# Nusselt numbers for a shell and tube heat exchanger

Hallo, CE friends.
I am mechanical engineer and a new member of this Forum, and I need your help for the design of a shell and tube heat exchanger which is needed to keep the temperature of a water pool below a set value.
The component is a counter-flow heat exchanger with single pass in the tube and shell sides, without baffles. For the tube side I am using the Gnielinski equation (turbulent flow): Nu=((f/8*(Re-1000)*Pr)*(1+((di/L)**2/3)))/(1+12,7*(f/8)**1/2*(Pr**2/3-1)), where the friction factor is f=(1,82*logRe-1,64)**(-2).
My difficult consists in determining the Nusselt correlations which better apply to the shell side. I think I could likewise use the same above correlation for the longitudinal region of the shell, of course considering now the eq. hydraulic diameter. Should the use of this equation be correct?
And what are the best Nu correlations to be used for the cross flows in the regions of the inlet and outlet nozzles, and what is the contribution (weights) of each of these Nusselts (logitudinal and cross flows) in the resulting Nusselt of the shell side? How are these weights achieved (calculated)? Are they a function of the heat exchanger geometry?

Any help will be appreciated.
I thank you in advance for helping me in this matter.

jkf

## Replies

• Elisa
No answer yet. All the best jkf.
• jkf
Thank you, Elisa.

jkf
• Michiel
Hi JKF,

I'm also a mechanical engineer. I'm working on a shell and tube heat exchanger without any baffles. I'm faceing the same problem as you (did). I'm looking for a way to determine the Nussults Number on the shell side.

Can you tell me wich correlation you used? And what characteristic lenght did you uses, in the Nussults Number as well as the Reynolds Number?

Hope you can help me.

Greetings Michiel van Oostrum (Holland)
• Voltaire
Hi

You have given too little info for a meaningful answer

Is it vertical or horizontal? What is the arrangement of the nozzles and so on i.e. factors that affect N[sub]Nu[/sub].
The entrance effects are not significant for L/D > 60. Below this limit Nusselt recommended (for 10 < L/D < 400 and properties evaluated at bulk temperature) N[sub]Nu[/sub] = 0.036N[sub]Re[/sub][sup]0.8[/sup]N[sub]Pr[/sub][sup]1/3[/sup](L/D)[sup]-0.054[/sup] (Perry)
Entrance effects can be correlated by h[sub]m[/sub]/h = 1 + F(D/L) where the coefficient h depends on whether heating or cooling takes place and F is the entrance factor. See Boelter, Young, and Iverson (NACA Tech. Note 1451, 1948) for values of F.
Perry gives these values:
Fully developed velocity profile 1.4
Abrupt contraction entrance 6
90° right-angle bend 7
180° round bend 6

Also look up the Colburn correlation Kern is always a good referencel [DQ Kern, Process Heat Transfer, McGraw-Hill, 1965].

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