Open Access

ARTICLE

Numerical Analysis of Heat and Mass Transfer in Tangent Hyperbolic Fluids Using a Two-Stage Exponential Integrator with Compact Spatial Discretization

Mairaj Bibi¹, Muhammad Shoaib Arif ², Yasir Nawaz³, Nabil Kerdid^4,*

1 Department of Mathematics, COMSATS University Islamabad, Park Road, Islamabad, 45550, Pakistan
2 Department of Mathematics and Sciences, College of Science and Humanities, Prince Sultan University, Riyadh, 11586, Saudi Arabia
3 Department of Mathematics, Faculty of Engineering and Computing, National University of Modern Languages (NUML), Islamabad, 44000, Pakistan
4 Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 90950, Riyadh, 11623, Saudi Arabia

* Corresponding Author: Nabil Kerdid. Email:

Computer Modeling in Engineering & Sciences 2025, 145(1), 537-569. https://doi.org/10.32604/cmes.2025.070362

Received 14 July 2025; Accepted 17 September 2025; Issue published 30 October 2025

Abstract

This study develops a high-order computational scheme for analyzing unsteady tangent hyperbolic fluid flow with variable thermal conductivity, thermal radiation, and coupled heat and mass transfer effects. A modified two-stage Exponential Time Integrator is introduced for temporal discretization, providing second-order accuracy in time. A compact finite difference method is employed for spatial discretization, yielding sixth-order accuracy at most grid points. The proposed framework ensures numerical stability and convergence when solving stiff, nonlinear parabolic systems arising in fluid flow and heat transfer problems. The novelty of the work lies in combining exponential integrator schemes with compact high-order spatial discretization, enabling accurate and efficient simulations of tangent hyperbolic fluids under complex boundary conditions, such as oscillatory plates and varying thermal conductivity. This approach addresses limitations of classical Euler, Runge–Kutta, and spectral methods by significantly reducing numerical errors (up to 45%) and computational cost. Comprehensive parametric studies demonstrate how viscous dissipation, chemical reactions, the Weissenberg number, and the Hartmann number influence flow behaviour, heat transfer, and mass transfer. Notably, heat transfer rates increase by 18.6% with stronger viscous dissipation, while mass transfer rates rise by 21.3% with more intense chemical reactions. The real-world relevance of the study is underscored by its direct applications in polymer processing, heat exchanger design, radiative thermal management in aerospace, and biofluid transport in biomedical systems. The proposed scheme thus provides a robust numerical framework that not only advances the mathematical modelling of non-Newtonian fluid flows but also offers practical insights for engineering systems involving tangent hyperbolic fluids.

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