Open Access

ARTICLE

MHD Thermosolutal Flow in Casson-Fluid Microchannels: Taguchi–GRA–PCA Optimization

Amina Mahreen¹, Fateh Mebarek-Oudina^2,3,4,*, Amna Ashfaq¹, Jawad Raza¹, Sami Ullah Khan⁵, Hanumesh Vaidya⁶

1 Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari, 61100, Pakistan
2 Department of Mathematical Sciences, Saveetha School of Engineering, SIMATS, Chennai, 602105, Tamilnadu, India
3 Department of Pure and Applied Mathematics, School of Mathematical Sciences, Sunway University, Bandar Sunway, Petaling Jaya, 47500, Selangor Darul Ehsan, Malaysia
4 Department of Physics, Faculty of Sciences, University of 20 Août 1955-Skikda, Skikda, 21000, Algeria
5 Department of Mathematics, Namal University, Mianwali, 42250, Pakistan
6 Department of Mathematics, Vijayanagara Sri Krishnadevaraya University, Ballari, 583105, Karnataka, India

* Corresponding Authors: Fateh Mebarek-Oudina. Email: ,

(This article belongs to the Special Issue: Advances in Computational Nano-Fluids)

Fluid Dynamics & Materials Processing 2025, 21(11), 2829-2853. https://doi.org/10.32604/fdmp.2025.072492

Received 28 August 2025; Accepted 17 November 2025; Issue published 01 December 2025

Abstract

Understanding the complex interaction between heat and mass transfer in non-Newtonian microflows is essential for the development and optimization of efficient microfluidic and thermal management systems. This study investigates the magnetohydrodynamic (MHD) thermosolutal convection of a Casson fluid within an inclined, porous microchannel subjected to convective boundary conditions. The nonlinear, coupled equations governing momentum, energy, and species transport are solved numerically using the MATLAB bvp4c solver, ensuring high numerical accuracy and stability. To identify the dominant parameters influencing flow behavior and to optimize transport performance, a comprehensive hybrid optimization framework—combining a modified Taguchi design, Grey Relational Analysis (GRA), and Principal Component Analysis (PCA)—is proposed. This integrated strategy enables the simultaneous assessment of skin friction, Nusselt number, and Sherwood number, providing a rigorous multi-objective evaluation of system performance. Comparative validation with benchmark results from the literature confirms the accuracy and reliability of the present formulation and its numerical implementation. The results highlight the intricate coupling among flow slip, buoyancy effects, and convective transport mechanisms. Increased slip flow enhances axial velocity, while a higher solutal Biot number intensifies concentration gradients near the channel walls. Conversely, a lower thermal Biot number diminishes the temperature field, indicating weaker heat transfer across the boundaries. PCA results reveal that the first principal component (PC1) accounts for most of the system variance, demonstrating the dominant influence of coupled flow and transport parameters on overall system performance.

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