# What is the value of Nusselt number in laminar flow?

In a laminar flow along an Annular cross section with heating in one side and insulation in the other, what is the value of the Nusselt number in this flow? and is the diameter in the Nusselt expression Nu=h*D/k the hydraulic diameter?

• When do you typically use the hydraulic diameter? Also could you clarify what you mean with the two sides? Is the fluid inside the pipe heated? – idkfa Jan 17 '17 at 8:30
• well imagine a cylindrical annulus where the water is flowing in the annulus part (book.transtutors.com/qimage/image09262014624.png), since we have a convective heat exchange, i want to know how to calculate the Nusselt number of this specific flow. – majededdine Jan 17 '17 at 15:44

For

$Re < 2300$

$0.1 \leq Pr \leq \infty$

$0.1 \leq Pr \frac{d}{h} < 10^4$

I found the correlation

$Nu_m = \left( 49.37 + (1.615\frac{Pe \cdot d}{h})^{\frac{1}{3}} -0.7)^3\right)^{\frac{1}{3}} K$

With

d = hydraulic diameter

h = length of pipe

$K = 1$ for gases

$K = \left(\frac{Pr_f}{Pr_w}\right)^{0.11}$ for liquids

$Pr_f$ = Pr for fluid temperature

$Pr_w$ = Pr for wall temperature

Source

I'm not a native speaker, so someone please feel free to add a source for that correlation in English.

And if the geometry is not circular, you use the hydraulic diameter, as always.

You may derive it from

$d_h = \frac {4 A}{U}$

Where

A denotes the crosssectional area and U the circumference.

• Excellent correlations, although those written in the answer are not the same as those in the source so i suggest rewriting them, Danke! – majededdine Jan 19 '17 at 9:19
• Thank you! I was replying via mobile and apparantly forgot the $^3$. I fixed it now. – idkfa Jan 19 '17 at 12:00