## 1 Introduction  
Traditional printing technology with high-viscosity metal slurry fluids is gradually becoming unable to meet current work production needs due to cost, efficiency, and limitations of the process itself [1, 2]. In order to achieve high-speed and cost-efficient printing, various new production and processing technologies have been explored, such as pattern transfer printing (PTP\({}^{\text{TM}}\)) [3, 4], flex trail-printing [5], laser chemical metal deposition [6], direct printing technology [7], and so on. In recent years, there has been growing interest in direct printing technology utilizing multi-nozzle arrays. The main challenge in this research is ensuring a uniform flow of high-viscosity metal slurry fluid across each channel, so as to ensure consistent flow at each channel or within an acceptable margin of error. The ultimate objective of this paper was to achieve uniform flow distribution in compact parallel channels. Two main approaches exist in the structural study of multi-nozzle array direct printing with high-viscosity metal slurry fluids. The first approach, proposed by [PERSON] [8, 9], involved the use of a single syringe connecting 2 to 3 nozzles and controlling the extrusion of fluids through a valve. By juxtaposing multiple syringes, multi-nozzle array printing was achieved. To meet the need for more nozzles, [PERSON] et al. [10] designed a symmetrical structure to achieve multi-material, multi-nozzle 3D printing. However, due to the structure's design, larger spacing between the nozzles was required that was not conducive to compact parallel printing, which limited its use. To solve the problem, the second approach involves the use of a box structure [11; 12; 13] with an inlet for feeding and pressure provided at the top of the box, while the required nozzle size and number are precision machined at the bottom for extrusion printing. Research indicated that homogeneous pressure and flow distribution within the print head was crucial in achieving homogeneous mass flow at all nozzles. However, the study had two drawbacks: (a) it did not explain how this structure affected the pressure distribution and ensured the smoothness and uniformity of the extrusion effect of each nozzle; (b) the integrated configuration of the structure may not be suitable for high-viscosity slurry fluids that are prone to clogging. Thus, there is a need to design a compact and detachable structure that can achieve uniform and smooth parallel printing, while explaining its flow behavior. In the study of heat exchangers, in order to efficiently carry away the heat from a variety of extremely high temperature and high-pressure applications, researchers have designed U- and Z-type parallel multi-channel structures for uniform heat transfer. The current research contains the analysis of the causes and theory of non-uniform flow distribution in a manifold system [14; 15; 16], the influence of structural parameters on flow distribution [17; 18; 19; 20; 21], and the prediction of flow distribution in the heat exchangers [22; 23]. Additionally, various inlet manifold structures are proposed to achieve uniform flow, including modified airfoil-type channels [24], a plate-fin shunt tube [25], and rectangular, trapezoidal, and triangular header structures [26]. In the study of the uniform flow of heat exchangers, the structure dimension is large and the fluids are mostly low-viscosity Newtonian fluids, such as water. The flow uniformity of non-Newtonian fluids in heat exchangers has rarely been investigated in the available literature. Our study applied a multi-nozzle array of high-viscosity slurry fluids for direct printing technology by designing a compact parallel channel for consistent flow distribution in each channel.