I am trying to calculate HTC's in a laminar flow regime using correlation for flow over a flat plate.

Nu = 0.664 * Re**1/2 * Pr 1/3

The Nusselt number, Nu = h * L / k Reynolds Number Re = rho * U * L/ mu Prandtl number Pr = mu * Cp/ k

h - heat transfer coefficient

My question is : In these correlations L is the length of the plate, so when calculating HTC's on a cell by cell basis, should I use the cell dimension as the characteristic length ? That does not seem appropriate to me. Any suggestions / comments/ alternative methods for calculating HTC's in a laminar flow ?

Your formula gives the AVERAGE Nusselt number over the entire length of the plate, from 0 to L, where L is from the leading edge.

The formula for the LOCAL Nusselt number, at x, also measured from the leading edge, is

Nu_local = h * x / k = 0.332 * PR^(1/3) * Re^(1/2),

where Re = rho * U * x / mu .

I've taken these from Alan Chapman's "Heat Transfer," now long out of print. But the example is a pretty fundamental boundary layer analysis, so you should find it in most senior or 5th-level heat transfer texts.

So on a cell-by-cell basis, use the local formula that I've typed in above and the local distance (x) from the leading edge to the cell for which you're evaluating h.

check out "Fundamentals of Heat and Mass Transfer" - Incropera & Dewitt. It lists all kinds of correlation for flow over a flat plate. Also, a point to note is, check your Reynolds number and Prandtl no because the relation you will use depends on what are the values of this two numbers. hope this helps !!!