What is the accurate and best way to calculate bulk or mean temperature?
 

Hello all. Hope all are well. I wanted to ask which of the following is a better way to calculate bulk or mean temperature for heat transfer coefficient and consequently Nusselt number calculation in pipe flow.

1. Applying an area weighted average i.e. (integral of uxT in section)/(pi×r^2×u)

or

2. Applying a mass weighted average. I saw this in an older post that suggested applying surface integral on a plane that cuts cross section of pipe or on a line perpendicular to the mean direction of flow and then calculating mass weighted average temperature.

or
3. Apply the Grashof equation for heat transfer in a pipe for calculating average bulk (average film) temperature by using beta (coefficient of thermal expansion).

Would be extremely grateful for help. Hope to hear from someone soon. Thanks.

Hello everyone. Hope all are well. I would extremely grateful if someone could help me out. Thanks.

Hello all. I have been waiting for a reply but none came. I would be extremely grateful if someone could help me out. If you help someone today you will be helped in the future too. We should share our knowledge and expertise for the benefit of others and humanity. Thanks.

I think mass weighted average temperature is the correct way to get bulk or mean because they have mass conservation theory inside.


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Thanks a lot Quang Le Dang. I'll try it. Waiting for other expert opinions tooon this matter.

You should be doing some sort of mass-weighted average.

1. is a mass weighted averaged assuming constant density and is only valid such. Otherwise there's no reason to weight the integral by u.
2. is what you want to do usually.

The point of using the bulk temperature is so that the heat transfer coefficient and Nusselt number can be related (via an energy balance) to the energy entering and leaving the control volume (i.e. Q=mdot*cp*dT)

Thanks a lot Lucky Tran. My Density is constant. What do you mean by saying that mass averaged calculation of a parameter always assume a constant density? And what do you mean by weighting the integral by u? If Density is constant does that mean I have to weight the integral by u? Hope to hear from you. Thanks.

Just use 2. It's even easier in Fluent because you can simply do a mass-weighted average. It's straightforward. If you cannot understand when 1. is correct and when 1. is incorrect, then just use 2. 1. only gives you the bulk temperature if density and specific heat are constants. 1. is in general wrong, but only correct if density is a constant.

OR you can just use 2.

Concerning 3. In internal flows, we generally do not use film temperature. Film temperature is applicable to external flows, but not so much in internal flows. In internal flows there is no such thing as freestream temperature so there is no appropriate freestream reference to even define the film with.

Thank you LuckyTran. I had the same suspicion about three and you confirmed it. I think 2 is more suited to my internal flow even though the density is constant because first its easy, second it has built in conservation of mass (although I think conservation is built into FVM itself!), and thirdly h and Nu number can be accurately related (via an energy balance) to net energy balance (i.e. Q=mdot*cp*dT).

how did you manage doing it in fluent as I am stuck there too?
thank you in advance