MLPG Application of Nanofluid Flow Mixed Convection Heat Transfer in a Wavy Wall Cavity

Procuring a numerical solution through an application of the meshless local Petrov-Galerkin method (MLPG) on the fluid flow and mixed convection in a complex geometry cavity filled with a nanofluid is the scope of the present study. The cavity considered is a square enclosure having a lower temperature sliding lid at the top, a differentially higher temperature wavy wall at the bottom, and two thermally insulated walls on the sides. The nanofluid medium used is a water-based nanofluid, Al2O3-water with various volume fractions of its solid. To carry out the numerical simulations, the developed governing equations are determined in terms of the stream function-vorticity formulation. The weighting function in the weak formulation of the governing equations is taken as unity, and the field variables are approximated using the MLS interpolation. Capability as well as adaptability of the proposed meshless technique is ascertained by close comparisons of the illustrated results obtained through the mesh-free method with those obtained through a traditional method already existing in the literature. Effective viscosity and thermal conductivity of the solid-liquid mixture are determined using the Brinkman and Maxwell models, respectively. A parametric study conducted through the present method to gain insight into the nanofluid convective heat transfer performance shows rational and deducible results. The study reveals that, distributions of the local Nusselt number along the wavy hot wall closely follow the pattern of the wall's geometry for different Richardson numbers and the nanoparticles volume fractions considered.