Thermal and flow characteristics in a square chamber with a nanoencapsulated phase-change material–water nanofluid under a linear temperature variation at all walls

In this study, the two-dimensional, steady-state, and incompressible flow and thermal behaviors of a water-based nanoencapsulated phase-change material (NE-PCM) nanofluid within a closed chamber were investigated, considering the impact of buoyancy. A novel approach was introduced by implementing linearly varying temperature conditions along all chamber walls. The effective dynamic viscosity and thermal conductivity correlations, derived experimentally, were used to model the governing equations. These equations were then rendered dimensionless through suitable transformations and solved using the Galerkin finite-element method. Results showed that the phase change region’s width increased with higher Rayleigh numbers, scaled phase change bonds, NE-PCM volume fractions, and fusion temperatures between 0.1 and 0.5, but decreased with fusion temperatures between 0.6 and 0.9. The highest Nusselt number occurred along the bottom wall for a fusion temperature range of 0.4–0.5. For optimal thermal performance, a square chamber with linearly varying temperature walls and a fusion temperature of 0.5 is recommended.