Suspension of nanoparticles impacts on MHD unsteady flow over an infinite vertical porous surface with Dufour and TGDHS: An RSM analysis

Abstract

This study examines the effects of electromagnetic fields, the Dufour effect, temperature-gradient-dependent heat sources (TGDHS), and radiation absorption on hybrid nanofluid flow over an infinite vertical permeable surface. It specifically investigates the thermal transport characteristics of single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) within the TGDHS framework. The governing equations are solved using a perturbation method, with MATLAB simulations yielding graphical and tabulated results for key physical parameters. The results demonstrate substantial variations in skin friction, heat transfer rates, Nusselt number, and Sherwood number. The hybrid dispersion of SWCNTs and MWCNTs produces a significant heat transfer reduction ranging from 3.20 % to 12.06 %. Response surface methodology (RSM) exhibits excellent predictive performance, achieving an R²value of 99.99 %. Strategic adjustment of magnetic field strength, surface permeability, and heat source intensity effectively enhances or controls heat and mass transfer rates. These findings provide critical guidance for designing advanced thermal management systems. © 2026 The Authors.