This investigation includes a geometric optimization for a compact heat exchanger built from hexagonal channels based on constructal design. A three-dimensional numerical analysis based on the finite volume method was conducted to identify hydrodynamic and thermal behaviors of the counterflow arrays. We considered several configurations for the inactive channel that emerged from packing the hexagonal channels within the compact heat exchanger in such a way that the heat transfers with lower thermal resistance from the hot to the cold streams. The hexagonal arrays considered for the computational fluid dynamics (CFD) study is first assumed to be well insulated. The hot and cold fluids (water) flow with variable Reynolds numbers: 10, 100, 200, and 300. The inactive hexagonal channel is filled with various size trapezoids and triangles to find the best configuration attains lower thermal and flow resistances. The results are presented in terms of heat transfer effectiveness, thermal conductance, and the thermal-to-flow performances ratio. The CFD code was verified with an experimental work to assess the accuracy of the current numerical analysis. Triangular channels (ß = 1) employed in the inactive region showed better performance for the counterflow hexagonal bundle. High-pressure drop is associated with the trapezoidal shape especially with smaller hydraulic diameter (small cross-sectional area).