The discontinuous finite element method (also known as the discontinuous Galerkin method) embodies the advantages of both finite element and finite difference methods. It can be used in convection-dominant applications while maintaining geometric flexibility and higher local approximations throught the use of higher-order elements. Element-by element connection propagates the effect of boundary conditions and the local formulation obviates the need for global matrix assembly. All of this adds up to a method which is not unduly memory-intensive and uniquely useful for working with computational dynamics, heat transfer and fluid flow calculations. Discontinuous Finite Elements in Fluid Dynamics and Heat Transfer offers its readers a systematic and practical introduction to the discontinuous finite element method. It moves from a brief review of the fundamental laws and equations governing thermal and fluid systems, through a discussion of different approaches to the formulation of discontinuous finite element solutions for boundary and initial value problems, to their applicaton in a variety of thermal-system and fluid-related problems, including: heat conduction problems; convection-dominant problems; compressible and incompressible flows; external radiation problems; internal radiation and radiative transfer; free- and moving-boundary problems; micro- and nanoscale heat transfer and fluid flow; thermal fluid flow under the influence of applied magnetic fields. Mesh generation and adaptivity, parellelization algorithms and a priori and a posteriori error analysis are also introduced and explained, rounding out a comprehensive review of the subject. Each chapter features worked examples and exercises illustrating situations ranging from simple benchmarks to practical engineering questions. This textbook is written to form the foundations of senior undergraduate and graduate learning and also provides scientists, applied mathematicians and research engineers with a thorough treatment of basic concepts, specific techniques and methods for the use of discontinuous Galerkin methods in computational fluid dynamics and heat transfer applications.