The efficacy of many biomedical therapies can be improved when the physical processes which underlie the treatment modality are thoroughly understood. Many treatments make use of transport processes that are deeply embedded in mechanical engineering theory and practice. The research documented in this thesis is firmly based on fluid-mechanic, heat-transfer, mass-transfer, and particle transport theory. The thesis encompasses three categories of biomedical applications: drug distribution, thermal-based surgery, and drug delivery by means of particle transport.The first application dealt with a drug-eluting stent and with the distribution of the drug both into the artery wall by diffusion as well as into the blood flowing in the lumen via advection. This conjugate problem was redefined in dimensionless form and solved by numerical simulation to yield universal solutions. The solutions revealed the existence of a mass transfer boundary layer adjacent to the surface of the stent. Upstream diffusion, opposite to the direction of the advection, occurred. The results showed that the mass transfer into the flowing blood was orders of magnitude larger than the diffusive transfer into the artery walls. The focus of the second application was an in-depth, a fundamentals-based investigation of a new, minimally invasive treatment for menorrhagia. The involved physical processes include vapor transport into the uterine cavity, heat liberated by phase-change, and heat penetration into human tissue by means of conduction and blood perfusion. Cell necrosis was achieved by elevated temperatures sustained for a sufficient period of time. The outcome of this work was the depth of tissue necrosis corresponding to a given duration of the treatment. The predicted depths of necrosis compared favorably with clinical results. The final focus was the creation of a new methodology for the accurate delivery to targeted sites of drug particulates administered either through the mouth or the nose. The drug particles are carried through the respiratory system by an air stream. A numerical-based solution process was developed utilizing the laws of fluid mechanics, the physics of particle transport, and impaction theory. The final solution proved capable of predicting the landing locations of particles based on their respective sizes.