Multi-objective optimization of spherically dimpled tubes for enhanced thermal-hydraulic performance

In this paper, the thermo-hydraulic performance of spherical dimpled tubes is numerically investigated, and their geometric parameters are optimized using a statistical design approach. A validated three-dimensional numerical model is developed for (i) smooth and (ii) dimpled tubes to accurately predict turbulent flow and heat transfer characteristics. The heat transfer enhancement mechanisms are first examined through detailed flow and thermal field analyses using the one-factor-at-a-time (OFAT) method over a Reynolds number ( Re ) range of 5000–15,000. The investigated geometric parameters include dimple diameter, dimple pitch, and number of dimple stars. Subsequently, Response Surface Methodology (RSM) combined with the Box-Behnken Design (BBD) is employed at Re = 5000 to evaluate the effects of these parameters on the Nusselt number ( Nu ), friction factor ( f ), and performance evaluation criterion ( PEC ). Quadratic and modified quadratic regression models are developed and evaluated using analysis of variance (ANOVA). The ANOVA results reveal that dimple diameter has a significant positive effect on Nu but also increases f . Increasing the dimple pitch reduces Nu , while the interaction between dimple diameter and number of dimple stars significantly affects f and PEC . Multi-objective optimization based on the desirability function identifies the optimal geometric configuration, with prediction errors of less than 3% for all response variables. A comparison with the OFAT approach demonstrates that the BBD-based optimization provides a more efficient and systematic framework for identifying the optimal dimple geometry while substantially reducing the computational effort required for design optimization.