Analysis of Thermal and Hydrodynamic Behavior of Nanofluid Flow Through Porouse Cylindre in Stepped Channel with Elastic Upper Wall

This study aims to investigate forced convection and heat transfer in a two-dimensional channel featuring a backward-facing step, a stationary adiabatic porous cylinder, and a deformable upper wall. The research addresses the complex coupling of fluid–structure interaction and porous media effects, a novel configuration not extensively explored in the existing literature. A numerical approach based on the finite element method within an arbitrary Lagrangian–Eulerian (ALE) framework is employed to simulate laminar flow and heat transfer over ranges of Reynolds (10 ≤ Re ≤ 200), Darcy (10⁻⁶ ≤ Da ≤ 10⁻¹), and Cauchy (10⁻⁷ ≤ Ca ≤ 10⁻⁴) numbers. The results, illustrated through isotherms, streamline patterns, and both local and average Nusselt number distributions, demonstrate that increasing the Reynolds number significantly enhances convective heat transfer. A decrease in the cylinder’s porosity strengthens vortex formation and thermal gradients, leading to a 36.4% increase in the average Nusselt number. Moreover, greater wall elasticity yields a modest 2.3% improvement in heat transfer. Regarding fluid–structure interaction, the maximum deformation of the upper elastic wall increases markedly with the Cauchy number, decreases by approximately 52.6% as the Reynolds number increases from 10 to 200, and reaches a peak at an intermediate Darcy number (Da = 10⁻³), highlighting the coupled influence of flow inertia and porous permeability. These findings provide quantitative insights into the interplay between structural deformation and porous media, contributing to the optimization of thermal management strategies in deformable thermo-fluidic systems.