<p>The present research focuses on the flow and heat transfer of Newtonian and viscoplastic liquids flowing through a heated tube row. It investigates the evolution of the system configurations to improve its performance based on the constructal design method (CDM). The method's implementation is associated with the design of experiments and computational fluid dynamics (CFD). Viscoplastic fluids with rheology predicted by a biviscosity equation based on the Bingham model were considered. The Plastic number gave the fluids' viscoplasticity degree, which varied between 0 and 0.75. The Bejan number gave the flow intensity, which ranged between 10⁴ and 10⁵. Three levels of evolution of the system were treated with one, two, and four degrees of freedom. A central composite design of simulations was performed. The results were fitted into polynomial curves for the one degree of freedom system and response surfaces with quadratic functions for the two and four degrees of freedom systems as functions of the distances between tubes and the diameter ratios between the main tubes and the additional tubes. As the system’s complexity was increased by adding smaller diameter tubes, increases between 20.82 and 41.16% in heat transfer density could be achieved for Bejan number cases 10⁴ and 32.27–63.67% for Bejan number 10⁵. The viscoplasticity impairs the convective process by forming unyielded and high viscosity zones. Through design evolution, it has been possible to obtain heat transfer densities for high-yield stress fluids comparable to those of Newtonian or low-yield stress fluids.</p>