The heat transfer coefficient is defined by dividing the wall heat flux by a temperature difference. The temperature difference in the denominator is chosen, not measured — and when the choice changes, h changes while the physics does not.
Three common choices
Free-stream temperature. Natural in external flow: the undisturbed flow temperature far from the body.
Bulk (mixing-cup) temperature. Correct for internal flow: the mass-weighted mean temperature at that section. The standard choice for pipes and ducts, and it varies along the axis.
Adjacent cell temperature. What solvers sometimes use by default. It depends on the mesh: change the cell size and h changes. In that form it cannot be used for a material or design comparison.
Why it matters
If a report says "h = 45 W/m²K" without stating the reference, that number cannot be compared against another study. On the same problem the three definitions can give values differing by a factor — particularly in the entrance region and after separation.
Local or averaged
This is the second source of ambiguity. A surface-averaged h hides the hot spot. Under an impinging jet the local h at the centre is several times the average. If the acceptance criterion is the hot spot, working with an average h moves the result to the unsafe side, not the safe one.
The practical consequence
Solving the fluid rather than supplying h as an input removes exactly this ambiguity. See the conjugate heat transfer note.
If h is going into a report, three things belong with it: the definition of the reference temperature, whether it is local or averaged, and the surface it was averaged over.
References
- Shah, R. K. & Sekulić, D. P. (2003). Fundamentals of Heat Exchanger Design. John Wiley & Sons. DOI: 10.1002/9780470172605
- Churchill, S. W. & Chu, H. H. S. (1975). Correlating equations for laminar and turbulent free convection from a vertical plate. International Journal of Heat and Mass Transfer, 18(11), 1323–1329. DOI: 10.1016/0017-9310(75)90243-4