This study examines an analysis of flow dynamics and thermal characteristics of a time-dependent elecromagnetized Tiwari–Das type nanofluid through a vertical stretchy/shrinky plate in a porous channel, shedding light on its potential applications for enhancing heat transfer in thermal systems. Therefore, theoretical analysis of thermal gyration and mixed convective effect of unsteady magnetized and electrically conducting nanofluid ( \(Al_2O_3\) and \(TiO_2\) ) past a vertical permeable stretchy/shrinky plate of Tiwari–Das model is considered. The developed governing dimensional partial differential model with boundary conditions were transformed into dimensionless ordinary differential equation and are approximately solved using Chebyshev collocation technique. To standardize the simulation accuracy, validation of the outcomes are compared with the literature. It can be deduced that magnification of magnetic and nanoparticles terms presence are seen to increase and reduce the velocity of the flow respectively. Also, it is seen that the temperature of the system can be enhanced by enlarging thermal radiative and viscous dissipative terms. The skin friction and Nusselt number of the setup can be enhanced by improving the thermal radiation term. These outcomes will be significant to scientists and engineers to experimentally manage heat transfer in cooling and high-temperature systems.
