Dear Mohammad, in my opinion we should use the definition of bulk temperature, that is velocity Uz at integral in denominator should be speed values, positive or negative, along circulation section.  Gianluca

Hi, my intuitive opinion is the following. If you try to use even simple numerical integration scheme for the both integrals, then you receive the positive and negative summands in each integral. But the negative ones will not compensate the positive ones  due to the general flow direction, if I understand correctly the problem. And the result for the average temperature will be positive. If you take absolute values for the velocity, then you are not take into account the circulation of a flow substituing it by straight flow.

Thus, I think you do not need to use absolute values.

Dear Mohammad,

the integration, as you have already specified, is done over the cross section of the pipe. Therefore, assuming you are solving it by means of a velocity profile, you should use the proper profile for Uz, at the circular section you are interested. However, since the velocity profile is obtained from the momentum equation, you will need to deal with the pressure variation along the flow direction. Normally, for exercises purposes, this is done in a fully developed region (constant pressure variation, say along 'z'). Of course this is not your case, so the comment here is to make you aware of the problem.

I have done some recently numerical analisys in problems where recirculation takes place. In these cases, I used the inlet temperature as a reference, instead of the bulk temperature ('mass weighted').

Good luck!

Regards,

Hi there,

As indicated in Theory Guide of Ansys Fluent, you should use absolute value. I have attached a piece of Guide for your information.

Regards

Thank you Ehsan,

I have seen this guide before. Exactly I have a curved cross-section which I should obtain the bulk temperature from it. But as I think my obtained values don't match with the values in the contour. So it makes me doubt.

Hello

I think the actual formula is integral (rho*v*T*dA)/integral(rho*v*dA)

Now in terms of dA and V, the dot product should ideally consider the sign automatically. But as you are using directly the value of dA as 2*pi*r, I think you should opt for positive values i.e absolute values.

Thanks

Dear Mr. Fazli

I think the integration will be the gross (net) of all cells (directional Velocity * Temperature) within the section for the numerator, and also same for the denominator, where integration of all cells values for directional velocity in any direction. The results are the net of the ratio of these two integrations. So, you don't need to take absolute value for any directional quantity.

Have a good day.