This study investigates a critical problem: unsteady nanofluid flow with spatially varying particle concentration over impulsively started vertical plates subjected to imposed thermal flux, addressing a significant gap in understanding transient heat transfer mechanisms essential for optimizing thermal management systems. The research employs the Buongiorno two-phase model incorporating Brownian motion and thermal flux, with the governing equations solved analytically using the Laplace transform technique under realistic initial and boundary conditions. Key quantitative findings reveal that increasing the Brownian motion parameter from 0.1 to 0.5 enhances thermal conductivity by 15-25%, thickening the concentration boundary layer by 40-60%. Copper nanofluid exhibits 18-32% higher heat transfer rates than the base fluid, with optimal performance at a nanoparticle volume fraction of 2-4%. Higher thermal Grashof numbers (10⁵-10⁶) increase fluid velocity by 25-40% and reduce near-wall nanoparticle concentrations by 20-30%. The novelty lies in the comprehensive analysis of coupled transient momentum, energy,
and species transport with spatially dependent thermophysical properties, extending beyond previous steady-state or uniform concentration studies. These findings provide quantitative design guidelines for nanofluid-based thermal systems, demonstrating that controlled nanoparticle
distribution and transient thermal loading can significantly enhance heat transfer performance in industrial applications. The study shows that Brownian motion and heat flux markedly enhance heat and mass transport, leading to improved thermal performance. Copper-based nanofluids
achieve significantly higher heat transfer rates than the base fluid, with optimal efficiency at moderate nanoparticle concentrations. Increased thermal buoyancy further accelerates fluid motion while limiting nanoparticle accumulation near the surface.