1
$\begingroup$

I have a situation that I have a combination of free and forced convection over a cylinder. Remembering back from heat transfer, to combine these I use the formula

$$Nu_{\mathrm{comb}}^n = Nu_{\mathrm{forced}}^n + Nu_{\mathrm{free}}^n$$

And that's fine. However, what dimension do I use to find $h_{\mathrm{comb}}$? Because

$$Nu_{\mathrm{forced}} = \frac{h_{\mathrm{forced}} k}{D}$$

while

$$Nu_{\mathrm{free}} = \frac{h_{\mathrm{free}} k}{L}$$

Improve this question
$\endgroup$
  • $\begingroup$ Can you provide more details? Are you trying to calculate an effective heat transfer coefficient $h_{comb}$ that will be valid for both forced and free? Or you have two separate regions that are exposed to different regimes? $\endgroup$ – Physther Feb 3 '17 at 22:07
  • $\begingroup$ And by the way, the formulas are wrong. L is in the numerator $\endgroup$ – Physther Feb 3 '17 at 22:14
  • $\begingroup$ Sorry, it was a typo. $${Nu}_{free}=\frac{h_{free} L}{k}$$ and $${Nu}_{forced}=\frac{h_{forced} D}{k}$$ $\endgroup$ – user1543042 Feb 4 '17 at 5:04
  • $\begingroup$ I'm trying to calculate the combined heat transfer coefficient $\endgroup$ – user1543042 Feb 4 '17 at 5:05
  • $\begingroup$ Okay. Then my answer should be okay $\endgroup$ – Physther Feb 4 '17 at 8:47
1
$\begingroup$

Okay, I'm not 100% sure if I got the question right but, to combine natural and forced convection for flow over a cylinder (I assumed horizontal) you have the following formula: $$Nu_{comb}=(Nu_{free}^n+Nu_{forced}^n)^{1/n}\tag{1}$$ where $n$ depends on your cylinder type (horizontal or vertical). Next you need to calculate the Nu for each regime (free and forced). For the natural convection over a horizontal cylinder, you have this correlation: $$Nu_{free}=\left(0.6+\frac{0.387Ra^{1/6}}{[1+(0.559/Pr)^{9/16}]^{8/27}}\right)^2\tag{2}$$ You can find whatever correlation you find better for your situation.

For the forced convection, you have this correlation: $$Nu_{forced} = 0.989Re^{0.330}Pr^{1/3}\tag{3}$$ (for 0.4 < Re < 4) For other type of flows you can find different Nusselt correlations. You can find them on the internet.

Then you replace them in Eq. 1 and finally you get: $$h_{comb}=\frac{k_{fluid}\cdot Nu_{comb}}{D}\tag{4}$$ where D is the diameter of your cylinder.

You can find some Nusselt correlations here and here

Improve this answer
$\endgroup$
  • $\begingroup$ Thanks for pointing it out. The link expired, so I updated it. $\endgroup$ – Physther May 6 '17 at 14:31

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.