Modeling and simulation of radiative MHD nanofluid flow with Joule heating over a variable-thickness sheet

This study investigates the unsteady squeezing flow and heat transfer characteristics of a graphene-oxide/water nanofluid confined between two parallel plates undergoing time-dependent motion. A similarity transformation is used to convert the governing nonlinear partial differential equations into a set of coupled boundary-value problems, which are then solved using a modified operational matrix method (OMM). The proposed formulation avoids the stiffness commonly encountered in traditional OMM by introducing a forward-based coefficient computation strategy, reducing computational effort while maintaining high accuracy. The numerical results are validated through L2 truncation error, boundary-condition deviation analysis, and comparison of the local Nusselt number against reference solutions, showing an error on the order of 10−14. A detailed parametric investigation is conducted to examine the influence of Brownian motion (Nb), thermophoresis (Nt), squeeze number (S), Eckert number (Ec), and Lewis number (Le) on velocity, temperature, and concentration distributions. The results show that increasing Nb by 0.1 leads to approximately a 6%–12% rise in peak temperature gradients, while higher Nt enhances thermal diffusion and reduces concentration gradients by nearly 8%–15% depending on ζ. The squeeze parameter accelerates the flow and increases the wall shear stress by about 10%, whereas Ec significantly boosts the thermal boundary layer due to viscous dissipation effects. Source terms associated with nanoparticle diffusion, viscous heating, and unsteady squeezing motion play a key role in shaping the overall transport behavior. Overall, the modified OMM offers a fast, stable, and highly accurate alternative for solving nonlinear nanofluid boundary-value problems, and the presented results provide deeper insight into the thermal and mass transport mechanisms of graphene-oxide nanofluids under unsteady squeezing motion.