Innovative mathematical correlations for estimating mono-nanofluids' density: Insights from white-box machine learning

Abstract

The current research offers credible mathematical models solely for estimating mono-nanofluids' density (ρ_nf), which can be useful for thermal engineering calculations required by various industries and applications. Accordingly, a comprehensive data bank encompassing 4004 experimental data-points was utilized to execute two rigorous machine-learning techniques: Group Method of Data Handling (GMDH) and Gene Expression Programming (GEP). Subsequently, two high-accuracy correlations were fine-tuned based on the four independent variables: average nanoparticle diameter (d_np), nanoparticle mass concentration (ϕ_m), nanoparticle density (ρ_np), and base-fluid density (ρ_bf). Two variables pressure (P) and temperature (T), with rather minor impacts on the density of the mono-nanofluids under investigation, were excluded in the final correlations as a result of the modeling process and the intelligent operation of the machine-learning techniques. By performing multiple statistical and graphical analyses, comparative evaluations highlighted the superior performance and outstanding accuracy of the GEP-based correlation (with AAPRE=0.6614% and R²=0.9671). Moreover, sensitivity analysis and parametric trend assessments revealed that ϕ_m and ρ_bf were the most crucial variables affecting ρ_nf values, with relevancy factors of approximately 0.72 and 0.71, respectively. By considering the GEP-based correlation's outputs and applying the leverage statistical approach, a considerable portion (96.33%) of the total data-points was identified as valid data.