On optimization of natural convection flows

Sammanfattning: Two different techniques are presented for enhancing the thermal  performance of natural convection cooled heat sinks. The physics is  described by solving the conjugate heat transfer problem with a  spectral element method. The temperature distribution is computed in  two sub-domains, whose solution is then conjugated. Additionally, the  contribution of the natural convection to the heat transfer is  evaluated by solving the complete incompressible Navier–Stokes  equations in the fluid domain. One method focuses on the natural convection driven flow. The  disturbances about a base flow are sought, which yield the maximal  transient growth of a quadratic functional measuring the thermal  performance. The “optimal initial condition” method is used for  identifying the above mentioned perturbations. The control variable is  the initial state of the perturbation and the problem is subject to  the constraints enforced by the linearized governing equations. This  method is validated in a simple two--dimensional setup and then  applied to a periodic heat sink. The second approach is a topology optimization of the heat sink  itself. The design of the solid is optimized for maximizing the heat  flux. The control variable is a so-called material distribution  function that describes the presence of solid and fluid in the domain.  By modifying the design of the heat sink, the flow is optimally  conveyed and, by convection, it  extracts the maximal possible amount  of heat from the solid. The constraints are given by the governing  equations, the position of the heat sink, and some manufacturing  constraints (\textit{i.e.}, the maximal volume, or the minimal  thickness). After a validation in a two--dimensional setup, the method  is applied to a three--dimensional case. Complex tree-like shaped heat  sinks induce an increase of the thermal performance by 5 to 16\%,  depending on the conditions considered.