Analysis of concentration susceptibility and specific heat impact in a time-dependent controlled flow over a slow rotating disk

Concentration, susceptibility, and specific heat are fundamental topics in thermodynamics and materials science, since they affect material responses to variations in temperature and concentration. These qualities are essential for optimizing chemical processes, engineering systems, and environmental applications that require precise control over energy transfer and reaction behavior. In combination, active and passive control strategies provide significant tools for modifying nanomaterial performance, allowing designs to efficiently govern transport processes and help to create solutions in developing technologies and healthcare applications. Inspired by these applications, this study investigates the unsteady magnetohydrodynamic flow of electrically conducting Boger fluid over a slowly rotating stretching disk under active and passive nanoparticle control, incorporating concentration susceptibility, Soret–Dufour, and specific heat effects. The governing equations are transformed into ordinary differential equations (ODEs) and solved using a Fibonacci Wavelet-based collocation technique, with validation against the Runge–Kutta–Fehlberg fourth- and fifth-order methods. The results reveal that increasing the solvent fraction enhances both radial and tangential velocity, whereas higher relaxation time and magnetic parameters suppress the flow due to viscoelastic resistance and Lorentz forces. Thermal and concentration fields are significantly influenced by thermophoresis, Brownian motion, and cross-diffusion effects, with active control yielding superior heat and mass performance compared to passive control. These findings provide deeper insights into controlled nanofluid transport relevant to thermal management and hydrogen energy systems.