Numerical heat transfer

The application of numerical methods to the analysis of heat-transfer problems is examined and illustrated in a textbook for advanced students of engineering and applied mathematics. The basic methods are introduced, including finite-difference, finite-element, variational, global-function, central-integration, least-squares, collocation, higher-order-element, method-of-moments, perturbation, and nonlinear two-point boundary-value techniques, and their numerical stability, consistency, convergence, accuracy, and efficiency are evaluated. The fundamental modes of heat transfer (conduction, convection, and radiation) are then analyzed, with an emphasis on laminar forced convection, and the treatment of additional phenomena such as free and mixed convection, turbulence, and combustion is explained. An analysis of the error bounds of the various methods and a detailed comparison of the finite-difference and finite-element methods are included.