Magnetohydrodynamic transient flow of dual-parameter fractional maxwell nanofluids past a vertical plate with generalised dual-phase-lagging heat conduction under ramped wall temperature conditions

We investigate the two-dimensional transient magnetohydrodynamic flow and heat transfer of radiative nanofluids past a vertical plate subjected to ramped wall temperature conditions. The dual-parameter generalised Maxwell constitutive relation is introduced to precisely capture the viscoelastic behaviour of nanofluids, while incorporating both mathematical rigour and physical insight. The governing fractional integrodifferential equations for momentum and heat transfer are derived, with the latter incorporating the Rosseland approximation and a modified dual-phase-lag heat flux model. A fast numerical algorithm for approximating the fractional operators is proposed to efficiently solve the resulting fully coupled nonlinear system, significantly reducing computational complexity and memory demands. The numerical results highlight the opposing effects of temporal parameters, such as relaxation time and phase lag, along with their associated fractional-order parameters on momentum and thermal boundary layers. Notably, the fractional integral parameter has a more substantial impact on velocity profiles within the boundary layer than the fractional derivative parameter. Under ramped wall temperature conditions, the phase lag of the temperature gradient exerts a stronger influence on the nanofluid temperature distribution compared to isothermal conditions, while the fractional derivative of the temperature gradient plays a relatively reduced role. Compared to the single-parameter model, the dual-parameter fractional Maxwell nanofluid model demonstrates smoother variations in velocity and temperature and exhibits a thicker boundary layer. This study provides key insights into the applications of fractional integrodifferential models for the design and optimization of thermal systems involving nanofluids.