Direct Design of Shape in Internal Convection Heat Transfer Problems

One of the interesting and practical problems in thermo-fluid sciences is referred to finding the shape of a boundary on which a specific distribution of pressure, temperature or heat flux is known. Because solving such problems using experimental, semi-experimental and analytical methods is time-consuming or even impossible in some practical situations, myriad numerical methods have been introduced to solve surface shape design (SSD) problems. In all the numerical algorithms, an initial guess is modified through a numerical process until the desirable distribution of the target variable is achieved. All the numerical algorithms use three computational tools, i.e. grid generator, flow solver and shape updater to solve an SSD problem. In most of numerical algorithms, not only the three mentioned tools work separately but the shape updater is also not derived from the governing equations. In this article, to solve SSD problems containing convection heat transfer, a new shape design algorithm called direct design method is presented in which grid generator, flow solver and shape updater work simultaneously and also the shape updater is directly derived from the governing equations. Some SSD problems containing convection heat transfer in which instead of the boundary shape the distribution of the heat flux is known are solved using the proposed algorithm. The obtained results show the capability of the method in solving SSD problems containing internal convection heat transfer.