Partial Differential Equations in Applied Mathematics (Mar 2025)
Study of multilayer flow of non-Newtonian fluid sandwiched between nanofluids
Abstract
This theoretical investigation examines the nonlinear convective heat transport and multilayer flow of a non-Newtonian fluid within a vertical slab, incorporating viscous heating effects. The middle layer of the slab contains a third-grade fluid, while the outer layers are filled with a water-based Ag-MgO hybrid nanoliquid. Continuity in temperature, heat flux, velocity, and shear stress is maintained at the interfaces of the fluid layers. The thermal buoyancy force is modeled using the nonlinear Boussinesq approximation. The governing system comprises conservation equations for mass, momentum (Navier-Stokes), and energy for each of the three layers. These differential equations are non-dimensionalized, and the resulting dimensionless four-point nonlinear boundary value problem is transformed into a two-point boundary value problem before being solved numerically. For limiting cases, analytical and semi-analytical solutions are computed and used as benchmark results to validate the numerical method employed. Entropy generation analysis indicates that higher third-grade fluid parameters reduce the magnitude of velocity and temperature fields, as well as entropy production across all regions. The third-grade fluid parameter shows a decreasing influence on velocity and temperature fields throughout the system. The continuity of interfacial conditions induces a dragging effect; despite the absence of third-grade fluid parameters in regions I and III, their influence is apparent in these regions. The Bejan number slightly decreases at the walls with increasing third-grade fluid parameters, exhibiting a dual effect in the third-grade fluid layer. Near the walls, the Bejan number decreases as the nanoparticle volume fraction increases. Findings of this work may have applications in polymer industries and processes involving high temperatures.
