This study aims to develop a reliable computational–statistical framework to predict and minimize hydrodynamic drag in unsteady magnetohydrodynamic (MHD) Carreau fluid flow over a rotating cone with Joule heating, supporting the design of energy-efficient heat-transfer equipment. The governing PDEs are reduced via similarity transformations and solved numerically using a shooting method to quantify how key parameters (Weissenberg, magnetic, unsteady, Prandtl and Eckert numbers) influence tangential and azimuthal skin-friction. Response surface methodology with ANOVA and sensitivity analysis is then used to identify dominant effects and parameter interactions for optimization.
The governing boundary-layer PDEs for MHD Carreau flow over a rotating cone with Joule heating are reduced to a coupled set of nonlinear ODEs using similarity transformations. The resulting boundary-value problem is solved numerically via a shooting scheme by replacing the far-field condition with a finite truncated boundary and iterating on unknown initial slopes to satisfy the boundary conditions. A response surface methodology (RSM) quadratic model is then built for the tangential and azimuthal skin-friction coefficients, with ANOVA and sensitivity analysis used to quantify significant main and interaction effects.
The coupled numerical–statistical framework shows that all considered inputs and their interactions are statistically significant in predicting drag (via ANOVA), and the RSM quadratic models exhibit strong predictive capability for both tangential and azimuthal skin-friction coefficients. The results indicate that increasing fluid elasticity (higher Weissenberg number) slightly reduces skin friction (approximately 0.35%). Sensitivity analysis identifies the Weissenberg number and unsteadiness as the most influential factors for tangential drag.
This work introduces an integrated computational–statistical framework for drag prediction and minimization in Carreau flow over a rotating cone with Joule heating by coupling similarity-based numerical solutions (shooting) with RSM, ANOVA and sensitivity analysis. Unlike prior studies that mainly report one-factor parametric trends, the proposed approach quantifies both main and interaction effects and delivers accurate quadratic surrogate models for tangential and azimuthal skin-friction. The framework provides a practical optimization tool for energy-efficient thermal/rotating equipment and related biomedical/industrial systems.
