Cu-water micropolar nanofluid natural convection within a porous enclosure with heat generation

Abstract This investigation is concerned with natural convection within a porous enclosure occupied by Cu-water micropolar nanofluid at the presence of the heat generated in both solid and fluid phases of the porous medium. Darcy model is applied to simulate macroscopic flow dynamics. A vector equation, angular velocity describing microelements rotation, is added to common equations to satisfy the conservation of angular momentum. The governing equations are reduced to a non-dimensional form and then solved numerically using the Galerkin finite element method using a non-uniform structured grid with quadratic elements. The influence of dimensionless parameters like external Darcy-Rayleigh number Ra E  = 1–10 3 , internal Darcy-Rayleigh number Ra I  = 1–10 4 , Darcy number Da  = 10 − 4 –10 − 1 , porosity e = 0.1–0.9, nanoparticles volume fraction φ = 0.0–0.1, vortex viscosity number Δ = 0–2, the ratio of heat generation within the solid phase to fluid phase q r  = 0–2 on the velocity, temperature, and angular momentum fields are investigated. Additionally, the rate of heat transfer through porous medium are studied as these key parameters are varied. It is found that an increment in Darcy number leads to a slight decline in the strength of fluid flow and micro-rotation of particles. When vortex viscosity number Δ increases, the strength of vortices rotating in porous medium and micro-rotation of particles grow and reduce, respectively. The effect of Ra I on thermal and dynamic characteristics of flow is more essential at high values of Δ.