Heat transfer coefficient is the property in natural/ forced convection and to be derived upon conditions of study. The range of heat transfer coefficient (h) depends on whether it is considered on a flat plate, tubes, ducts etc. and subjected to free (natural) convection or forced convection. In general heat transfer coefficient in natural convection is far less compared to forced convection. In natural convection, the heat is taken away slowly by buoyancy force and in forced convection, the heat is taken away fastly by velocity.
For general audience working in the field of convective heat transfer, I would suggest to use the Nusselt number for various orientation and then calculated the h value based on the characteristic length and the thermal conductivity of the fluid.
The convective heat transfer coefficient is not a property of the fluid. It is an experimentally determined parameter and depends on properties like surface geometry, nature of fluid motion, properties of the fluid, fluid velocity, inclination of the surface, etc... Typical values of h for free convection of gases vary from 5 to 25 (W/(m^2 K) and for forced convection of gases the interval is from 25 to 250 units (W/ (m^2 K).
Convective heat transfer coefficient is the heat transferred for a unit temperature difference between the fluid and unit area of surface in unit time. In laminar flow, even the molecules are moving, heat transfer take place by conduction. In turbulent flow, the motion of molecules be random and mixing take place and heat transfer will be from cold to hot region or hot to cold region. As it is governed by equation, Q = h A (Temp. difference), convective heat transfer coefficient should be from liquid to surface or surface to liquid or in between fluids. In convection phenomena, heat transfer coefficient has to be estimated compulsorily before estimating the heat flow by empirical correlations only and there is no other alternative (other properties be given). Hence heat transfer coefficient is taken to be the primary and important parameter in convection studies (natural/ forced) in order to calculate heat transfer likewise thermal conductivity in conduction and emissivity in radiation.