A topology optimization method for a coupled thermal–fluid problem using level set boundary expressions

This paper presents a topology optimization method for a coupled thermal–fluid problem based on the two- and three-dimensional steady-state Navier–Stokes and energy equations. In this research, the optimization problem is formulated as a heat exchange maximization problem to obtain structures that function as high-performance cooling devices. Such devices, for example, liquid-cooled heat sinks, have recently attracted considerable attention as an engineering application for thermal cooling devices. The proposed optimization method employs level set boundary expressions and a Tikhonov-based regularization scheme enables qualitative control of the geometric complexity of the optimal configurations. Using the developed methodology, we provide two- and three-dimensional numerical examples that confirm the applicability, from an engineering standpoint, of the optimization method for the design of cooling devices.