# Heat transfer characteristics in narrow rectangular channel

Please take a look at following figure: 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.

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