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We consider a model for density-based topology optimization (TO) of stationary heat transfer problems with designdependent internal convection in 3D structures with periodic design obtained by extruding a 2D design in 3D. The internal convection takes place at the interface between a solid material and a cooling fluid in internal channels through the design domain. The objective of the TO is to minimize the maximum temperature, which is approximated by means of an L p norm. The finite element method is used to discretize the state problem and the resulting optimization problem is solved using gradient-based methods. The internal convection is modeled to be dependent on the design density gradient in the continuous problem. In discrete form, it is approximated as proportional to the difference in design densities of adjacent elements in the finite element mesh. The theory is illustrated by numerical examples based on a simplified guide vane geometry.

We propose a topology optimization‐based method for optimal design of cooling systems in the form of a mathematical game between two players trying to reach a compromise between limiting the amount of a cooling medium used and obtaining low temperatures in the design domain. The flow of the cooling medium is governed by a Stokes–Brinkman flow model with penalty, while the temperature is governed by a stationary convection–diffusion problem whose solution is approximated using a finite element method with consistent stabilization. Existence of solution for the continuum problems and finite element convergence are shown. The idea and performance of the proposed design method are illustrated by numerical examples based on a problem‐setting inspired by an industrial design problem for a gas turbine part. The method exhibits good convergence and is able to generate meaningful design concepts representing various levels of compromise between limited use of cooling medium and low temperatures.

Funding Acknowledgements Type of funding sources: Public hospital(s). Main funding source(s): The Swedish Research Council and the Medical Research of Southeast Sweden Introduction Cost-effectiveness evaluations of psychological interventions, such as Internet-delivered cognitive behavioural therapy (iCBT) programs, in patients with cardiovascular disease (CVD) are rare. In a recent study we reported that a 9-week iCBT program (n=72) compared to an online discussion forum (ODF) (n=72) had moderate to large effect on depression in CVD outpatients. Purpose To evaluate the cost-effectiveness of this intervention. Methods Cost-effectiveness analysis of a RCT, using an incremental cost-effectiveness ratio (ICER). The costs and effects included in the ICER are from baseline to one year post intervention, but also costs for guidance and support to patients in iCBT and ODF groups. Data on healthcare costs were retrieved from healthcare registries, and the EQ-5D-3L was used to calculate the quality-adjusted life years (QALYs). The ICER can be seen as the additional costs needed to gain an additional QALY by the iCBT compared to ODF. Results At 12-month follow-up, the QALY was significantly higher in iCBT compared to the ODF group (0.713 vs.0.598, p=.007). The mean difference of 0.115 corresponds with 42 extra days in best imaginable health status in favour of the iCBT group over the course of one year. The ICER for iCBT versus ODF was €18,865 per QALY saved. The cost-effectiveness plane indicated that iCBT is a cheaper and more effective intervention in 24.5% of the cases, and in 75% a costlier and more effective intervention than ODF. Only in about 0.5% of the cases, there was an indication of a costlier, but less effective intervention compared to ODF. Conclusions The ICER of €18,865 was lower than the cost-effectiveness threshold range of €23,400-€35,100 as proposed by the NICE guidelines, suggesting that the iCBT treatment of depressive symptoms in patients with CVD is cost-effective.