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Please take a look at following figure: Rectangular narrow channel with heat transfer by convection

System considered is a narrow rectangular channel of 2.5 mm depth (W x L is 60 mm x 150 mm). Since channel has low depth, it can be considered as mini-channel. Bottom surface is hot and at $~ 100\,^o \text{C}$, top surface is initially at ambient $20\,^o \text{C}$. Air flow enters channel at $20\,^o \text{C}$. I want to know how for such narrow channel heat transfer is defined for air as working fluid. Specifically: $$ Nu = f(Re, Pr)$$ a correlation of Nusselt number as function of Reynolds and Prandtl number. Re range is in 500 - 2000. Any suggestion of literature reference are welcome.

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From "Heat Transfer, 2nd Edition" by A.F. Mills, equation 4.51 gives a formula for the average Nusselt number for flow between two parallel plates. This might be appropriate for your duct because you can probably ignore the sides and just treat it like two parallel plates:

$$ \overline{Nu} = 7.54 + \frac{0.03\frac{D_H}{L}Re\cdot Pr}{1+0.016 \left[ \frac{D_H}{L}Re\cdot Pr\right]^\frac{2}{3}} $$

Here, $D_H$ is the hydraulic diameter, which is just twice the plate spacing for your case. $L$ is the plate length, and $Nu$, $Re$, and $Pr$ are the Nusselt, Reynolds, and Prandtl numbers.

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  • $\begingroup$ Hi, Thanks for taking time. I have a doubt though. Does this correlation hold true for mini-channels i.e. paralle plates separated by 2.5mm or less distance? Anyway I will refer that book and find out for myself. Than you for input. $\endgroup$
    – user1768201
    Feb 27, 2016 at 8:22
  • $\begingroup$ The correlation should work on that scale too. The only difference would be how fast the flow becomes fully-developed. I would expect a narrower channel to have a shorter entrance length than a wide channel. That equation I think assumes that the flow develops quickly. I don't have the book with me now but I'll check when I can get to it. $\endgroup$
    – Carlton
    Feb 27, 2016 at 15:37

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