The numerical modeling of the heat and mass transfer and of the fluid flow processes in manufacturing, particularly in the thermal processing of materials, is discussed in this paper. Several important processes such as polymer extrusion, glass fiber drawing, chemical vapor deposition, and casting are considered in detail. The governing equations, the relevant boundary conditions and the basic approach to numerically model many of these processes are presented. The importance of material properties in an accurate mathematical and numerical modeling is brought out, along with the coupling between the process and the resulting characteristics. The concerns and computational difficulties that arise due to various aspects such as the non-Newtonian behavior of plastics, exponential temperature dependence of glass viscosity, complex geometry, free surface flow, conjugate transport, material movement, chemical reactions, and phase change are considered. Some of the important methods to treat these complexities are presented. A few typical numerical results are presented on some important materials processing systems.

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