## 2 Materials and Methods
### Microchannels Geometry  
In this work, four types of microchannels were used: a straight channel and three with the angles between each section modified separately. The straight channel was introduced as the element by which the appropriate ranges of flows analyzed in zigzag channels were selected. We established the flow rate for the straight microchannel with a specific objective: to illustrate a scenario where heat removal from the solid surface is not optimized. This baseline scenario was intentionally chosen to highlight a condition that is less than ideal, with discernible room for improvement in heat transfer performance. By doing so, we created a reference point against which the enhancements in heat transfer efficiency, achieved through the introduction of zigzag modifications to the channel geometry, could be quantitatively assessed. Figure 1 presents a dimeric view of the multi-channel shape. Figure 1 presents the details of the single channel with the corresponding sizes used in formulations. The dimensions used in the calculations are given in Table 1.  
The zigzag profiles were designed using the typical CAD based approach to construct a solid using a leading line. The leading line was formed into a zigzag shape, and the channel solid profile was created by dragging its envelope in a path's preset direction and shape. This ensures that the cross-section always has the specified width.  
Figure 1: (a) Dimetric view of the channels used in simulations. The case presented for zigzag number n = 7. (b) Perspective view of the channel inlet/outlet. Dimensions presented are explained in Table 1.  
The process of creating the mesh for the CFD simulations in Ansys Fluent 2022 R1 was conducted in accordance with standard procedures, without the use of any special optimization techniques. A tetrahedral mesh was employed for both the flow and solid domains, as this is a common choice due to its flexibility in representing complex geometries. The domains were defined in the SpaceClaim 2022 R1 geometry drawing software, and the same global settings were applied to both domains during the meshing step. The grid element size was determined based on a prior convergence analysis using mass balancing, which ensured adequate model accuracy (Figure in Section 2.4). The interface between the domains was left at the default settings, allowing Fluent to manage the heat exchange automatically.  
For all calculated cases, it was assumed that the top and side faces defined symmetry conditions. Inlets to channels were defined by the velocity vector normal to the inlet face, and outlets were defined by a pressure condition specifying the absence of pressure jump at the outlet and, thus, defined free channel discharge. For the sake of graphic clarity, both drawings (Figures 1 and 2) show only the shape of the solid body, while the inner void cavity was also modeled with an appropriately embedded flow space. Interface type conditions were defined between the rigid solid and the body, defining the flow space, which allowed heat transport between the fluid and the solid to be taken into account.  
The bottom face has a temperature boundary condition was defined (see Equation (10)).