Global sensitivity analysis with ANOVA-RSM for heat transfer assessment in thin needle driven flow of bio-convective Sutterby nanofluid

Abstract

The thermal transmission ability of non-Newtonian fluid plays an important role in the emerging sustainable energy and renewable resource applications, and requires careful analysis and enhancement. Therefore, the present work intends to analyze heat transfer characteristics of the Sutterby nanofluid flow over a vertical thin needle using the ANOVA-RSM approach. Also, this study examines the detailed case of Sakiadis and Blasius flow containing gyrotactic microorganisms. Additionally, the impact of Brownian movement and thermophoresis of tiny nanoparticles is cited using the Buongiorno model. The equations governing the Sutterby fluid flow were converted into a dimensionless form and solved with the bvp4c technique. The findings are presented visually, accompanied by relevant physical interpretations. Additionally, sensitivity analysis is applied to quantify the parameters pertinent to this investigation to get the desired results. Quantitative analysis of the CCD results shows that the Nusselt number can increase by approximately 283% for the Blasius flow and about 270% for the Sakiadis flow relative to the baseline case. The sensitivity analysis indicates that the Brownian motion parameter ($Nb$) and thermophoresis parameter ($Nt$) are the dominant factors, contributing approximately $45\text{\%–}55\text{\%}$ of the total output variance within the considered parameter ranges for both Blasius and Sakiadis flows. In contrast, the bioconvection parameter ($\lambda$) shows a comparatively small contribution (less than 1%), suggesting a relatively limited influence on the Nusselt number under the present modeling assumptions and parameter bounds.