AbstractThe present work performs a numerical analysis of the geometrical investigation of a two-dimensional channel with two alternated isothermal rectangular blocks subjected to turbulent forced convective flows. Constructal Design associated with Exhaustive Search is used to investigate the influence of the geometry of the isothermal blocks over the performance of the cooling convective flows in a multi-objective viewpoint, i.e., considering the pressure drop and heat transfer rate. The time-averaged equations of continuity, momentum, and energy conservation are solved with the finite volume method. The k–$$\omega $$ ω shear stress transport model is used for the closure of turbulence. The effect of the two proposed degrees of freedom, the height/length ratio of the two blocks ($$H_{1}/L_{1}$$ H 1 / L 1 and $$H_{2}/L_{2})$$ H 2 / L 2 ) , is analyzed in relation to the proposed objectives. Regarding the thermal purpose, the geometry with the highest insertion into the channel led to the best performance, while the opposite configuration led to the best fluid dynamic performance. This behavior was similar to that previously found in the literature for forced convective laminar flows. For a multi-objective perspective, the use of technique for order preference by similarity to ideal solution indicated that asymmetric blocks led to the best multi-objective performance when both performance indicators had the same weight.