This textbook for advanced graduate and post-graduate courses presents the applications of the modern heat transfer and fluid flow mathematical models in engineering, biology, and medicine. By writing this work, the author continues the introduction of brand-new efficient methods in fluid flow and heat transfer that have been developed and widely used during the last 50 years after computers became common. While his previous two monographs presented these contemporary methods on an academic level in heat transfer only or in both areas heat transfer and fluid flow on the preliminary level, this manual introduces the modern approaches in studying corresponding mathematical models—a core of each research means determining its efficiency and applicability. Two types of new mathematical models are considered: the conjugate models in heat transfer and in fluid flow and models of direct numerical simulation of turbulence. The current situation of applications of these models is presented in two parts: applications of conjugate heat transfer in engineering (Part I) and applications of conjugate fluid flow (peristaltic flow) in medicine and biology and applications in engineering of direct numerical simulation (Part II). These parts contain theory, analysis of mathematical models, and methods of problem solution introduced via 134 detailed and 231 shortly reviewed examples selected from a list of 448 cited original papers adopted from 152 scientific general mathematic, computing, and different specific oriented journals, 42 proceedings, reports, theses, and 37 books. This list of 448 references comprehends the whole period of the new methods existing from the 1950s to present time, including more than 100 results published during the last 5 years among which more than half of the studies were issued in 2014 to 2016.