Q: Car is grinding after driving a distance but nothing wrong with brakes ?

Hi there. It sounds like it could either axle or wheel bearing related. Low lubricant in either of these can create what your experiencing once heated up during use. A visual inspection of the axle boots may help in identifying a likely cause. If the boots have been leaking or are torn/open, then this may be the cause of your noise and will need to be replaced. Wheel bearings usually require an experienced technician to determine which, if any, are failing. The technician will know the process that needs to be followed safely to located the failed bearing. I suggest having a qualified technician perform an inspection to avoid replacing unnecessary parts. Your Mechanic has several available technicians that can assist you with a grinding noise inspection.