Convective heat transfer coefficient, h

Hi, Will someone please help me understand the apparent discrepancy I'm noting between convective heat transfer coefficients (h) calculated two different ways using the same input data?

For the sake of explanation, let's say I have an object with known properties: shape, mass, density, specific heat, thermal conductivity, etc. and object temperature at start and at the finish time. I also know the constant environmental temperature & properties (typically air).

In the first case, I calculate h using one-dimensional transient conduction (Fourier number, then Biot number from A, lamba table).

In the second case, I assume natural convection and calculate h (Prandtl, Grashof, Raleigh and Nusselt numbers).

I've replicated "h" results from several one-dimensional transient conduction text book problems. I've also replicated "h" results from several natural convection text book problems. However, when I calculate h using both methods for a common set of inputs, the values differ significantly. The h values from natural convection calculations are much less than those estimated using one-dimensional transient conduction -- even though the input values are the same.

I would expect some discrepancy given the nature of the correlations, but I'm surprised how different the values are.

Any insight would be greatly appreciated. Thanks!