Artificial neural network model and multi-objective optimization of microchannel heat sinks with diamond-shaped pin fins

In this study, laminar, steady-state, incompressible flow with conjugate heat transfer was investigated for one flow passage of a microchannel with staggered diamond-shaped pin fin array. CFD analyzes were performed with OpenFOAM for various configurations and in all cases, the rhomboidal area of each pin fin was kept constant at 0.16 mm², and the bottom surface of the substrate was subjected to a uniform heat flux of 69.3 kW/m². Water with temperature-sensitive viscosity was taken as the cooling fluid, and copper with constant thermophysical properties was used for the solid domain. Parametric analyzes have been conducted for various combinations of geometric design variables such as pin fin angle (α), longitudinal pitch-to-diameter ratio (S_L/D) and transverse pitch-to-diameter ratio (S_T/D) with the flow attribute represented by pin fin Reynolds number (Re_D). In the parametric investigations, α ranged from 30^∘ to 90^∘; Re_D ranged from 20 to 100, and S_L/D and S_T/D were between 2.5 and 4.5. A multi-layer artificial neural network model (ANN), which was coded in Python and trained with parametric CFD results, was utilized to estimate off-design pin fin Nusselt numbers (Nu_D) and pin fin Poiseuille numbers (Po_D), two objective functions representing thermal and hydrodynamic character, respectively. Non-dominated Sorting Genetic Algorithm (NSGA-II) was used to optimize the microchannel configuration, in which the individuals have been evaluated based on the multi-layer neural network prediction model. The constructed multi-layer neural network model predicted Nu_D and Po_D with average errors of 1.39% and 1.02%, respectively. Among all design variables considered, α was found to be the most dominant one on Nu_D and Po_D. Following the genetic algorithm, the majority of the optimal solutions appeared at S_T/D around 2.5 and at Re_D equal to 20 or 100. Over the entire range of Re_D, NSGA-II suggested combinations of optimal α and S_L/D yielding 4<Nu_D<11 and 6<Po_D<32 appropriate for thermal or hydrodynamic demands.