Our team is working on the designing of heat exchanger and we find out that the flow regime for our case is Laminar. As per D. Q. kern pg 103. the Nuseelt number for laminar flow does not depends upon the viscosity of the fluid. The relation is as follows:
Nu = 1.86 *[(Re*Pr*D/L)^1/3]*[(mu/muw)^0.14]
Also, the heat transfer coefficient are related to Nusselt number as
Nu = hde/k
However, when we cross checked the same in HTRI, we found out that the heat transfer coefficient (h) for the fluids vary with viscosity.
Is there some modified relationship that is used for laminar flow?
see in the following useful link.
lup.lub.lu.se/student-papers/record/8900243/file/8900249.pdf
Check this-
http://classes.engineering.wustl.edu/che473/handouts/heat%20exchangers.pdf
Dear Piysh,
I do not quite understand your point. You recall the relationship of Sieder and Tate :
Nu = 1.86 *[(Re*Pr*D/L)^1/3]*[(mu/muw)^0.14]
You then say that Nu does not depend on the viscosity, whereas in the formula the Reynolds number Re depends on the viscosity.
With my best regards
Prof. Bachir ACHOUR
Thank you all for your reply.
Dear Bachir,
I think you are considering the last term which is a correction term added in Sieder Tate equation. However, to see whether the heat transfer coefficient remains constant or not we performed series of HTRI run.
Run 1: The viscosity is taken as that of water and generated using the HTRI simulation itself.
Run 2: We increases the viscosity of water with a factor of 5 maintaining its variation with temperature same as it was in original case (Run 1)
Run 3: We restrict the viscosity and keep it constant irrespective of the temperature. So let's say for the range of 30 degC to 200 degC the viscosity remains constant (say 50 cP)
Run 4: Again we maintain the viscosity constant with respect to temperature. However, this time we increases its value to 100 cP.
Results:
In Run 1 and Run 2 we expect the viscosity function as it is a function of temperature. However, we found out that for the Run 3 and Run 4 the Nusselt number changes with Viscosity.
This is something that raise the question. Which extra factor is coming that is playing a critical role in the dependency of heat transfer coefficient on the viscosity?
Dear Anirbid and Mohammad,
Thank you for providing the literature. The literature definitely provide us with formulas that are not used conventionally and also they shows the dependency of heat transfer coefficient on the viscosity even in laminar flow.
Dear Piyush,
Thank you for the reply. I am not referring to the last term of the equation but to the Reynolds number Re which is in the brackets.
With my best regards
Prof. Bachir ACHOUR
Dear Bachir,
As in the formula, both the Reynolds number and Prandtl number has same power factor the viscosity term get cancel out. Leaving behind just other viscosity independent terms.
Best Regards
Piyush Jain
Hello Piyush Jain,
As per the co relation it is that nusselt no is independent of viscosity of the fluid so according to you the HTRI answer for nusselt no should not vary.
But since for a fluid properties like density, specific heat and thermal conductivity are dependent on temperature.
So this properties will have effect on reynolds no and prandtl no and change the nusselt no.
Also as per your case in Run 3 & Run 4 keeping the viscosity constant, the properties are still varying. So Nusselt no. has to vary
Regards
Vishwam Shah
Dear Vishwam,
For all the cases, the variation in the fluid properties like density, specific heat, thermal conductivity etc. are same. i.e. the variation in the density of fluid would be same for all the four runs. Same thing is applicable to other properties.
The only thing that we are changing is viscosity. That's why the variation in Heat transfer coefficient is of little surprise.
Regards
Piyush Jain
Hello Piyush Jain,
As you correctly said that the properties are not changing and and as per the correlation the nusselt no should not change.
Also in this the correction factor will come into account. The wall viscosity does not remain constant with the viscosity, so there can be little increase in nusselt no.
Regards
Vishwam Shah
Dear Vishwam.
We conducted run no. 3 and 4 to check the effect of correction factor only. We input viscosity as a constant i.e. it does not vary with temperature. In that case, the wall viscosity will remains same as that of the bulk viscosity and hence the correction factor will become 1.
Regards
Piyush Jain
Dear Piysh,
See in the following handbook by Spalding ^.
http://hedhme.com/index/?link_id=10985&article_id=168
Heat transfer coefficient (h) for the fluids vary with viscosity. Fluids are classifed into Newtonian and Non-Newtonian fluids based on relationship between shear stress and shear strain. Shear stress is related to dynamic visocity and velosity gradient. Prof. Mykhaylo Tkach suggested good heat transfer data book.
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