[QustFelix]

Hi,guys.

According to classic heat transfer knowledge ,the Nusselt number in a fully developed tube with constant heat flux should be 4.36 .

CFD code like fluent is so powerful ,so I want to validate the problem in fluent .And if I model right ,I should get the right Nusselt Number.

But maybe there is something wrong in my model process , I just can not get the Nusselt number as described above .

These is the process below.


according to experience ：the length of entry region l=0.05Re×Pr。

Material is water ： and I set Re=100.
Re=Rho×velocity×D/viscousity. then I get inlet veloctiy=0.1m/s.

Pr（30Celsius-60Celsius）is about 3 .then we get the entry length l=0.05×100×3=0.15m.


I build a cylinder in Gambit with the dimension below：
D=0.1m,L=0.3m.

Boundary condition:

inlet velocity :v=0.1m/s .T=300K. outflow in outlet。
heat flux of wall =q=400W/m^2.
the conductivity of water :lamda=0.6.

I use the 3D single precise solver to solve the problem. Set the residual to 10-4. At the same time ,I set a temperature monitor point in the middle point at the tube .


The calculation of Nusselt number:

Nu=h*D/Lamda.
h=q/DletaT=q/(Twall-Tref).
Twall is the temperature of wall of the tube ,Tref is the average temperature of the section I choose in the fully developed region.

I create a section in fully developed region .

plot temperature coutour of this section ,and I get max temperature in the wall is 300.948K .

The difficulty comes as I want to calculate the average temperature of the section I created.

According to heat transfer textbook ,Tref=Tm=(Intergral of（u×T）in seciton ）/（pi×(D/2)^2×Veloctiy）。

The result of the section is 0.002341306。So Tref=Tm=0.002341341/（3.1415926×0.05^2×0.1）=298.2555K.

Then h=q/(Twall-Tref)=400/（300.948-298.2555 ）k=148.560817084494 w/(m^2.k).

At last ,I get Nu=h×D/Lamda=148.560817084494*0.01/0.6=2.4760136180749 ！= 4.36.

I don't know what was wrong with the above process .Can somebody so kind to point the error in my process ?