Heat Transfer and Fluid Dynamics

Abstract

Heat transfer and fluid dynamics represent important applications that can be very easily represented and solved as optimization problems using the GAMS technology. These applications are two-dimensional and are described by partial differential equations that, by standard discretizations lead to large and sparse matrices. Hence, the corresponding optimization problems are large-scale. The first application from this chapter is the optimal solution of the heat transfer problem in rectangular domains with heterogeneous conductivity. For this application both the stationary and the time-dependent temperature field in rectangular domains are considered. The second application is the optimal solution of fluid flow problems in a rectangular area. Two problems are considered. The first one is the stationary flow of an incompressible fluid in a rectangular area, and area; the second one is the stationary flow of an incompressible fluid in a rectangular area in the presence of an obstacle. All these applications are taken from McKinney and Savitsky (2003).