Open Access

ARTICLE

Spectral Quasi-Linearization Study of Variable Viscosity Casson Nanofluid Flow under Buoyancy and Magnetic Fields

B. Rajesh¹, Fateh Mebarek-Oudina^2,3,4,*, N. Vishnu Ganesh¹, Qasem M. Al-Mdallal⁵, Sami Ullah Khan⁶, Murali Gundagnai⁷, Hillary Muzara⁸

1 PG and Research Department of Mathematics, Ramakrishna Mission Vivekananda College, Mylapore, Chennai, 600004, India
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 Mathematical Sciences, United Arab Emirates University, Al Ain, Abu Dhabi, P.O. Box 15551, United Arab Emirates
6 Department of Mathematics, Namal University, Mianwali, 42250, Pakistan
7 Department of Mathematics, Geethanjali College of Engineering and Technology, Cheeryal, 501301, India
8 Department of Mathematics and Computational Sciences, University of Zimbabwe, Mount Pleasant, Harare, P.O. Box MP167, Zimbabwe

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

Frontiers in Heat and Mass Transfer 2025, 23(4), 1243-1260. https://doi.org/10.32604/fhmt.2025.066782

Received 17 April 2025; Accepted 14 July 2025; Issue published 29 August 2025

Abstract

The behavior of buoyancy-driven magnetohydrodynamic (MHD) nanofluid flows with temperature-sensitive viscosity plays a pivotal role in high-performance thermal systems such as electronics cooling, nuclear reactors, and metallurgical processes. This study focuses on the boundary layer flow of a Casson-based sodium alginate Fe₃O₄ nanofluid influenced by magnetic field-dependent viscosity and thermal radiation, as it interacts with a vertically stretching sheet under dissipative conditions. To manage the inherent nonlinearities, Lie group transformations are applied to reformulate the governing boundary layer equations into similarity forms. These reduced equations are then solved via the Spectral Quasi-Linearization Method (SQLM), ensuring high accuracy and computational efficiency. The analysis comprehensively explores the impact of key parameters—including mixed convection intensity, magnetic field strength, Casson fluid properties, temperature-dependent viscosity, thermal radiation, and viscous dissipation (Eckert number)—on flow characteristics and heat transfer rates. Findings reveal that increasing magnetic field-dependent viscosity diminishes both skin friction and thermal transport, while buoyancy effects enhance heat transfer but lower shear stress on the surface. This work provides critical insights into controlling heat and momentum transfer in Casson nanofluids, advancing the design of thermal management systems involving complex fluids under magnetic and buoyant forces.

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