Every thermal calculation eventually needs a convection coefficient, and h is the one number in heat transfer you cannot look up. Conductivity is a material property. Emissivity is a surface property. But h depends on the flow, the geometry, the orientation and the temperature difference itself — so it has to be calculated, from a correlation that somebody fitted to experiments.
Why guessing is so tempting and so risky
People reach for remembered values: "about 5 for natural convection in air", "25 outdoors in wind", "1000 for water". Those are not useless — they are the right order of magnitude, and the first is genuinely close for a warm vertical surface. But h can swing by a factor of five across the range of conditions a single design might see, and it usually appears in the denominator of the answer.
The three numbers that decide everything
Reynolds (Re = VL/ν) says whether forced flow is laminar or turbulent. Prandtl (Pr = ν/α) is a fluid property — how momentum diffuses relative to heat. Rayleigh (Ra = GrPr) replaces Reynolds when there is no fan or pump and buoyancy is doing the work. Every correlation is just Nu = f(Re, Pr) or Nu = f(Ra, Pr), and h falls out of h = Nu·k/L.
Picking the right correlation
Match the geometry first, then check the range. A flat plate uses distance from the leading edge; a tube uses its inside diameter, not its length; a cylinder in crossflow uses its outside diameter. Getting the characteristic length wrong is more common than getting the correlation wrong, and it changes the answer directly. The correlation reference lists what L means for each case.
The laminar tube result that surprises people
In fully developed laminar tube flow the Nusselt number is constant — 3.66 for a constant wall temperature, 4.36 for constant heat flux. It does not depend on velocity at all. Pumping harder buys you nothing until the flow turns turbulent; only a smaller diameter raises h. That single fact explains a lot of disappointing heat exchanger retrofits.
Evaluate properties at the right temperature
For external flow use the film temperature, the average of the surface and the free stream. For internal flow use the bulk mean temperature of the fluid. Using the surface temperature alone is the standard mistake and shifts h by 10–20% when the temperature difference is large.
Treat the answer as a band
These correlations carry roughly ±20–25% uncertainty even when used correctly, and considerably more outside their fitted range — where they do not fail loudly, they simply return a plausible wrong number. So calculate h, then ask whether the design still works at the pessimistic end. If it does not, you need a test, not a better correlation. Run the cases on the Convection Coefficient tool, which reports whether your inputs fall inside the valid range, then feed h into Fin Efficiency, Pipe Insulation or Heat Exchanger NTU.