I encountered a problem in my project work on heat exchangers where to find heat transfer coefficients on the defined conditions the Reynolds number came to be 1753.8 while the Prandtl number is 3.916. I am unable to find any particular relation for finding Nusselt Number and thereafter the heat transfer coefficient.
Please help me in finding the appropriate way to approach the problem.
To the conditions of the problem, I would advise you to use the correlation of Sieder and Tate (Id. Eng. Chem., 1429, 1936). But this correlation is advisable when Nu> = 3.72 due to the fact that in lower values, developed profile conditions are present.
Use the Sieder-Tate correlation for Nusselt number in the laminar flow regime:
Nu = 1.86Re1/3Pr1/3(D/L)1/3(mub/muw)0.14
where Nu = Nusselt number, Re = Reynolds number, Pr = Prandtl number, D = tube diameter, L = tube length, mub = bulk viscosity, muw = viscosity near wall
When tube length is sufficiently long, most of the heat transfer occurs in the thermally fully developed region and here Nu remains constant regardless of the physical parameters. For uniform wall temperature, Nu is ~ 3.66 and when a wall heat flux boundary condition is applicable, Nu takes a constant value of ~ 4.36.
See the below reference:
http://web2.clarkson.edu/projects/subramanian/ch330/notes/Heat%20Transfer%20in%20Flow%20Through%20Conduits.pdf
If you have a flow in non-circular section you could apply the proposed equations for circular one taking equivalent diameter in the place of d when calculating Re and Nu numbers. Another approach is to search equations proposed particularly for annular section between concentric tubes /as it seems to be your problem/. See pages 200 and 214 of Coulson and Richardson Chemical Engineering, vol.1, revised second edition for more information regarding Davis' and Sieder-Tate' equations or the current literature on heat transfer.
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