# Does Nu number calculation changes according to Gz number for each point of length?

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 June 16, 2017, 03:24 Does Nu number calculation changes according to Gz number for each point of length? #1 Senior Member   Shomaz ul Haq Join Date: Aug 2015 Location: Islamabad, Pakistan Posts: 177 Rep Power: 3 Sponsored Links Dear all, Hello. Hope all are well. My question is regarding forced laminar convection in pipe flows. In deciding a split Nu number (i.e. with two functions based on Gr number) correlation to be used, do we select the length of the whole pipe in calculation of Gr number that will in turn decide which half correlation to be used or check Gz number for each point of length? I want to compare Nu number variation in z direction from CFD and Shah correlation. Would be grateful for help. Hope to hear from someone. Thanks.

June 16, 2017, 10:48
#2
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Erik
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Yes, The nusselt number should change while the flow is thermally developing. I ran a case once and found it took quite a while for it to become thermally developed. My constant Heat flux case was still not fully developed 1000 pipe radii downstream.
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 June 16, 2017, 14:03 #3 Senior Member   Shomaz ul Haq Join Date: Aug 2015 Location: Islamabad, Pakistan Posts: 177 Rep Power: 3 Thanks a lot Erik. It clears my perspective. Also my flow develops before reaching the outlet at 1 m. My diameter is the same as yours coincidentally. But still my question remains. Do we calculate Gr number for every point along length of pipe? (for example there is Gz number involved in Shah and London correlation). Another thing is that the heat transfer coefficient (h) stabilizes to a value of about ~(100-150) which is very low as compared to literature (I compared the same although for a diameter of 4.75 mm) and your result. Why is that? I am simulating at a Re number of 500. Moreover, my Nu number stabilizes to a value near 4.364 (good agreement) but again h gives a very low value. Would be grateful for help. Hope to hear from someone. Thanks.

 June 19, 2017, 16:50 #4 Senior Member   Erik Join Date: Feb 2011 Location: Earth (Land portion) Posts: 659 Rep Power: 13 The flow may be developed, but I doubt it is thermally developed in 1 meter? If Nu is correct, then so will be h, since h = Nu*k/Lc. You can't have one correct and one incorrect. I get 133 W/m^2/K for h in the constant heat flux case, so I don't know what is wrong/different with the literature cases you are looking at.

 June 19, 2017, 17:56 #5 Senior Member   Join Date: Jun 2009 Posts: 679 Rep Power: 15 Are you plotting local Nusselt number as a function of axial length, or mean Nusselt number as a function of axial length ? How are you defining "thermally developed flow"? What percentage of the asymptotic value are you using to define such length ?

 June 19, 2017, 19:16 #6 Senior Member   Shomaz ul Haq Join Date: Aug 2015 Location: Islamabad, Pakistan Posts: 177 Rep Power: 3 Erik that's what I thought too that if Nu number is correct h must be too. You confirmed my suspicions. Also if you were getting an h of around 133 W/m^2/K then my h values must be correct according to what I've input. There must be something different in the models in literature. Opaque how can I tell if my Nu number is local or mean?Also my Nu number is within 1-2% of the asymptote value? Is it an accurate and good enough estimate? Thanks both of you.

 June 21, 2017, 04:35 #7 Senior Member   Shomaz ul Haq Join Date: Aug 2015 Location: Islamabad, Pakistan Posts: 177 Rep Power: 3 Can anyone tell me what would be the expression to calculate average heat transfer coefficient in a pipe? Its formula is h(x)=(1/L)∫_0^L[h(x)dx]. I need it to calculate average Nu number. I am using areaAve(Wall Heat Transfer Coefficient)@Wall Is it a correct expression? or should I use h(x) that I calculated using my own expression earlier. Would be grateful for help. Hope to hear from someone. Thanks.

 June 22, 2017, 10:18 #8 Senior Member   Erik Join Date: Feb 2011 Location: Earth (Land portion) Posts: 659 Rep Power: 13 If you have defined Heat Transfer Coefficient yourself, and correctly, then yes. areaAve(WallHTC)@Wall would be correct, and equal to the Integral expression you wrote.

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