Integrated Taguchi-GRA-PCA for optimizing the heat transfer performance of trihybrid Casson nanofluid flow over stretching sheet with quadratic velocity

The necessity for effective heat transfer fluids in various technical and business applications has resulted in extensive study into nanofluids. Nanofluids' unique attribute is significantly better thermal conductivity than other conventional fluids, making them an appealing option for improving thermal system functionality. This study uses computational methods to investigate a two-dimensional steady magneto-hydrodynamics (MHD) flow using an incompressible, electrically conducting trihybrid nanofluid (THNF) across a stretching/shrinking surface. The fluid flows along a flat surface that can either expand or contract and can modify its speed in a curved way. We considered surface velocity to be in quadratic form $u_w\left(x\right)=ax+b{x}^2$. The work aims to analyze the heat transfer in the THNF flow subjected to the magnetic field. The study examined the effects on the flow and thermal fields of the governing factors, which include the shrinking/stretching parameter $\lambda$, suction/injection parameter $S$, Casson fluid parameter $\beta \text{,}$ and magnetic parameter $M$. The governing partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) and then solved numerically. We have also utilized Grey Relational Analysis (GRA) and Principal Component Analysis (PCA) to optimize the response function by utilizing the best combination of the values of physical parameters $\left\{\lambda ,\beta ,M,Rd\right\}$. The results show that with the increase in the stretching parameter $\lambda \in \left\{0.1,0.4,0.7,1\right\}$, the velocity profile $\left(f^{\prime }\left(\eta \right)\right)$ got improved. The study also revealed that both the Taguchi-GRA and Taguchi-GRA-PCA methods identified the same ideal parameter set. The best parameters combination identified is $\left\{\lambda 4,\beta 1,M4,Rd2\right\}$.