A numerical study of mixed convection heat transfer in a lid-driven cavity using $Al_2O_3$-water nanofluid

This study aims a numerical investigation of steady, laminar mixed convection heat transfer in a two-dimensional cavity by employing a finite volume method with a fourth-order approximation of convective terms, when nanoparticles are present. With the aim of solving two-dimensional momentum and energy conservation equations, a finite volume method on a non-uniform staggered grid is utilized. Second-order central differences are utilized to approximate diffusion terms in momentum and energy equations, while the development of a non-uniform four-point fourth-order interpolation (FPFOI) scheme is performed for the convective terms. Continuity and momentum equations are solved using the SIMPLE (SemiImplicit Method for Pressure-Linked Equation) algorithm. In order to evaluate heat transfer enhancement, various viscosity and thermal conductivity models were employed. Numerical solution results were obtained in different models in cases where Gr number is between $10^3 and 10^5$ , Re number is 10-100-1000 and nanoparticle volumetric fraction is 0-5%.