In CFD (Computational Fluid Dynamics) simulations, the space is discretised into a huge number of tiny cells and, therefore, one has the opportunity to use a model of heat transfer that takes into account such amount of detail. Newton's law of cooling gives the rate of heat transfer between a surface and a moving fluid,
$$\dot{Q} = h \cdot A \cdot \Delta T,$$ where $h$ is the heat transfer coefficient (that depends on both thermal and hydrodynamic properties of the flow), $A$ is the surface area and $\Delta T$ is the difference of between the fluid and surface temperatures. The model does not go into the details of local heat transfer between each tiny element of fluid but regards the transfer as a whole (as if both fluid and surface were irreducible). I don't know how the law could be used in a CFD simulation. For instance, which cells of the fluid would be regarded in the formula: the ones immediately in the vicinity, or others some far away? The result would be highly dependent on the chosen cells: the near ones would have a temperature very similar to the one of the wall, while the far ones may not. Also, heat is in reality transferred through collisions between particles or by diffusion, the so-called conduction (as well as by radiation). Convection may correspond to the motion of a big bulk of fluid but the transfer of heat is still made microscopically through conduction. A law for heat conduction such as Fourier's law may describe well local heat transfer, and, therefore, couldn't it be used for any case (heat transfer between two elements of fluid and between an element of fluid and an element of surface)?
The convection law seems to be solely appropriate for back-of-the-envelope calculations where one does not want to deal with the local details of fluid flow. Still, I know that it is used in many CFD codes such as Ansys Fluent. But how do these codes deal with the problem of defining the cells associated with the "vicinity fluid" that transfer heat?
