Continuity Between Statistical Mechanics and Fluid Dynamics

Indeed, you can and I remember reading such books many years ago, while studying math. I really do not remember the name of the book as I read it out of the similar curiosity such as you are raising.

You may search through books on Statistical Physics on amazon.com.

I remember studying a similar case at the university (many years ago...) solving such a problem by defining a control volume over the fluid jet normal to the jet velocity vectors. It's a classical case of defining control volume and calculate energy loss by the energy balance between the jet nozzle and the outgoing fluid.

I agree that the fluid should heat the plate, by frictional effects. Don't remember of seeing a case calculating heat transfer itself inside the fluid and from the fluid to the plate. I think, for a really precise point of view, these two effects should be considered, along with pressure and speed loss in the fluid. Air? So, depending on the velocity, include also compressible effects. A good application of Navier-Stokes (including all terms...).

After all, you'll need a good experimental procedure to check your theory... fluids are hard to mate; it's very easy to see big differences between predicted and measured values.

You're right, the fluid should heat the plate through frictional effects (shear between the fluid and plate), but what I'm getting at is; (I think) the heating calculated through frictionion shearing should be equal to the heat transferred to the plate if analysed using statistical mechanics methods.

Fundamentally both are the same process. The shear forces on a plate incurred by a jet impinging on it are derived from macrostate descriptions of the fluid molecules interacting with the plate, whereas a statistical mechanics analysis is derived from a microstate description of the molecules interacting with the plate (this analysis looks more like classical heat transfer than some hydrodynamic phenomenon like drag)

Fundamentally, the molecular processes are the same (they have to be right!). I'm hypothesising whether by approaching the analysis of the frictional effects by considering them to be a molecular process, can the drag coefficient of a body be analytically derived?

The shearing frictional process between a fluid and immovable body is afterall very similar (on a molecular level) to a conventional heat transfer process. Friction occurs through the collision of molecules in the fluid with molecules in the plate.

The only difference I can see here is that the molecules have some aggregate velocity rather than an isotropic velocity distribution (which would be the case if a static fluid at a higher temperature were transferring heat conventionally to the plate).

It may be that the modelling of these statistical parameters is incredibly difficult (moreso than conventional macrostate fluid modelling techniques, e.g. CFD).