A numerical integration method is presented for the treatment of transient heat conduction problems. A Cartesian formulation is developed that is suitable for the treatment of irregular domains under general boundary conditions. The qualities of the scheme are demonstrated, in terms of both accuracy and computational efficiency, by comparison with analytical and numerical solutions. Results for the basic two-dimensional annular geometry show that the method has nearly second-order accuracy in space and time, at least in simple cases. Finally, a complex multiconnected domain is considered, to test the method performance under more severe conditions, including the presence of multiple length scales. The numerical experiment demonstrates that the numerical scheme is efficient, stable, and convergent.

Heat transfer enhancing surfaces are of interest for a wide range of industrial applications. The aim of this article is to provide a robust automated method for the design of two-dimensional enhanced surfaces. Multiobjective optimization algorithms are employed; the competing objectives addressed are the maximization of the heat transfer and the minimization of the pressure drop for Re = 1,000 and Pr = 0.74. The surfaces are parameterized with Bézier curves, and a finite-volume solver is used for the computational fluid dynamics analysis. The optimization is based on different algorithms used sequentially. Finally, a robust design assessment analysis is carried out on two configurations.