Mixed convective transient nanofluid flow through a vertical porous channel with entropy and Navier slip effects

The present study investigates transient nanofluid flow in a vertical porous channel with buoyancy effects and Navier slip at the walls, with particular emphasis on thermodynamic irreversibility, entropy generation, and mixed convection. The study formulates dimensionless, coupled nonlinear governing equations for velocity, temperature, and entropy generation. These equations are solved numerically using a finite-difference scheme (FDS) that is second-order accurate in space and first-order accurate in time, capturing both transient and steady-state behaviors. Parametric analyses are conducted for permeability (Darcy number), buoyancy (Grashof number), pressure gradient, Biot number, Prandtl number, Brinkman number, and distinct Navier slip coefficients at the heated and cooled walls. Increasing permeability and buoyancy accelerate the flow and enhance convective heat transfer, but intensify entropy generation near the walls where velocity and temperature gradients are highest. Stronger pressure forcing sharpens the centerline velocity and increases near-wall irreversibility. Higher Biot and Prandtl numbers reduce velocity and temperature levels across the channel, while potentially increasing entropy generation due to steeper thermal gradients. Increased viscous dissipation raises temperatures near the heated wall and amplifies entropy generation near both plates.