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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.

Algo
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user1768201
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1 Answers1

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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.

Carlton
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