[Shomaz ul Haq]

Dear all,

Hello. Hope all are well. I wanted to ask is there a correlation for Nu number in laminar pipe flow with constant wall heat flux? I have searched a lot but couldn't find any for constant wall heat flux boundary condition. For example there is the Dittus Boelter correlation for Nu laminar pipe flow but with constant wall temperature boundary condition. I want to compare my results with a correlation and can't find one. Would be grateful for help. Hope to hear from someone. Thanks.

[Opaque]

Are you looking for the Nusselt number value for fully developed laminar flow in pipes for either uniform wall temperature or uniform wall heat flux ?

or the correlation for developing laminar flow in pipes, i.e. flow within the entrance length region ?

[Shomaz ul Haq]

Thanks Opaque. A correlation for laminar developing flow. Yes.

[Opaque]

https://www.iitg.ernet.in/director/files/Chapter3.pdf

It has the correlation for mean Nusselt number in the thermal entrance region (fully developed flow)..

It also has the reference for the classic work forced convective heat transfer for laminar flow in pipes from RK Shah, and A.L. London

Another interesting recent work from Giudice

http://iopscience.iop.org/article/10...7/1/012041/pdf

That should help

[Shomaz ul Haq]

Thank you Opaque. I have explored in detail the correlations in both references but unfortunately couldn't find a correlation that met my conditions. My model has wall boundary condition of constant heat flux and thermophysical properties are not temperature dependent. Moreover, it is a combined entry length problem i.e. hydrodynamically and thermally developing or simultaneously developing. It is not a

1. hydrodynamically and thermally developed problem or a
2. hydrodynamically developed and thermally developing problem (Graetz problem)

The first reference has some good correlations but again none that matches my problem. I found the attached correlation that is the first image attached. But still my question is this valid for hydronamically and thermally developing flows?

where Tm is the bulk mean temperature at any cross section that is the second image attached.

which for wall boundary condition of constant heat flux becomes the third image attached.

Also I think when you say "thermal entrance region (fully developed)", you mean either "hydrodynamically developed and thermally developing flow" or "hydrodynamically and thermally developed flow" in which case the Nu number approximates 4.364 and remains constant.

The second reference also makes a good attempt at finding a correlation for Nu number but again with varying temperature and viscosity.

What I am looking for is a correlation that describes the Nu in terms of Re and Pr like Dittus Boelter but with constant wall heat flux and hydrodynamically and thermally developing problem. Would be grateful for help. Hope to hear from someone soon. Thanks.

[Shomaz ul Haq]

Dear all,

Hello. Hope all are well. I would be extremely grateful for help. Hope to hear from someone. Thanks.