Reddit mentions of Numerical Heat Transfer and Fluid Flow (Computational Methods in Mechanics & Thermal Sciences)

OP, if you're looking for a basic CFD book to start (other than conceptual materials for Fluid Mechanics, Heat Transfer, Thermodynamics) I strongly recommend Numerical Heat Transfer and Fluid Flow by Patankar. It's a bit pricy for such a small book but it's worth every penny, especially if you're looking to write your own basic code.

If you want to learn the math/theory behind it, I suggest this book
It's actually one of the easier technical textbooks I've read in the sense that things are explained clearly and intuitively. But if you're looking to learn how to perform the simulations, then like others mentioned, using the software whether it's through tutorials or projects would be best.

I don't, but I'm in the minority of the field. It definitely required a lot of catch-up in my first couple years. If you want to try and break in I can make some suggestions for self-teaching.

Linear Algebra is the backbone of all numerical modeling. I can make two suggestions to start with:

• I was very impressed with Jim Hefferon's book. It's part of an open courseware project so is available for free here (along with full solutions) but for $13 used I'd rather just have the book.
  
  
• The Gilbert Strang course on MIT Open Courseware is very good as well. I didn't like his book as well, but the video lectures are excellent as supplemental material for when I had questions from Hefferon.
  
  As for the actual FEA/CFD implementations:
  
  
• Numerical Heat Transfer and Fluid Flow ($22, used) seems to the standard reference for fluid flow. I'm relatively new to CFD so can't comment on it, but it seems to pop up constantly in any discussion of models or development.
  
  
• Finite Element Procedures, ($28, used) and the associated Open Courseware site. The solid mechanics (FEA) is very well done, again, haven't looked much at the fluids side.
  
  
• 12 steps to Navier Stokes. If you're interested in Fluids, start here. It's an excellent introduction and you can have a basic 2D Navier Stokes solver implemented in 48 hours.
  
  Note that none of these will actually teach you the the software side, but most commercial packages have very good tutorials available. These all teach the math behind what the solver is doing. You don't need to be an expert in it but should have a basic idea of what is going on.
  
  Also, OpenFoam is a surprisingly good open source CFD package with a strong community. I'd try and use it to supplement your existing work if possible, which will give you experience and make future positions easier. Play with this while you're learning the theory, don't approach it as "read books for two years, then try and run a simulation".