Open Access

ARTICLE

Thermal Transport and Physics-Guided Optimization of MHD Buongiorno Nanofluid over a Porous Cylinder with Machine Learning Applications

Hameed Ullah Khan¹, Muhammad Naveed Khan^2,*, N. Ameer Ahammad³, Nurul Amira Zainal^4,*, Shahzad Sarwar⁵, Muhammad Imran Khan¹, Afef Dhahbi⁶

1 Department of Mathematics & Statistics, International Islamic University, Islamabad, Pakistan
2 School of Aeronautics and Astronautics, Zhejiang University, Hangzhou, Zhejiang, 310027, China
3 Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk, 71491, Saudi Arabia
4 Fakulti Teknologi dan Kejuruteraan Mekanikal, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, 76100, Durian Tunggal, Melaka, Malaysia
5 Department of Mathematics, King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, 31261, Saudi Arabia
6 Department of Financial and Accounting Management Programs, Applied College Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia

* Corresponding Authors: Muhammad Naveed Khan. Email: ; Nurul Amira Zainal. Email:

(This article belongs to the Special Issue: Computational Advances in Nanofluids: Modelling, Simulations, and Applications)

Computer Modeling in Engineering & Sciences 2026, 148(2), 18 https://doi.org/10.32604/cmes.2026.086863

Received 09 June 2026; Accepted 30 July 2026; Issue published 28 August 2026

Abstract

The thermal and solutal transport mechanisms in non-Newtonian fluids play a substantial role in energy systems, thermal management, polymer processing, and biomedical engineering. In this study, an integrated Local Non-Similarity Physics-Informed Neural Network framework is developed to investigate the non-similar boundary layer flow, heat, and mass transport of Williamson nanofluid through a horizontal porous cylinder under the combined effects of magnetohydrodynamics and porous media. The leading nonlinear system of equations that represents the problem is transformed into a coupled ordinary differential equation using the local non-similarity method. The resulting system is solved using a Physics guided Neural Network implemented in PyTorch, where the foremost equations and boundary conditions are incorporated into a physics-based loss function without requiring labeled training data. The influences of the magnetic parameter ($M$), surface heating parameter ($\gamma$), Prandtl number ($Pr$), Schmidt number ($Sc$), Brownian motion parameter ($N_b$), and thermophoretic parameter ($N_t$) on the velocity, temperature, concentration, skin friction coefficient, local Nusselt number and local Sherwood number are systematically investigated. The PINN predictions show excellent agreement with benchmark numerical solutions obtained using the Scipy boundary value solver, while maintaining low $L^2$ errors, confirming the accuracy and robustness of the proposed framework. The results demonstrate that the LNS-PINN approach provides an efficient and reliable mesh-free computational methodology for solving highly nonlinear non-similar transport problems involving coupled heat and mass transfer in non-Newtonian nanofluids.

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