluid mechanics (merely a mechanical engineering undergrad), but I believe that the selection of the significant length dimension should be the direction of the growth of the boundary layer. An example would be that of a horizontal cylinder and a vertical cylinder in natural convection. For the vertical cylinder, the significant length dimension is the height L. For the horizontal cylinder, the significant length dimension is the diameter D.
  • I just got an e-mail back from the TA for my heat transfer class. He confirmed that the above is correct, so I'll be updating the Nusselt Number main page.

Nusselt number vs Biot number

Could someone explain what the difference between the Nusselt number and the Biot number is? They have very similar expressions.

The Nusselt number is most useful in determining the convective heat transfer coefficient, whereas the Biot number is used in unsteady problems.

This is a typical exam question. The "$k$" in the Biot numer is of a solid, that in the Nusselt number of a fluid. Different meaning, different use... see a heat transfer textbook.

Yes the Biot and Nusselt numbers use different conductivities. But this Nusselt number page is wrong! The $h$ and $k$ are both in the fluid so the "ratio of convective to conductive heat transfer" in the fluid is one.

The real physical meaning of the Nusselt number is ${\rm {Nu}}\simeq L/\delta _{T}$ where $\delta _{T}$ is the thermal boundary layer thickness. Think about it. The heat flux, in power/area, is given by ${\vec {q}}\cdot {\hat {n}}=h(T_{s}-T_{fl})$ where $T_{s}$ is the temperature at the solid-liquid interface and $T_{fl}$ is the bulk fluid temperature. For a fluid thermal boundary layer of thickness $\delta _{T}$, this is equal to ${\vec {q}}\cdot {\hat {n}}\simeq k_{fl}/\delta _{T}(T_{s}-T_{fl})$, within a factor of two or so. So $h\simeq k_{fl}/\delta _{T}$.

Here is a reference on MIT Open Courseware which explains this very tersely - scroll to page 80.

Therefore, ${\rm {Nu}}\simeq L/\delta _{T}$. I propose correcting the Nusselt number - and Sherwood number - pages to reflect this.

Hazelsct (talk) 12:44, 28 July 2024 (UTC)

A better definition still is "dimensionless temperature gradient" as that does not require the fudge factor to convert $\Delta T/\delta _{T}$ to $\partial T/\partial y$. Googling the term "Nusselt number dimensionless temperature gradient" produces numerous references with this correct definition.

Hazelsct (talk) 22:31, 22 August 2024 (UTC)

how to calculate nusselt no.

For finding heat loss in natural convection we require heat transfer coefficient(h). For finding h we require nusselt no. Now how to calculate nusselt no. There are different equations for different cases.

in perpendicular

maybe the "in perpendicular to the flow direction" should be rephrased or something?

Ratio of convection to conduction transfer

This equality is far too general to be of any help. For instance, in natural convection in cavities is literal, in laminar internal flows can be descriptive of the situation and in turbulent and external flows is simply false. To explain fully what it means would require several pages. In addition, it tends to confuse students. For instance, they then mix-up Nusselt and Biot numbers, since the ratio is much more meaningful for the latter.

Xtobal (talk) 12:02, 14 April 2008 (UTC)

Fair enough. I have no problem with you removing that part of the equation now that you have explained that, but before it appeared more like vandalism because there was no explanation to why it was deleted. In the future I recommend that you used the edit summary. Thanks! --Wizard191 (talk) 12:55, 14 April 2008 (UTC)

I would like to add that I think the definition is still somewhat poor and could lead to the same confusion as mentioned above. The fact that the Nusselt number ends up being equal to the ratio of convective to conductive heat transfer in a fluid is a result of its formulation, not what it actually represents. Physically, the Nusselt number is actually the dimensionless temperature gradient at an interface. When this is applied to a convection interface you obtain the typical ratio as shown, which is what the Nusselt number equates to, not what it "is". I would like to see this better explained in here. More details can be found in intermediate heat transfer texts, including the free textbook "A Heat Transfer Textbook" by Linehard and Linehard. —Preceding unsigned comment added by 24.118.49.238 (talk) 13:37, 13 November 2008 (UTC)

Nu = f(Ra, Pr)

I guess you can say that (for natural convection) Nu is function of Ra & Pr but Ra = Pr*Gr. So isn't it more logical to just say Nu = f(Ra) or Nu = f(Gr,Pr). (and Nu = f(Re,Pr) for forced convection) —Preceding unsigned comment added by 134.184.120.160 (talk) 12:41, 17 August 2008 (UTC)

You're mostly correct, but I don't think you can say Nu = f(Ra), as the Prandtl number will generally affect the Nusselt number.

Hazelsct (talk) 22:34, 22 August 2024 (UTC)

references

Why are there citations for 3 editions of the same book...164.54.53.85 (talk) 19:40, 19 March 2010 (UTC)

Because people added content from three different editions so it must be noted. I know I have one of those editions, but I couldn't say I had it from one of the other editions referenced, therefore the three are noted. Wizard191 (talk) 20:59, 19 March 2010 (UTC)

Wrong definition ?

The definition for the Nusselt number as ratio of convective heat transfer over conductive heat transfer seems to be wrong, because it's the definition of the Peclet number (forced convection) or Rayleigh number (free convection). The correct definition is total heat transfer over conductive heat transfer. This implies that convection is not including conduction and is completely different. — Preceding unsigned comment added by Biglama (talk • contribs) 21:54, 10 December 2011 (UTC)

The term convection is somewhat ambiguous, since it is sometimes used as a synonym for advection, what seems to be your definition. I clarified that it includes both advection and conduction, which is also the primary definition in the convection article. Total heat transfer would also include radiative heat transfer and that is definitely incorrect. Han-Kwang (t) 09:49, 11 December 2011 (UTC)

Thank you for the accurate information especially about advection and yes my definition of convection was the definition of advection. Just a small question: why the total heat tranfer couldn't be used in the nusselt number definition ? There are some mathematical formulations which allow to define the radiative heat transfer as a linear function of temperature difference.

If dT is small, it is possible to describe the radiative equation q = 4*σ*A*ε*(T1⁴-T2⁴) as Taylors series to get q = 4*σ*A*ε*T2³(T1-T2) Biglama (talk) 12:40, 30 March 2012 (UTC)

I am not an expert but I had a lecture during my studies which provided a global overview of transport phenomena:

Biglama (talk) 12:55, 30 March 2012 (UTC)

The Nusselt number describes heat transfer at a fluid-solid interface. Because normal velocity at the interface is zero, total heat transfer is equal to conductive heat transfer. So how can one say "ratio of total heat transfer to conductive heat transfer"? That ratio is tautologically equal to one.

A more accurate definition/description is the dimensionless temperature gradient, as shown in the derivation on the Nusselt Number page. That is, it's roughly the ratio of characteristic length to boundary layer thickness. See above on the difference between Nusselt and Biot numbers.

I think we should rewrite this page completely to reflect this.

Hazelsct (talk) 22:27, 22 August 2024 (UTC)

Confusing introduction

'In this context, convection includes both advection and conduction.' How can convection include conduction?! | Moemin05 (talk) 16:49, 29 March 2012 (UTC)

It is a huge mess: some books consider that convection refers only to natural or free convection, others which define convection as advection+conduction and some as synonym of advection. The definition changes in the past several times and all modern books are not using the same definition Biglama (talk) 12:45, 30 March 2012 (UTC)

Does the fluid have to be flowing past the surface?

The context section says "An understanding of convection boundary layers is necessary to understanding convective heat transfer between a surface and a fluid flowing past it." The diagram also makes it look like the fluid is flowing past the surface and even has a variable "V" written on it, which I suppose is probably velocity. However, it's not clear to me from any of the rest of the description that the motion of the fluid parallel to the surface is considered or matters. Also, the reason I came to this page was because I was reading a paper that involved modelling convection in exoplanet mantles as part of modelling their thermal evolution (https://doi.org/10.1051/0004-6361/201935714), which contained

The heat fluxes at the top and bottom of the mantle (q_man-top and q_man-bot) are expressed in terms of the temperature drops across the top and bottom thermal boundary layers (ΔT_top and ΔT_bot), and the Nusselt number Nu for the entire mantle, i.e.,

$q_{\mathrm {man-j} }(t)=\mathrm {Nu} (t){\frac {k\Delta T_{\mathrm {j} }(t)}{h}},j=top,bot$

where k is the thermal conductivity of the mantle (either constant or temperature-dependent; Table 1) and h is the height of

the mantle.

This seems to me to be a case where a Nusselt number is being used in a situation where the fluid is not flowing parallel to the surface.DubleH (talk) 03:30, 12 December 2020 (UTC)