Talk:Nusselt number

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)

Agreed - the page is mess. Will be revising.... Fiske (talk) 22:16, 31 May 2026 (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)

The Prandtl number affects the Nusselt number independently of the Rayleigh number in most cases. Fiske (talk) 14:58, 2 June 2026 (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)

It's totally wrong, and I have deleted it. Fiske (talk) 22:09, 31 May 2026 (UTC)

Role of wall boundary condition (especially for laminar flows)

At present, the article is careless about the effect of wall boundary condition on the Nusselt number (or heat transfer coefficient). Especially in laminar flow, the equation for an isothermal wall is substantially different than for a constant flux wall.

I will try to correct this as time permits. Fiske (talk) 12:33, 4 June 2026 (UTC)

Inadequate discussion of internal flow

The thermal entry length should be mentioned, especially for laminar flow and high Pr where it can be very significant.

In addition, non-circular tube cross-sections should be mentioned, including parallel plates and rectangular channels. Fiske (talk) 12:35, 4 June 2026 (UTC)