# Topology Optimization of Functionally Graded Structure for Thermal Management of Cooling Plate
## 1 Introduction  
As an energy storage device, batteries have been widely used in fields such as mobile devices, household appliances, and electric vehicles due to the advantages of high energy density, long life cycle, and stable performance [1; 2; 3]. However, heat production problems arise during the charge and discharge of the battery, which may lead to a capacity reduction, inefficiency, and the risk of spontaneous combustion with temperature rise in the battery [4; 5]. Therefore, to further contribute to this research topic, a topology optimization pipeline for the cooling plate is presented to improve the heat dissipation efficiency and ensure the working performance and stability of the battery in this paper. When compared with air and phase change-based cooling systems, the liquid-based cooling system is of good performance regarding the trade-off between cooling efficiency, cost, and reliability, and it has been widely used in battery thermal management [6; 7; 8]. The liquid-based cooling system usually works using a cooling plate, and a coolant takes away the heat through flowing in the internal fluid channels [9; 10]. Current researches projects on cooling plate optimization mainly focus on the size and shape parameters. [PERSON] et al. [11] designed a straight mini-channel cold plate-based battery thermal management system and numerically investigated the effects of the number of channels, flow direction, inlet mass flow rate and ambient temperature on temperature rise and distribution. To further develop the performance of the cooling plate, snake, U-shape, and bionic wave-based runners have been investigated. [PERSON] et al. [12] presented a serpentine shape-based cooling plate to account for the average temperature, temperature uniformity, and pressure drop of the cooling plate and investigated the relationship between the objectives, distribution of the input heat flux, and the coolant flow rate. [PERSON] et al. [13] presentedan optimization pipeline that included the Gaussian process and NSGA-II methods for U-shaped cooling plate design and claimed that the U-shape channel can significantly decrease the pressure drop loss when compared with a serpentine channel cooling plate. [PERSON] et al. [14] proposed a novel and efficient liquid cooling scheme for battery thermal management by using a bionic wave-based channel, and they thoroughly investigated the effects of the discharge rate, channel shape, coolant mass flow rate, coolant inlet direction, and dynamic operation strategy on the battery maximum temperature and temperature variation. Even the size and shape optimization of the cooling plate can develop the performance regarding heat dissipation, while the prior knowledge-based method is troublesome in the process of the structure design of the cooling channel. Topology optimization [15; 16], a structure design method, offers an effective approach for structure design that satisfies prescribed constraints and boundary conditions, which makes it suitable for the optimal design of the cooling plate [17; 18]. [PERSON] et al. [19] proposed a density-based topology optimization framework for thermal cooling device optimization considering the performance of heat resistance, energy dissipation, and pressure drop. [PERSON] et al. [20] presented a novel cooling plate design for battery thermal management, which was of good performance regarding the trade-off between heat exchange efficiency and pressure drop. Numerical experiments demonstrated that the new design significantly developed the pressure drop and maximum temperature when compared against a traditional cooling plate. [PERSON] et al. [21] comprehensively studied the effect of different optimization objectives, including heat transfer terms such as heat transfer, outlet fluid enthalpy, and a solid domain temperature multi-objective function consisting of the kinetic energy difference and the heat transfer and their effects on the topology optimization flow channel shape and cooling performance. [PERSON] et al.