Reynolds number for parallel plate fin heat sink

[Cheetos]

I'm reading up on this article about heat sink calculation. Link

I'm confused about the Reynold's number equation. Eq 10.

It shows Re = (rho)(V)/(mu)(b)(b)/(L) b is the fin spacing and L is fin length.
The author treated hydraulic diameter, Dh, as b^2/L. I don't really understand why. I thought Dh = 4A/P. How did the length come into the equation? The author said it's the "modified channel Reynolds number"

 

[ione]

I suggest you to put your hands on the literature quoted in the references.

The definition for the modified Reynolds number is:
Re(mod) = Re* (b/L)

For a high aspect ratio (high H/b) the hydraulic diameter is:

Dh = 4A/P = 4 (H*b)/[2(H+b)] ≈ 4H*b/(2H) = 2b

There’s anyway a difference by a factor 2