I'm in an intro to PDE class, and so far we've only covered the Diffusion and wave equations. I'm working on a final project, and I'm very interested in how PDEs are used to model blood flow. I've google searched around a bit, and it looks like the navier-stokes equation is at the base of all these models. However, I cannot find which was the first introduced mathematical blood flow model (with PDEs). I was also wondering if blood flow modeling is part of PDEs or is it part of fluid dynamics?
Anyone has a favorite book/resource to study modeling of blood flow using PDEs? I would love to be linked to some initial resources to get started!