Nanofluids, which are suspensions of nanoparticles in base fluids, have demonstrated considerable potential in enhancing thermal conductivity, energy storage, and lubrication properties, as well as improving the cooling efficiency of electronic devices. Despite their promising applications, the industrial utilization of nanofluids remains in the early stages, with further research needed to fully explore their capabilities. This study investigates a generalized nanofluid model, incorporating fractal-fractional derivative (FFD), to better understand the thermophysical behaviors in vertical channel flow. The nanofluid consists of polystyrene nanoparticles uniformly dispersed in kerosene oil. An exact solution to the model is obtained by employing the Laplace transform technique (LTT) in combination with the numerical Zakian’s algorithm. The FFD operator with an exponential kernel is applied to extend the classical nanofluid model. Discretization of the generalized model is achieved using the Crank-Nicolson method, and numerical simulations are performed to solve the resulting equations. The study reveals that, at a nanoparticle volume fraction of 4% (0.04), the heat transfer rate of the nanofluid is significantly higher than that of the base fluid. Furthermore, the enhanced heat transfer leads to improvements in various thermophysical properties, such as viscosity, thermal expansion, and heat capacity, which are crucial for industrial applications. The numerical results are presented graphically to highlight the dependence of the flow and thermal dispersion characteristics on key physical factors. These findings suggest that the use of fractal-fractional models can provide a more accurate representation of nanofluid behavior, particularly for high-precision applications in heat transfer and energy systems.