**5. Conclusion**

the time-dependent finite element problem. In addition, they have utilized three materials in some of their examples using SIMP method. Jing et al. [105] utilized the BEM for the implementation of level-set method and considers design-dependent boundary conditions. The level-set method is used to represent the structural boundary and the boundary mesh for the BEM analysis is constructed on the iso-surface of the level-set function. Topological derivative is also utilized to make new holes. Cheng and Chen [106] utilized their volume-of-solid method for the topological design of the laminated metallic composite materials arranged in two predefined configurations. Similar to the previous paper, they have presented two new very interesting objective functions (*Q*˙/*V* and *Q*˙/*USD*). Dede et al. [107] recently demonstrated a complete product cycle development for developing a forced air-cooled heat-sink-made additive manufacturing (AM). They have applied SIMP-based topology optimization and had utilized a modified hat function to define the heat convection loading surface for their problem. A parabolic distribution of the heat-transfer coefficient was assumed in relation to the forced air cooling. Two-dimensional models are first tested and compared to some common heatsink geometries found in the market. A quarter of a 3D model was then implemented and volume reconstruction was also mentioned to obtain a water-tight design suitable for additive manufacturing. Experiments were then conducted and the topology-optimized structures are compared with the commercially available design. Results showed that the designed heat sink performed better compared to other heat sinks but due to the inferior material properties and porous structure of the AM-produced design, it was not performing as to its numerical design specifications. Alexandersen et al. [108] recently published the culmination of their buoyancy flow works by implementing a large-scale three-dimensional model of designed heat sinks. A total of 16.38 million design elements with 83.08 million degrees of freedom were solved in one of their examples for a passive heat-sink cooler for light-emitting diodes (LEDs). Lohan et al. [109] presented generative design algorithms for heat conduction. A dissertation study utilizing boundary element method was recently finished by Jing [109]. Dede [110] designed and fabricated a multi-device single-phase-branching microchannel cold plate. In this time period, highlight is given to product design cycles and actual realization of topology-optimized designs. It is also evident that trends are going for incorporation of fluid flow either directly (through coupled analysis of both the fluid and heat-transfer domains) or indirectly (through convection boundary conditions). Interests for transient problems have also re-emerged with techniques such as the equivalent temperature field being utilized to reduce the burden of the finite analysis for the governing equations of the system. Level-set method is also evolving rapidly by utilizing other techniques such as topological derivative and BEM to make up for their weak points. Density-based methods, especially SIMP, are still staple with most of the works for 3D modelling and thermo-fluidic systems. Massive implementations with millions of DOFs are also slowly being realized, mostly utilizing density-based methods. As an additional foresight, it can be mentioned that none of the above works have considered radiation effects, though some problem formulations can accommodate radiation by utilizing the convection form of radiation. In the future, this work could be sought but would pose the problem for the discretized method of properly identifying cavities and formations inside the evolving domain. View factor computation is also one complication which would be very

80 Heat Exchangers– Design, Experiment and Simulation

expensive to perform since radiating boundaries would change in each iteration.

In this chapter, we have re-introduced topology optimization with special focus on the progress of heat exchanger design over the past two decades. We have first given an overview of its historical background in terms of structural topology optimization. We have then conceptually introduced the different methods developed over the years in topology optimization. Learning references for each of the methods mentioned, together with MATLAB codes, were cited and is expected to help those who are interested in further learning and investigating topology optimization. A chronological review highlighting the different progress over the years related to heat exchanger design was also given.

Novel heat-transfer structures are still being realized to further drive design performance to its limits. Topology optimization, as a physics-based and automated layout optimization method, will indeed serve as a valuable design tool for heat-transfer systems. Heat exchanger designs arising from topology optimization has now been realized and continuous efforts are still being made to further improve both methods and implementation. Topology optimization is expected to play a bigger role in the coming years for heat exchanger design.
