## 1 Introduction
[PERSON] and [PERSON] [14] proposed an analytical/numerical methodology to consider the effects of preform compaction on resin flow for a deformable porous media, which is important for processes such as vacuum assisted resin transfer molding (VARTM) and Seeman composites resin infusion molding process (SCRIMP), where a flexible bag is generally used as part of the mold. The results showed that preform compaction affected resin flow and filling time. The numerical approach has also been used to define strategies for several LCM processes. Examples of the evaluation of gate placements in RTM processes seeking to prevent void content and minimize filling time had been widely reported in different works [15; 16; 17; 18; 19; 20]. The work of [PERSON] et al. [3] proposed strategies to improve the positioning of injection channels in one LRI process usingcomputational modeling. More precisely, the authors presented developments in two large structures to be filled with resin, a rotor blade, and a boat hull 20 m and 16 m long, respectively. The strategy adopted by the authors consisted of a main injection channel in the central region of the domain (the keel for the case of injection in the hull domain) with several bifurcated channels spread along the area of the domain (from the center to the periphery). Afterward, [PERSON] et al. [21] performed a numerical and experimental study for better characterization of a VARTM (vacuum assisted resin transfer molding) process, indicating the best strategies for the filling of a C-shaped stringer. The results indicated that the consideration of two exit regions (with vacuum) and one entering region of resin placed in the extremes of domain length was the best strategy to minimize filling time and prevent void formation. [PERSON] et al. [1] developed an iterative method based on a centroidal Voronoi diagram for optimization of the distribution of several channels to reduce the number of required tests. Recently, [PERSON] and [PERSON] [22] performed a numerical multi-objective optimization focusing on the choice of an optimal temperature profile, which minimizes the filling time and the risk of hindering resin flow due to excessive curing. For the optimization, the authors employed the genetic algorithm (GA) method. It achieved reductions of nearly 66% and 15% in filling time and final degree of cure, respectively, in comparison with standard solutions. [PERSON] et al. [23] investigated the behavior of resin impregnation in curved porous plates mimicking a VARTM process. They performed an experimental study investigating the influence of curvature angles and preform layers on the advancement of the resin front line. The results indicated that due to interaction between the preforms and void formation, the curved regions led to an augmentation of 15% to 30% of filling time in comparison with a linear region. [PERSON] et al. [24] performed an experimental and numerical study for the manufacturing of three-dimensional composite parts of complex shape. For the computational model, a numerical technique based on liquid resin flow into porous preform is coupled with a model that describes the fluid motion in unsaturated soils. The developed method allowed the prediction of inner and outer dry spots depending on the resin flow movement. Despite several important works reported, few studies can be found on the evaluation of the influence of the geometry of empty channels in the behavior of resin/air fluid flow into the porous domain. In the present study, a geometrical optimization of I and T-shaped empty channels over the required time to fill a porous rectangular plate is performed with the constructal design (CD) and exhaustive search (ES) methods. Constructal design is a method for assessment of design in any finite flow system based on the objectives and constraints principle.