Convection HTC's on Flat Plate Surfaces
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There are books devoted to this subject alone, and many expensive computer programs have been written to deal with this topic. We will focus on calculating the convection heat transfer coefficient (HTC, or simply, "h" ) on the surface of a flat plate at zero angle of attack to the flowing fluid (gas or liquid) stream.
The convection coefficient is related to the Nusselt
number by
h = Nu * k / X
where k is the fluid conductivity and
X is the characteristic dimension used in the Nusselt and Reynolds number calculations.
In a great majority of cases, the flow starts out as laminar and transitions to turbulent at some point along the plate. This point occurs when the local Reynolds number exceeds some critical value (commonly approximated at 500,000). The boundary layer "trips" from laminar to turbulent. The important implication is that the heat transfer along the plate is not constant, in fact it can have a significant spike where the boundary layer trips. That's the location you may see burn marks on the part.
There
is a relationship between the freestream turbulence of the incoming
fluid and the critical Reynold's number. Use this whenever you know the
freestream turbulence:
Scratch1 = sqrt [132,500 T2] - 1
Scratch2 = 39.2 T2
Rcrit =[ Scratch1 / Scratch2 ]2
for example, if freestream turbulence is 1%, T = .01 and Rcrit = 453,600.
In these cases, you need to calculate the Reynolds number (based on the distance from the leading edge) along the plate and constantly compare it to the critical ReN (say it's 500,000). Use the laminar local h equation up to that point. Beyond that point, calculate the local ReN, again based on the distance from the leading edge ( *not* from the trip point), but switch to the turbluent local h equation.
On the other hand..... If the upstream flow is known to be turbulent before it contacts the flat plate, then you should simply use the turbulent flat plate (TFP) equations, rather than the laminar-turbulent mixed flow equations. This is the practice most machninery engineers use because flow is most commonly turbulent inside machines. However you could get the same results from your mixed-flow spreadsheet by setting the critical Reynolds number to 1.0.
