Meshless local Petrov–Galerkin analysis of free convection of nanofluid in a cavity with wavy side walls

The problem of laminar natural convection of Al2O3–water nanofluid in a cavity with wavy side walls has been investigated using the meshless local Petrov–Galerkin method. The considered cavity is a square enclosure having left and right wavy side walls. The left and right vertical wavy walls of the enclosure are maintained at constant temperatures Th and Tc, respectively, with Th>Tc. The horizontal top and bottom walls of the cavity are kept insulated. 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 and adaptability of the proposed meshless technique is verified by comparisons of the obtained results through the present meshless method with those existing in the literature. Two different models proposed in the literature are considered for the effective dynamic viscosity of the nanofluid. Using the developed code, a parametric study is performed incorporating the two viscosity formulas, and the effects of the Rayleigh number and the volume fraction of the nanoparticles on the fluid flow and heat transfer inside the wavy enclosure are investigated in each case. The results show that significant differences exist between the rates of heat transfer in the cavity for the two viscosity models employed. At Ra=103 the average Nusselt number of the hot wall increases with increase in the volume fraction of the nanoparticles for both considered viscosity models. At other Rayleigh numbers (Ra=104, 105, and 106) the average Nusselt number estimated for Brinkman formula increases with increase in volume fraction of the nanoparticles while it decreases for Maiga's correlation.